4. Labor, Material and Equipment Utilization

4.1 Historical Perspective

Good project management in construction must vigorously pursue the efficient utilization of labor, material and equipment. Improvement of labor productivity should be a major and continual concern of those who are responsible for cost control of constructed facilities. Material handling, which includes procurement, inventory, shop fabrication and field servicing, requires special attention for cost reduction. The use of new equipment and innovative methods has made possible wholesale changes in construction technologies in recent decades. Organizations which do not recognize the impact of various innovations and have not adapted to changing environments have justifiably been forced out of the mainstream of construction activities.

Observing the trends in construction technology presents a very mixed and ambiguous picture. On the one hand, many of the techniques and materials used for construction are essentially unchanged since the introduction of mechanization in the early part of the twentieth century. For example, a history of the Panama Canal construction from 1904 to 1914 argues that:

[T]he work could not have done any faster or more efficiently in our day, despite all technological and mechanical advances in the time since, the reason being that no present system could possibly carry the spoil away any faster or more efficiently than the system employed. No motor trucks were used in the digging of the canal; everything ran on rails. And because of the mud and rain, no other method would have worked half so well. [1]

In contrast to this view of one large project, one may also point to the continual change and improvements occurring in traditional materials and techniques. Bricklaying provides a good example of such changes:

Bricklaying...is said not to have changed in thousands of years; perhaps in the literal placing of brick on brick it has not. But masonry technology has changed a great deal. Motorized wheelbarrows and mortar mixers, sophisticated scaffolding systems, and forklift trucks now assist the bricklayer. New epoxy mortars give stronger adhesion between bricks. Mortar additives and cold-weather protection eliminate winter shutdowns. [2]

Add to this list of existing innovations the possibility of robotic bricklaying; automated prototypes for masonry construction already exist. Technical change is certainly occurring in construction, although it may occur at a slower rate than in other sectors of the economy.

The United States construction industry often points to factors which cannot be controlled by the industry as a major explanatory factor in cost increases and lack of technical innovation. These include the imposition of restrictions for protection of the environment and historical districts, requirements for community participation in major construction projects, labor laws which allow union strikes to become a source of disruption, regulatory policies including building codes and zoning ordinances, and tax laws which inhibit construction abroad. However, the construction industry should bear a large share of blame for not realizing earlier that the technological edge held by the large U.S. construction firms has eroded in face of stiff foreign competition. Many past practices, which were tolerated when U.S. contractors had a technological lead, must now be changed in the face of stiff competition. Otherwise, the U.S. construction industry will continue to find itself in trouble.

With a strong technological base, there is no reason why the construction industry cannot catch up and reassert itself to meet competition wherever it may be. Individual design and/or construction firms must explore new ways to improve productivity for the future. Of course, operational planning for construction projects is still important, but such tactical planning has limitations and may soon reach the point of diminishing return because much that can be wrung out of the existing practices have already been tried. What is needed the most is strategic planning to usher in a revolution which can improve productivity by an order of magnitude or more. Strategic planning should look at opportunities and ask whether there are potential options along which new goals may be sought on the basis of existing resources. No one can be certain about the success of various development options for the design professions and the construction industry. However, with the availability of today's high technology, some options have good potential of success because of the social and economic necessity which will eventually push barriers aside. Ultimately, decisions for action, not plans, will dictate future outcomes.

4.2 Labor Productivity

Productivity in construction is often broadly defined as output per labor hour. Since labor constitutes a large part of the construction cost and the quantity of labor hours in performing a task in construction is more susceptible to the influence of management than are materials or capital, this productivity measure is often referred to as labor productivity. However, it is important to note that labor productivity is a measure of the overall effectiveness of an operating system in utilizing labor, equipment and capital to convert labor efforts into useful output, and is not a measure of the capabilities of labor alone. For example, by investing in a piece of new equipment to perform certain tasks in construction, output may be increased for the same number of labor hours, thus resulting in higher labor productivity.

Construction output may be expressed in terms of functional units or constant dollars. In the former case, labor productivity is associated with units of product per labor hour, such as cubic yards of concrete placed per hour or miles of highway paved per hour. In the latter case, labor productivity is identified with value of construction in constant dollars per labor hour.

Productivity at the Job Site

Contractors and owners are often concerned with the labor activity at job sites. For this purpose, it is convenient to express labor productivity as functional units per labor hour for each type of construction task. However, even for such specific purposes, different levels of measure may be used. For example, cubic yards of concrete placed per hour is a lower level of measure than miles of highway paved per hour. Lower-level measures are more useful for monitoring individual activities, while higher-level measures may be more convenient for developing industry-wide standards of performance.

While each contractor or owner is free to use its own system to measure labor productivity at a site, it is a good practice to set up a system which can be used to track productivity trends over time and in varied locations. Considerable efforts are required to collect information regionally or nationally over a number of years to produce such results. The productivity indices compiled from statistical data should include parameters such as the performance of major crafts, effects of project size, type and location, and other major project influences.

In order to develop industry-wide standards of performance, there must be a general agreement on the measures to be useful for compiling data. Then, the job site productivity data collected by various contractors and owners can be correlated and analyzed to develop certain measures for each of the major segment of the construction industry. Thus, a contractor or owner can compare its performance with that of the industry average.

Productivity in the Construction Industry

Because of the diversity of the construction industry, a single index for the entire industry is neither meaningful nor reliable. Productivity indices may be developed for major segments of the construction industry nationwide if reliable statistical data can be obtained for separate industrial segments. For this general type of productivity measure, it is more convenient to express labor productivity as constant dollars per labor hours since dollar values are more easily aggregated from a large amount of data collected from different sources. The use of constant dollars allows meaningful approximations of the changes in construction output from one year to another when price deflators are applied to current dollars to obtain the corresponding values in constant dollars. However, since most construction price deflators are obtained from a combination of price indices for material and labor inputs, they reflect only the change of price levels and do not capture any savings arising from improved labor productivity. Such deflators tend to overstate increases in construction costs over a long period of time, and consequently understate the physical volume or value of construction work in years subsequent to the base year for the indices.

4.3 Factors Affecting Job-Site Productivity

Job-site productivity is influenced by many factors which can be characterized either as labor characteristics, project work conditions or as non-productive activities. The labor characteristics include:

• age and experience of workforce
• leadership and motivation of workforce

• Job size and complexity.
• Job site accessibility.
• Labor availability.
• Equipment utilization.
• Contractual agreements.
• Local climate.
• Local cultural characteristics, particularly in foreign operations.

The non-productive activities associated with a project may or may not be paid by the owner, but they nevertheless take up potential labor resources which can otherwise be directed to the project. The non-productive activities include among other factors:

• Indirect labor required to maintain the progress of the project
• Rework for correcting unsatisfactory work
• Temporary work stoppage due to inclement weather or material shortage
• Time off for union activities
• Absentee time, including late start and early quits
• Non-working holidays
• Strikes

Each category of factors affects the productive labor available to a project as well as the on-site labor efficiency.

Labor Characteristics

Performance analysis is a common tool for assessing worker quality and contribution. Factors that might be evaluated include:

• Quality of Work - caliber of work produced or accomplished.
• Quantity of Work - volume of acceptable work
• Job Knowledge - demonstrated knowledge of requirements, methods, techniques and skills involved in doing the job and in applying these to increase productivity.
• Related Work Knowledge - knowledge of effects of work upon other areas and knowledge of related areas which have influence on assigned work.
• Judgment - soundness of conclusions, decisions and actions.
• Initiative - ability to take effective action without being told.
• Resource Utilization - ability to delineate project needs and locate, plan and effectively use all resources available.
• Dependability - reliability in assuming and carrying out commitments and obligations.
• Analytical Ability - effectiveness in thinking through a problem and reaching sound conclusions.
• Communicative Ability - effectiveness in using orgal and written communications and in keeping subordinates, associates, superiors and others adequately informed.
• Interpersonal Skills - effectiveness in relating in an appropriate and productive manner to others.
• Ability to Work Under Pressure - ability to meet tight deadlines and adapt to changes.
• Security Sensitivity - ability to handle confidential information appropriately and to exercise care in safeguarding sensitive information.
• Safety Consciousness - has knowledge of good safety practices and demonstrates awareness of own personal safety and the safety of others.
• Profit and Cost Sensitivity - ability to seek out, generate and implement profit-making ideas.
• Planning Effectiveness - ability to anticipate needs, forecast conditions, set goals and standards, plan and schedule work and measure results.
• Leadership - ability to develop in others the willingenss and desire to work towards common objectives.
• Delegating - effectiveness in delegating work appropriately.
• Development People - ability to select, train and appraise personnel, set standards of performance, and provide motivation to grow in their capacity. < li>Diversity (Equal Employment Opportunity) - ability to be senstive to the needs of minorities, females and other protected groups and to demonstrate affirmative action in responding to these needs.

These different factors could each be assessed on a three point scale: (1) recognized strength, (2) meets expectations, (3) area needing improvement. Examples of work performance in these areas might also be provided.

Project Work Conditions

Job-site labor productivity can be estimated either for each craft (carpenter, bricklayer, etc.) or each type of construction (residential housing, processing plant, etc.) under a specific set of work conditions. A base labor productivity may be defined for a set of work conditions specified by the owner or contractor who wishes to observe and measure the labor performance over a period of time under such conditions. A labor productivity index may then be defined as the ratio of the job-site labor productivity under a different set of work conditions to the base labor productivity, and is a measure of the relative labor efficiency of a project under this new set of work conditions.

The effects of various factors related to work conditions on a new project can be estimated in advance, some more accurately than others. For example, for very large construction projects, the labor productivity index tends to decrease as the project size and/or complexity increase because of logistic problems and the "learning" that the work force must undergo before adjusting to the new environment. Job-site accessibility often may reduce the labor productivity index if the workers must perform their jobs in round about ways, such as avoiding traffic in repaving the highway surface or maintaining the operation of a plant during renovation. Labor availability in the local market is another factor. Shortage of local labor will force the contractor to bring in non-local labor or schedule overtime work or both. In either case, the labor efficiency will be reduced in addition to incurring additional expenses. The degree of equipment utilization and mechanization of a construction project clearly will have direct bearing on job-site labor productivity. The contractual agreements play an important role in the utilization of union or non-union labor, the use of subcontractors and the degree of field supervision, all of which will impact job-site labor productivity. Since on-site construction essentially involves outdoor activities, the local climate will influence the efficiency of workers directly. In foreign operations, the cultural characteristics of the host country should be observed in assessing the labor efficiency.

Non-Productive Activities

The non-productive activities associated with a project should also be examined in order to examine the productive labor yield, which is defined as the ratio of direct labor hours devoted to the completion of a project to the potential labor hours. The direct labor hours are estimated on the basis of the best possible conditions at a job site by excluding all factors which may reduce the productive labor yield. For example, in the repaving of highway surface, the flagmen required to divert traffic represent indirect labor which does not contribute to the labor efficiency of the paving crew if the highway is closed to the traffic. Similarly, for large projects in remote areas, indirect labor may be used to provide housing and infrastructure for the workers hired to supply the direct labor for a project. The labor hours spent on rework to correct unsatisfactory original work represent extra time taken away from potential labor hours. The labor hours related to such activities must be deducted from the potential labor hours in order to obtain the actual productive labor yield.

Example 4-1: Effects of job size on productivity

A contractor has established that under a set of "standard" work conditions for building construction, a job requiring 500,000 labor hours is considered standard in determining the base labor productivity. All other factors being the same, the labor productivity index will increase to 1.1 or 110% for a job requiring only 400,000 labor-hours. Assuming that a linear relation exists for the range between jobs requiring 300,000 to 700,000 labor hours as shown in Figure 4-1, determine the labor productivity index for a new job requiring 650,000 labor hours under otherwise the same set of work conditions.

Figure 4-1: Illustrative Relationship between Productivity Index and Job Size

The labor productivity index I for the new job can be obtained by linear interpolation of the available data as follows:

This implies that labor is 15% less productive on the large job than on the standard project.

Example 4-2: Productive labor yield [3]

In the construction of an off-shore oil drilling platform, the potential labor hours were found to be L = 7.5 million hours. Of this total, the non-productive activities expressed in thousand labor hours were as follows:

• A = 417 for holidays and strikes
• B = 1,415 for absentees (i.e. vacation, sick time, etc.)
• C = 1,141 for temporary stoppage (i.e. weather, waiting, union activities, etc.)
• D = 1,431 for indirect labor (i.e. building temporary facilities, cleaning up the site, rework to correct errors, etc.)

Determine the productive labor yield after the above factors are taken into consideration.

The percentages of time allocated to various non-productive activities, A, B, C and D are:

The total percentage of time X for all non-productive activities is:

The productive labor yield, Y, when the given factors for A, B, C and D are considered, is as follows:

As a result, only 41% of the budgeted labor time was devoted directly to work on the facility.

Example 4-3: Utilization of on-site worker's time

An example illustrating the effects of indirect labor requirements which limit productive labor by a typical craftsman on the job site was given by R. Tucker with the following percentages of time allocation: [4]

Productive time Unproductive time     Administrative delays     Inefficient work methods     Labor jurisdictions and other work restrictions Personal time	40% 20% 20% 15% 5%

In this estimate, as much time is spent on productive work as on delays due to management and inefficiencies due to antiquated work methods.

4.4 Labor Relations in Construction

The market demand in construction fluctuates greatly, often within short periods and with uneven distributions among geographical regions. Even when the volume of construction is relatively steady, some types of work may decline in importance while other types gain. Under an unstable economic environment, employers in the construction industry place great value on flexibility in hiring and laying off workers as their volumes of work wax and wane. On the other hand, construction workers sense their insecurity under such circumstances and attempt to limit the impacts of changing economic conditions through labor organizations.

There are many crafts in the construction labor forces, but most contractors hire from only a few of these crafts to satisfy their specialized needs. Because of the peculiar characteristics of employment conditions, employers and workers are placed in a more intimate relationship than in many other industries. Labor and management arrangements in the construction industry include both unionized and non-unionized operations which compete for future dominance. Most industrial and utility construction is union. In the commercial building sector, non-union contractors have made inroads, while in the housing sector, most contractors are non-union. The heavy construction sector is primarily non-union.

Unionized Construction

The craft unions work with construction contractors using unionized labor through various market institutions such as jurisdiction rules, apprenticeship programs, and the referral system. Craft unions with specific jurisdiction rules for different trades set uniform hourly wage rates for journeymen and offer formal apprenticeship training to provide common and equivalent skill for each trade. Contractors, through the contractors' associations, enter into legally binding collective bargaining agreements with one or more of the craft unions in the construction trades. The system which bind both parties to a collective bargaining agreement is referred to as the "union shop". These agreements obligate a contractor to observe the work jurisdictions of various unions and to hire employees through a union operated referral system commonly known as the hiring hall.

The referral systems operated by union organizations are required to observe several conditions:

1. All qualified workers reported to the referral system must be made available to the contractor without discrimination on the basis of union membership or other relationship to the union. The "closed shop" which limits referral to union members only is now illegal.
2. The contractor reserves the right to hire or refuse to hire any worker referred by the union on the basis of his or her qualifications.
3. The referral plan must be posted in public, including any priorities of referrals or required qualifications.

While these principles must prevail, referral systems operated by labor organizations differ widely in the construction industry.

Contractors and craft unions must negotiate not only wage rates and working conditions, but also hiring and apprentice training practices. The purpose of trade jurisdiction is to encourage considerable investment in apprentice training on the part of the union so that the contractor will be protected by having only qualified workers perform the job even though such workers are not permanently attached to the contractor and thus may have no sense of security or loyalty. The referral system is often a rapid and dependable source of workers, particularly for a contractor who moves into a new geographical location or starts a new project which has high fluctuations in demand for labor. By and large, the referral system has functioned smoothly in providing qualified workers to contractors, even though some other aspects of union operations are not as well accepted by contractors.

Non-Unionized Construction

In recent years, non-union contractors have entered and prospered in an industry which has a long tradition of unionization. Non-union operations in construction are referred to as "open shops." However, in the absence of collective bargaining agreements, many contractors operate under policies adopted by non-union contractors' associations. This practice is referred to as "merit shop", which follows substantially the same policies and procedures as collective bargaining although under the control of a non-union contractors' association without union participation. Other contractors may choose to be totally "unorganized" by not following either union shop or merit shop practices.

The operations of the merit shop are national in scope, except for the local or state apprenticeship and training plans. The comprehensive plans of the contractors' association apply to all employees and crafts of a contractor regardless of their trades. Under such operations, workers have full rights to move through the nation among member contractors of the association. Thus, the non-union segment of the industry is organized by contractors' associations into an integral part of the construction industry. However, since merit shop workers are employed directly by the construction firms, they have a greater loyalty to the firm, and recognize that their own interest will be affected by the financial health of the firm.

Playing a significant role in the early growth and continued expansion of merit shop construction is the Associated Builders and Contractors association. By 1987, it had a membership of nearly 20,000 contractors and a network of 75 chapters through the nation. Among the merit shop contractors are large construction firms such as Fluor Daniel, Blount International, and Brown & Root Construction. The advantages of merit shops as claimed by its advocates are:

• the ability to manage their own work force
• flexibility in making timely management decisions
• the emphasis on making maximum usage of local labor force
• the emphasis on encouraging individual work advancement through continued development of skills
• the shared interest that management and workers have in seeing an individual firm prosper.

By shouldering the training responsibility for producing skill workers, the merit shop contractors have deflected the most serious complaints of users and labor that used to be raised against the open shop. On the other hand, the use of mixed crews of skilled workers at a job site by merit shop contractors enables them to remove a major source of inefficiencies caused by the exclusive jurisdiction practiced in the union shop, namely the idea that only members of a particular union should be permitted to perform any given task in construction. As a result, merit shop contractors are able to exert a beneficial influence on productivity and cost-effectiveness of construction projects.

The unorganized form of open shop is found primarily in housing construction where a large percentage of workers are characterized as unskilled helpers. The skilled workers in various crafts are developed gradually through informal apprenticeships while serving as helpers. This form of open shop is not expected to expand beyond the type of construction projects in which highly specialized skills are not required.

4.5 Problems in Collective Bargaining

In the organized building trades in North American construction, the primary unit is the international union, which is an association of local unions in the United States and Canada. Although only the international unions have the power to issue or remove charters and to organize or combine local unions, each local union has considerable degrees of autonomy in the conduct of its affairs, including the negotiation of collective bargaining agreements. The business agent of a local union is an elected official who is the most important person in handling the day to day operations on behalf of the union. The contractors' associations representing the employers vary widely in composition and structure, particularly in different geographical regions. In general, local contractors' associations are considerably less well organized than the union with which they deal, but they try to strengthen themselves through affiliation with state and national organizations. Typically, collective bargaining agreements in construction are negotiated between a local union in a single craft and the employers of that craft as represented by a contractors' association, but there are many exceptions to this pattern. For example, a contractor may remain outside the association and negotiate independently of the union, but it usually cannot obtain a better agreement than the association.

Because of the great variety of bargaining structures in which the union and contractors' organization may choose to stage negotiations, there are many problems arising from jurisdictional disputes and other causes. Given the traditional rivalries among various crafts and the ineffective organization of some of contractors' associations, coupled with the lack of adequate mechanisms for settling disputes, some possible solutions to these problems deserve serious attention: [5]

Regional Bargaining

Currently, the geographical area in a collective bargaining agreement does not necessarily coincide with the territory of the union and contractors' associations in the negotiations. There are overlapping of jurisdictions as well as territories, which may create successions of contract termination dates for different crafts. Most collective bargaining agreements are negotiated locally, but regional agreements with more comprehensive coverage embracing a number of states have been established. The role of national union negotiators and contractors' representatives in local collective bargaining is limited. The national agreement between international unions and a national contractor normally binds the contractors' association and its bargaining unit. Consequently, the most promising reform lies in the broadening of the geographic region of an agreement in a single trade without overlapping territories or jurisdictions.

Multicraft Bargaining

The treatment of interrelationships among various craft trades in construction presents one of the most complex issues in the collective bargaining process. Past experience on project agreements has dealt with such issues successfully in that collective bargaining agreements are signed by a group of craft trade unions and a contractor for the duration of a project. Project agreements may reference other agreements on particular points, such as wage rates and fringe benefits, but may set their own working conditions and procedures for settling disputes including a commitment of no-strike and no-lockout. This type of agreement may serve as a starting point for multicraft bargaining on a regional, non-project basis.

Improvement of Bargaining Performance

Although both sides of the bargaining table are to some degree responsible for the success or failure of negotiation, contractors have often been responsible for the poor performance of collective bargaining in construction in recent years because local contractors' associations are generally less well organized and less professionally staffed than the unions with which they deal. Legislation providing for contractors' association accreditation as an exclusive bargaining agent has now been provided in several provinces in Canada. It provides a government board that could hold hearings and establish an appropriate bargaining unit by geographic region or sector of the industry, on a single-trade or multi-trade basis.

4.6 Materials Management

Materials management is an important element in project planning and control. Materials represent a major expense in construction, so minimizing procurement or purchase costs presents important opportunities for reducing costs. Poor materials management can also result in large and avoidable costs during construction. First, if materials are purchased early, capital may be tied up and interest charges incurred on the excess inventory of materials. Even worse, materials may deteriorate during storage or be stolen unless special care is taken. For example, electrical equipment often must be stored in waterproof locations. Second, delays and extra expenses may be incurred if materials required for particular activities are not available. Accordingly, insuring a timely flow of material is an important concern of project managers.

Materials management is not just a concern during the monitoring stage in which construction is taking place. Decisions about material procurement may also be required during the initial planning and scheduling stages. For example, activities can be inserted in the project schedule to represent purchasing of major items such as elevators for buildings. The availability of materials may greatly influence the schedule in projects with a fast track or very tight time schedule: sufficient time for obtaining the necessary materials must be allowed. In some case, more expensive suppliers or shippers may be employed to save time.

Materials management is also a problem at the organization level if central purchasing and inventory control is used for standard items. In this case, the various projects undertaken by the organization would present requests to the central purchasing group. In turn, this group would maintain inventories of standard items to reduce the delay in providing material or to obtain lower costs due to bulk purchasing. This organizational materials management problem is analogous to inventory control in any organization facing continuing demand for particular items.

Materials ordering problems lend themselves particularly well to computer based systems to insure the consistency and completeness of the purchasing process. In the manufacturing realm, the use of automated materials requirements planning systems is common. In these systems, the master production schedule, inventory records and product component lists are merged to determine what items must be ordered, when they should be ordered, and how much of each item should be ordered in each time period. The heart of these calculations is simple arithmetic: the projected demand for each material item in each period is subtracted from the available inventory. When the inventory becomes too low, a new order is recommended. For items that are non-standard or not kept in inventory, the calculation is even simpler since no inventory must be considered. With a materials requirement system, much of the detailed record keeping is automated and project managers are alerted to purchasing requirements.

Example 4-4: Examples of benefits for materials management systems.[6]

From a study of twenty heavy construction sites, the following benefits from the introduction of materials management systems were noted:

• In one project, a 6% reduction in craft labor costs occurred due to the improved availability of materials as needed on site. On other projects, an 8% savings due to reduced delay for materials was estimated.
• A comparison of two projects with and without a materials management system revealed a change in productivity from 1.92 man-hours per unit without a system to 1.14 man-hours per unit with a new system. Again, much of this difference can be attributed to the timely availability of materials.
• Warehouse costs were found to decrease 50% on one project with the introduction of improved inventory management, representing a savings of $ 92,000. Interest charges for inventory also declined, with one project reporting a cash flow savings of $ 85,000 from improved materials management.

Against these various benefits, the costs of acquiring and maintaining a materials management system has to be compared. However, management studies suggest that investment in such systems can be quite beneficial.

4.7 Material Procurement and Delivery

The main sources of information for feedback and control of material procurement are requisitions, bids and quotations, purchase orders and subcontracts, shipping and receiving documents, and invoices. For projects involving the large scale use of critical resources, the owner may initiate the procurement procedure even before the selection of a constructor in order to avoid shortages and delays. Under ordinary circumstances, the constructor will handle the procurement to shop for materials with the best price/performance characteristics specified by the designer. Some overlapping and rehandling in the procurement process is unavoidable, but it should be minimized to insure timely delivery of the materials in good condition.

The materials for delivery to and from a construction site may be broadly classified as : (1) bulk materials, (2) standard off-the-shelf materials, and (3) fabricated members or units. The process of delivery, including transportation, field storage and installation will be different for these classes of materials. The equipment needed to handle and haul these classes of materials will also be different.

Bulk materials refer to materials in their natural or semi-processed state, such as earthwork to be excavated, wet concrete mix, etc. which are usually encountered in large quantities in construction. Some bulk materials such as earthwork or gravels may be measured in bank (solid in situ) volume. Obviously, the quantities of materials for delivery may be substantially different when expressed in different measures of volume, depending on the characteristics of such materials.

Standard piping and valves are typical examples of standard off-the-shelf materials which are used extensively in the chemical processing industry. Since standard off-the-shelf materials can easily be stockpiled, the delivery process is relatively simple.

Fabricated members such as steel beams and columns for buildings are pre-processed in a shop to simplify the field erection procedures. Welded or bolted connections are attached partially to the members which are cut to precise dimensions for adequate fit. Similarly, steel tanks and pressure vessels are often partly or fully fabricated before shipping to the field. In general, if the work can be done in the shop where working conditions can better be controlled, it is advisable to do so, provided that the fabricated members or units can be shipped to the construction site in a satisfactory manner at a reasonable cost.

As a further step to simplify field assembly, an entire wall panel including plumbing and wiring or even an entire room may be prefabricated and shipped to the site. While the field labor is greatly reduced in such cases, "materials" for delivery are in fact manufactured products with value added by another type of labor. With modern means of transporting construction materials and fabricated units, the percentages of costs on direct labor and materials for a project may change if more prefabricated units are introduced in the construction process.

In the construction industry, materials used by a specific craft are generally handled by craftsmen, not by general labor. Thus, electricians handle electrical materials, pipefitters handle pipe materials, etc. This multiple handling diverts scarce skilled craftsmen and contractor supervision into activities which do not directly contribute to construction. Since contractors are not normally in the freight business, they do not perform the tasks of freight delivery efficiently. All these factors tend to exacerbate the problems of freight delivery for very large projects.

Example 4-5: Freight delivery for the Alaska Pipeline Project [7]

The freight delivery system for the Alaska pipeline project was set up to handle 600,000 tons of materials and supplies. This tonnage did not include the pipes which comprised another 500,000 tons and were shipped through a different routing system.

The complexity of this delivery system is illustrated in Figure 4-2. The rectangular boxes denote geographical locations. The points of origin represent plants and factories throughout the US and elsewhere. Some of the materials went to a primary staging point in Seattle and some went directly to Alaska. There were five ports of entry: Valdez, Anchorage, Whittier, Seward and Prudhoe Bay. There was a secondary staging area in Fairbanks and the pipeline itself was divided into six sections. Beyond the Yukon River, there was nothing available but a dirt road for hauling. The amounts of freight in thousands of tons shipped to and from various locations are indicated by the numbers near the network branches (with arrows showing the directions of material flows) and the modes of transportation are noted above the branches. In each of the locations, the contractor had supervision and construction labor to identify materials, unload from transport, determine where the material was going, repackage if required to split shipments, and then re-load material on outgoing transport.

Figure 4-2: Freight Delivery for the Alaska Pipeline Project

Example 4-6: Process plant equipment procurement [8]

The procurement and delivery of bulk materials items such as piping electrical and structural elements involves a series of activities if such items are not standard and/or in stock. The times required for various activities in the procurement of such items might be estimated to be as follows:

Activities	Duration (days)	Cumulative Duration
Requisition ready by designer Owner approval Inquiry issued to vendors Vendor quotations received Complete bid evaluation by designer Owner approval Place purchase order Receive preliminary shop drawings Receive final design drawings Fabrication and delivery	0 5 3 15 7 5 5 10 10 60-200	0 5 8 23 30 35 40 50 60 120-260

As a result, this type of equipment procurement will typically require four to nine months. Slippage or contraction in this standard schedule is also possible, based on such factors as the extent to which a fabricator is busy.

4.8 Inventory Control

Once goods are purchased, they represent an inventory used during the construction process. The general objective of inventory control is to minimize the total cost of keeping the inventory while making tradeoffs among the major categories of costs: (1) purchase costs, (2) order cost, (3) holding costs, and (4) unavailable cost. These cost categories are interrelated since reducing cost in one category may increase cost in others. The costs in all categories generally are subject to considerable uncertainty.

Purchase Costs

The purchase cost of an item is the unit purchase price from an external source including transportation and freight costs. For construction materials, it is common to receive discounts for bulk purchases, so the unit purchase cost declines as quantity increases. These reductions may reflect manufacturers' marketing policies, economies of scale in the material production, or scale economies in transportation. There are also advantages in having homogeneous materials. For example, a bulk order to insure the same color or size of items such as bricks may be desirable. Accordingly, it is usually desirable to make a limited number of large purchases for materials. In some cases, organizations may consolidate small orders from a number of different projects to capture such bulk discounts; this is a basic saving to be derived from a central purchasing office.

The cost of materials is based on prices obtained through effective bargaining. Unit prices of materials depend on bargaining leverage, quantities and delivery time. Organizations with potential for long-term purchase volume can command better bargaining leverage. While orders in large quantities may result in lower unit prices, they may also increase holding costs and thus cause problems in cash flow. Requirements of short delivery time can also adversely affect unit prices. Furthermore, design characteristics which include items of odd sizes or shapes should be avoided. Since such items normally are not available in the standard stockpile, purchasing them causes higher prices.

The transportation costs are affected by shipment sizes and other factors. Shipment by the full load of a carrier often reduces prices and assures quicker delivery, as the carrier can travel from the origin to the destination of the full load without having to stop for delivering part of the cargo at other stations. Avoiding transshipment is another consideration in reducing shipping cost. While the reduction in shipping costs is a major objective, the requirements of delicate handling of some items may favor a more expensive mode of transportation to avoid breakage and replacement costs.

Order Cost

The order cost reflects the administrative expense of issuing a purchase order to an outside supplier. Order costs include expenses of making requisitions, analyzing alternative vendors, writing purchase orders, receiving materials, inspecting materials, checking on orders, and maintaining records of the entire process. Order costs are usually only a small portion of total costs for material management in construction projects, although ordering may require substantial time.

Holding Costs

The holding costs or carrying costs are primarily the result of capital costs, handling, storage, obsolescence, shrinkage and deterioration. Capital cost results from the opportunity cost or financial expense of capital tied up in inventory. Once payment for goods is made, borrowing costs are incurred or capital must be diverted from other productive uses. Consequently, a capital carrying cost is incurred equal to the value of the inventory during a period multiplied by the interest rate obtainable or paid during that period. Note that capital costs only accumulate when payment for materials actually occurs; many organizations attempt to delay payments as long as possible to minimize such costs. Handling and storage represent the movement and protection charges incurred for materials. Storage costs also include the disruption caused to other project activities by large inventories of materials that get in the way. Obsolescence is the risk that an item will lose value because of changes in specifications. Shrinkage is the decrease in inventory over time due to theft or loss. Deterioration reflects a change in material quality due to age or environmental degradation. Many of these holding cost components are difficult to predict in advance; a project manager knows only that there is some chance that specific categories of cost will occur. In addition to these major categories of cost, there may be ancillary costs of additional insurance, taxes (many states treat inventories as taxable property), or additional fire hazards. As a general rule, holding costs will typically represent 20 to 40% of the average inventory value over the course of a year; thus if the average material inventory on a project is $ 1 million over a year, the holding cost might be expected to be $200,000 to $400,000.

Unavailability Cost

The unavailability cost is incurred when a desired material is not available at the desired time. In manufacturing industries, this cost is often called the stockout or depletion cost. Shortages may delay work, thereby wasting labor resources or delaying the completion of the entire project. Again, it may be difficult to forecast in advance exactly when an item may be required or when an shipment will be received. While the project schedule gives one estimate, deviations from the schedule may occur during construction. Moreover, the cost associated with a shortage may also be difficult to assess; if the material used for one activity is not available, it may be possible to assign workers to other activities and, depending upon which activities are critical, the project may not be delayed.

4.9 Tradeoffs of Costs in Materials Management.

To illustrate the type of trade-offs encountered in materials management, suppose that a particular item is to be ordered for a project. The amount of time required for processing the order and shipping the item is uncertain. Consequently, the project manager must decide how much lead time to provide in ordering the item. Ordering early and thereby providing a long lead time will increase the chance that the item is available when needed, but it increases the costs of inventory and the chance of spoilage on site.

Let T be the time for the delivery of a particular item, R be the time required for process the order, and S be the shipping time. Then, the minimum amount of time for the delivery of the item is T = R + S. In general, both R and S are random variables; hence T is also a random variable. For the sake of simplicity, we shall consider only the case of instant processing for an order, i.e. R = 0. Then, the delivery time T equals the shipping time S.

Since T is a random variable, the chance that an item will be delivered on day t is represented by the probability p(t). Then, the probability that the item will be delivered on or before t day is given by:

4.1

If a and b are the lower and upper bounds of possible delivery dates, the expected delivery time is then given by:

4.2

The lead time L for ordering an item is the time period ahead of the delivery time, and will depend on the tradeoff between holding costs and unavailability costs. A project manager may want to avoid the unavailable cost by requiring delivery on the scheduled date of use, or may be to lower the holding cost by adopting a more flexible lead time based on the expected delivery time. For example, the manager may make the tradeoff by specifying the lead time to be D days more than the expected delivery time, i.e.,

4.3

where D may vary from 0 to the number of additional days required to produce certain delivery on the desired date.

In a more realistic situation, the project manager would also contend with the uncertainty of exactly when the item might be required. Even if the item is scheduled for use on a particular date, the work progress might vary so that the desired date would differ. In many cases, greater than expected work progress may result in no savings because materials for future activities are unavailable.

Example 4-7: : Lead time for ordering with no processing time.

Table 4-1 summarizes the probability of different delivery times for an item. In this table, the first column lists the possible shipping times (ranging from 10 to 16 days), the second column lists the probability or chance that this shipping time will occur and the third column summarizes the chance that the item arrives on or before a particular date. This table can be used to indicate the chance that the item will arrive on a desired date for different lead times. For example, if the order is placed 12 days in advance of the desired date (so the lead time is 12 days), then there is a 15% chance that the item will arrive exactly on the desired day and a 35% chance that the item will arrive on or before the desired date. Note that this implies that there is a 1 - 0.35 = 0.65 or 65% chance that the item will not arrive by the desired date with a lead time of 12 days. Given the information in Table 4-1, when should the item order be placed?

Table 4-1  Delivery Date on Orders and Probability of Delivery for an Example

Delivery Date t	Probability of delivery on date t p(t)	Cummulative probability of delivery by day t Pr{T t}
10	0.10	0.10
11	0.10	0.20
12	0.15	0.35
13	0.20	0.55
14	0.30	0.85
15	0.10	0.95
16	0.05	1.00

Suppose that the scheduled date of use for the item is in 16 days. To be completely certain to have delivery by the desired day, the order should be placed 16 days in advance. However, the expected delivery date with a 16 day lead time would be:

= (10)(0.1) + (11)(0.1) + (12)(0.15) + (13)(0.20) + (14)(0.30) + (15)(0.10) + (16)(0.05) = 13.0

Thus, the actual delivery date may be 16-13 = 3 days early, and this early delivery might involve significant holding costs. A project manager might then decide to provide a lead time so that the expected delivery date was equal to the desired assembly date as long as the availability of the item was not critical. Alternatively, the project manager might negotiate a more certain delivery date from the supplier.

4.10 Construction Equipment

The selection of the appropriate type and size of construction equipment often affects the required amount of time and effort and thus the job-site productivity of a project. It is therefore important for site managers and construction planners to be familiar with the characteristics of the major types of equipment most commonly used in construction. [9]

Excavation and Loading

One family of construction machines used for excavation is broadly classified as a crane-shovel as indicated by the variety of machines in Figure 4-3. The crane-shovel consists of three major components:

• a carrier or mounting which provides mobility and stability for the machine.
• a revolving deck or turntable which contains the power and control units.
• a front end attachment which serves the special functions in an operation.

The type of mounting for all machines in Figure 4-3 is referred to as crawler mounting, which is particularly suitable for crawling over relatively rugged surfaces at a job site. Other types of mounting include truck mounting and wheel mounting which provide greater mobility between job sites, but require better surfaces for their operation. The revolving deck includes a cab to house the person operating the mounting and/or the revolving deck. The types of front end attachments in Figure 4-3 might include a crane with hook, claim shell, dragline, backhoe, shovel and piledriver.

Figure 4-3  Typical Machines in the Crane-Shovel Family

A tractor consists of a crawler mounting and a non-revolving cab. When an earth moving blade is attached to the front end of a tractor, the assembly is called a bulldozer. When a bucket is attached to its front end, the assembly is known as a loader or bucket loader. There are different types of loaders designed to handle most efficiently materials of different weights and moisture contents.

Scrapers are multiple-units of tractor-truck and blade-bucket assemblies with various combinations to facilitate the loading and hauling of earthwork. Major types of scrapers include single engine two-axle or three axle scrapers, twin-engine all-wheel-drive scrapers, elevating scrapers, and push-pull scrapers. Each type has different characteristics of rolling resistance, maneuverability stability, and speed in operation.

Compaction and Grading

The function of compaction equipment is to produce higher density in soil mechanically. The basic forces used in compaction are static weight, kneading, impact and vibration. The degree of compaction that may be achieved depends on the properties of soil, its moisture content, the thickness of the soil layer for compaction and the method of compaction. Some major types of compaction equipment are shown in Figure 4-4, which includes rollers with different operating characteristics.

The function of grading equipment is to bring the earthwork to the desired shape and elevation. Major types of grading equipment include motor graders and grade trimmers. The former is an all-purpose machine for grading and surface finishing, while the latter is used for heavy construction because of its higher operating speed.

Figure 4-4  Some Major Types of Compaction Equipment

Drilling and Blasting

Rock excavation is an audacious task requiring special equipment and methods. The degree of difficulty depends on physical characteristics of the rock type to be excavated, such as grain size, planes of weakness, weathering, brittleness and hardness. The task of rock excavation includes loosening, loading, hauling and compacting. The loosening operation is specialized for rock excavation and is performed by drilling, blasting or ripping.

Major types of drilling equipment are percussion drills, rotary drills, and rotary-percussion drills. A percussion drill penetrates and cuts rock by impact while it rotates without cutting on the upstroke. Common types of percussion drills include a jackhammer which is hand-held and others which are mounted on a fixed frame or on a wagon or crawl for mobility. A rotary drill cuts by turning a bit against the rock surface. A rotary-percussion drill combines the two cutting movements to provide a faster penetration in rock.

Blasting requires the use of explosives, the most common of which is dynamite. Generally, electric blasting caps are connected in a circuit with insulated wires. Power sources may be power lines or blasting machines designed for firing electric cap circuits. Also available are non-electrical blasting systems which combine the precise timing and flexibility of electric blasting and the safety of non-electrical detonation.

Tractor-mounted rippers are capable of penetrating and prying loose most rock types. The blade or ripper is connected to an adjustable shank which controls the angle at the tip of the blade as it is raised or lowered. Automated ripper control may be installed to control ripping depth and tip angle.

In rock tunneling, special tunnel machines equipped with multiple cutter heads and capable of excavating full diameter of the tunnel are now available. Their use has increasingly replaced the traditional methods of drilling and blasting.

Lifting and Erecting

Derricks are commonly used to lift equipment of materials in industrial or building construction. A derrick consists of a vertical mast and an inclined boom sprouting from the foot of the mast. The mast is held in position by guys or stifflegs connected to a base while a topping lift links the top of the mast and the top of the inclined boom. A hook in the road line hanging from the top of the inclined boom is used to lift loads. Guy derricks may easily be moved from one floor to the next in a building under construction while stiffleg derricks may be mounted on tracks for movement within a work area.

Tower cranes are used to lift loads to great heights and to facilitate the erection of steel building frames. Horizon boom type tower cranes are most common in highrise building construction. Inclined boom type tower cranes are also used for erecting steel structures.

Mixing and Paving

Basic types of equipment for paving include machines for dispensing concrete and bituminous materials for pavement surfaces. Concrete mixers may also be used to mix portland cement, sand, gravel and water in batches for other types of construction other than paving.

A truck mixer refers to a concrete mixer mounted on a truck which is capable of transporting ready mixed concrete from a central batch plant to construction sites. A paving mixer is a self propelled concrete mixer equipped with a boom and a bucket to place concrete at any desired point within a roadway. It can be used as a stationary mixer or used to supply slipform pavers that are capable of spreading, consolidating and finishing a concrete slab without the use of forms.

A bituminous distributor is a truck-mounted plant for generating liquid bituminous materials and applying them to road surfaces through a spray bar connected to the end of the truck. Bituminous materials include both asphalt and tar which have similar properties except that tar is not soluble in petroleum products. While asphalt is most frequently used for road surfacing, tar is used when the pavement is likely to be heavily exposed to petroleum spills.

Construction Tools and Other Equipment

Air compressors and pumps are widely used as the power sources for construction tools and equipment. Common pneumatic construction tools include drills, hammers, grinders, saws, wrenches, staple guns, sandblasting guns, and concrete vibrators. Pumps are used to supply water or to dewater at construction sites and to provide water jets for some types of construction.

Automation of Equipment

The introduction of new mechanized equipment in construction has had a profound effect on the cost and productivity of construction as well as the methods used for construction itself. An exciting example of innovation in this regard is the introduction of computer microprocessors on tools and equipment. As a result, the performance and activity of equipment can be continually monitored and adjusted for improvement. In many cases, automation of at least part of the construction process is possible and desirable. For example, wrenches that automatically monitor the elongation of bolts and the applied torque can be programmed to achieve the best bolt tightness. On grading projects, laser controlled scrapers can produce desired cuts faster and more precisely than wholly manual methods. [10] Possibilities for automation and robotics in construction are explored more fully in Chapter 16.

Example 4-8: Tunneling Equipment [11]

In the mid-1980's, some Japanese firms were successful in obtaining construction contracts for tunneling in the United States by using new equipment and methods. For example, the Japanese firm of Ohbayashi won the sewer contract in San Francisco because of its advanced tunneling technology. When a tunnel is dug through soft earth, as in San Francisco, it must be maintained at a few atmospheres of pressure to keep it from caving in. Workers must spend several hours in a pressure chamber before entering the tunnel and several more in decompression afterwards. They can stay inside for only three or four hours, always at considerable risk from cave-ins and asphyxiation. Ohbayashi used the new Japanese "earth-pressure-balance" method, which eliminates these problems. Whirling blades advance slowly, cutting the tunnel. The loose earth temporarily remains behind to balance the pressure of the compact earth on all sides. Meanwhile, prefabricated concrete segments are inserted and joined with waterproof seals to line the tunnel. Then the loose earth is conveyed away. This new tunneling method enabled Ohbayashi to bid $5 million below the engineer's estimate for a San Francisco sewer. The firm completed the tunnel three months ahead of schedule. In effect, an innovation involving new technology and method led to considerable cost and time savings.

4.11 Choice of Equipment and Standard Production Rates

Typically, construction equipment is used to perform essentially repetitive operations, and can be broadly classified according to two basic functions: (1) operators such as cranes, graders, etc. which stay within the confines of the construction site, and (2) haulers such as dump trucks, ready mixed concrete truck, etc. which transport materials to and from the site. In both cases, the cycle of a piece of equipment is a sequence of tasks which is repeated to produce a unit of output. For example, the sequence of tasks for a crane might be to fit and install a wall panel (or a package of eight wall panels) on the side of a building; similarly, the sequence of tasks of a ready mixed concrete truck might be to load, haul and unload two cubic yards (or one truck load) of fresh concrete.

In order to increase job-site productivity, it is beneficial to select equipment with proper characteristics and a size most suitable for the work conditions at a construction site. In excavation for building construction, for examples, factors that could affect the selection of excavators include:

1. Size of the job: Larger volumes of excavation will require larger excavators, or smaller excavators in greater number.
2. Activity time constraints: Shortage of time for excavation may force contractors to increase the size or numbers of equipment for activities related to excavation.
3. Availability of equipment: Productivity of excavation activities will diminish if the equipment used to perform them is available but not the most adequate.
4. Cost of transportation of equipment: This cost depends on the size of the job, the distance of transportation, and the means of transportation.
5. Type of excavation: Principal types of excavation in building projects are cut and/or fill, excavation massive, and excavation for the elements of foundation. The most adequate equipment to perform one of these activities is not the most adequate to perform the others.
6. Soil characteristics: The type and condition of the soil is important when choosing the most adequate equipment since each piece of equipment has different outputs for different soils. Moreover, one excavation pit could have different soils at different stratums.
7. Geometric characteristics of elements to be excavated: Functional characteristics of different types of equipment makes such considerations necessary.
8. Space constraints: The performance of equipment is influenced by the spatial limitations for the movement of excavators.
9. Characteristics of haul units: The size of an excavator will depend on the haul units if there is a constraint on the size and/or number of these units.
10. Location of dumping areas: The distance between the construction site and dumping areas could be relevant not only for selecting the type and number of haulers, but also the type of excavators.
11. Weather and temperature: Rain, snow and severe temperature conditions affect the job-site productivity of labor and equipment.

By comparing various types of machines for excavation, for example, power shovels are generally found to be the most suitable for excavating from a level surface and for attacking an existing digging surface or one created by the power shovel; furthermore, they have the capability of placing the excavated material directly onto the haulers. Another alternative is to use bulldozers for excavation.

The choice of the type and size of haulers is based on the consideration that the number of haulers selected must be capable of disposing of the excavated materials expeditiously. Factors which affect this selection include:

1. Output of excavators: The size and characteristics of the excavators selected will determine the output volume excavated per day.
2. Distance to dump site: Sometimes part of the excavated materials may be piled up in a corner at the job-site for use as backfill.
3. Probable average speed: The average speed of the haulers to and from the dumping site will determine the cycle time for each hauling trip.
4. Volume of excavated materials: The volume of excavated materials including the part to be piled up should be hauled away as soon as possible.
5. Spatial and weight constraints: The size and weight of the haulers must be feasible at the job site and over the route from the construction site to the dumping area.

Dump trucks are usually used as haulers for excavated materials as they can move freely with relatively high speeds on city streets as well as on highways.

The cycle capacity C of a piece of equipment is defined as the number of output units per cycle of operation under standard work conditions. The capacity is a function of the output units used in the measurement as well as the size of the equipment and the material to be processed. The cycle time T refers to units of time per cycle of operation. The standard production rate R of a piece of construction equipment is defined as the number of output units per unit time. Hence:

4.4

4.5

The daily standard production rate P_e of an excavator can be obtained by multiplying its standard production rate R_e by the number of operating hours H_e per day. Thus:

4.6

where C_e and T_e are cycle capacity (in units of volume) and cycle time (in hours) of the excavator respectively.

In determining the daily standard production rate of a hauler, it is necessary to determine first the cycle time from the distance D to a dump site and the average speed S of the hauler. Let T_t be the travel time for the round trip to the dump site, T_o be the loading time and T_d be the dumping time. Then the travel time for the round trip is given by:

4.7

The loading time is related to the cycle time of the excavator T_e and the relative capacities C_h and C_e of the hauler and the excavator respectively. In the optimum or standard case:

4.8

For a given dumping time T_d, the cycle time T_h of the hauler is given by:

4.9

The daily standard production rate P_h of a hauler can be obtained by multiplying its standard production rate R_h by the number of operating hours H_h per day. Hence:

4.10

This expression assumes that haulers begin loading as soon as they return from the dump site.

The number of haulers required is also of interest. Let w denote the swell factor of the soil such that wP_e denotes the daily volume of loose excavated materials resulting from the excavation volume P_e. Then the approximate number of haulers required to dispose of the excavated materials is given by:

4.11

While the standard production rate of a piece of equipment is based on "standard" or ideal conditions, equipment productivities at job sites are influenced by actual work conditions and a variety of inefficiencies and work stoppages. As one example, various factor adjustments can be used to account in a approximate fashion for actual site conditions. If the conditions that lower the standard production rate are denoted by n factors F₁, F₂, ..., F_n, each of which is smaller than 1, then the actual equipment productivity R' at the job site can be related to the standard production rate R as follows:

4.12

On the other hand, the cycle time T' at the job site will be increased by these factors, reflecting actual work conditions. If only these factors are involved, T' is related to the standard cycle time T as:

4.13

Each of these various adjustment factors must be determined from experience or observation of job sites. For example, a bulk composition factor is derived for bulk excavation in building construction because the standard production rate for general bulk excavation is reduced when an excavator is used to create a ramp to reach the bottom of the bulk and to open up a space in the bulk to accommodate the hauler.

In addition to the problem of estimating the various factors, F₁, F₂, ..., F_n, it may also be important to account for interactions among the factors and the exact influence of particular site characteristics.

Example 4-9: Daily standard production rate of a power shovel [12]

A power shovel with a dipper of one cubic yard capacity has a standard operating cycle time of 30 seconds. Find the daily standard production rate of the shovel.

For C_e = 1 cu. yd., T_e = 30 sec. and H_e = 8 hours, the daily standard production rate is found from Eq. (4.6) as follows:

In practice, of course, this standard rate would be modified to reflect various production inefficiencies, as described in Example 4-11.

Example 4-10: Daily standard production rate of a dump truck

A dump truck with a capacity of 6 cubic yards is used to dispose of excavated materials at a dump site 4 miles away. The average speed of the dump truck is 30 mph and the dumping time is 30 seconds. Find the daily standard production rate of the truck. If a fleet of dump trucks of this capacity is used to dispose of the excavated materials in Example 4-9 for 8 hours per day, determine the number of trucks needed daily, assuming a swell factor of 1.1 for the soil.

The daily standard production rate of a dump truck can be obtained by using Equations (4.7) through (4.10):

Hence, the daily hauler productivity is:

Finally, from Equation (4.12), the number of trucks required is:

implying that 8 trucks should be used.

Example 4-11: Job site productivity of a power shovel

A power shovel with a dipper of one cubic yard capacity (in Example 4-9) has a standard production rate of 960 cubic yards for an 8-hour day. Determine the job site productivity and the actual cycle time of this shovel under the work conditions at the site that affects its productivity as shown below:

Work Conditions at the Site		Factors
Bulk composition		0.954
Soil properties and water content		0.983
Equipment idle time for worker breaks		0.8
Management efficiency		0.7

Using Equation (4.11), the job site productivity of the power shovel per day is given by:

The actual cycle time can be determined as follows:

Noting Equation (4.6), the actual cycle time can also be obtained from the relation T'_e = (C_eH_e)/P'_e. Thus:

Example 4-12: Job site productivity of a dump truck

A dump truck with a capacity of 6 cubic yards (in Example 4-10) is used to dispose of excavated materials. The distance from the dump site is 4 miles and the average speed of the dump truck is 30 mph. The job site productivity of the power shovel per day (in Example 4-11) is 504 cubic yards, which will be modified by a swell factor of 1.1. The only factors affecting the job site productivity of the dump truck in addition to those affecting the power shovel are 0.80 for equipment idle time and 0.70 for management efficiency. Determine the job site productivity of the dump truck. If a fleet of such trucks is used to haul the excavated material, find the number of trucks needed daily.

The actual cycle time T'_h of the dump truck can be obtained by summing the actual times for traveling, loading and dumping:

Hence, the actual cycle time is:

The jobsite productivity P'_h of the dump truck per day is:

The number of trucks needed daily is:

so 8 trucks are required.

4.12 Construction Processes

The previous sections described the primary inputs of labor, material and equipment to the construction process. At varying levels of detail, a project manager must insure that these inputs are effectively coordinated to achieve an efficient construction process. This coordination involves both strategic decisions and tactical management in the field. For example, strategic decisions about appropriate technologies or site layout are often made during the process of construction planning. During the course of construction, foremen and site managers will make decisions about work to be undertaken at particular times of the day based upon the availability of the necessary resources of labor, materials and equipment. Without coordination among these necessary inputs, the construction process will be inefficient or stop altogether.

Example 4-13: Steel erection

Erection of structural steel for buildings, bridges or other facilities is an example of a construction process requiring considerable coordination. Fabricated steel pieces must arrive on site in the correct order and quantity for the planned effort during a day. Crews of steelworkers must be available to fit pieces together, bolt joints, and perform any necessary welding. Cranes and crane operators may be required to lift fabricated components into place; other activities on a job site may also be competing for use of particular cranes. Welding equipment, wrenches and other hand tools must be readily available. Finally, ancillary materials such as bolts of the correct size must be provided.

In coordinating a process such as steel erection, it is common to assign different tasks to specific crews. For example, one crew may place members in place and insert a few bolts in joints in a specific area. A following crew would be assigned to finish bolting, and a third crew might perform necessary welds or attachment of brackets for items such as curtain walls.

With the required coordination among these resources, it is easy to see how poor management or other problems can result in considerable inefficiency. For example, if a shipment of fabricated steel is improperly prepared, the crews and equipment on site may have to wait for new deliveries.

Example 4-14: Construction process simulation models

Computer based simulation of construction operations can be a useful although laborious tool in analyzing the efficiency of particular processes or technologies. These tools tend to be either oriented toward modeling resource processes or towards representation of spatial constraints and resource movements. Later chapters will describe simulation in more detail, but a small example of a construction operation model can be described here. [13] The process involved placing concrete within existing formwork for the columns of a new structure. A crane-and-bucket combination with one cubic yard capacity and a flexible "elephant trunk" was assumed for placement. Concrete was delivered in trucks with a capacity of eight cubic yards. Because of site constraints, only one truck could be moved into the delivery position at a time. Construction workers and electric immersion-type concrete vibrators were also assumed for the process.

The simulation model of this process is illustrated in Figure 4-5. Node 2 signals the availability of a concrete truck arriving from the batch plant. As with other circular nodes in Figure 4-0, the availability of a truck may result in a resource waiting or queueing for use. If a truck (node 2) and the crane (node 3) are both available, then the crane can load and hoist a bucket of concrete (node 4). As with other rectangular nodes in the model, this operation will require an appreciable period of time. On the completion of the load and hoist operations, the bucket (node 5) is available for concrete placement. Placement is accomplished by having a worker guide the bucket's elephant trunk between the concrete forms and having a second worker operate the bucket release lever. A third laborer operates a vibrator in the concrete while the bucket (node 8) moves back to receive a new load. Once the concrete placement is complete, the crew becomes available to place a new bucket load (node 7). After two buckets are placed, then the column is complete (node 9) and the equipment and crew can move to the next column (node 10). After the movement to the new column is complete, placement in the new column can begin (node 11). Finally, after a truck is emptied (nodes 12 and 13), the truck departs and a new truck can enter the delivery stall (node 14) if one is waiting.

Figure 4-5: Illustration of a Concrete-Placing Simulation Model

Application of the simulation model consists of tracing through the time required for these various operations. Events are also simulated such as the arrival times of concrete trucks. If random elements are introduced, numerous simulations are required to estimate the actual productivity and resource requirements of the process. For example, one simulation of this process using four concrete trucks found that a truck was waiting 83% of the time with an average wait at the site of 14 minutes. This type of simulation can be used to estimate the various productivity adjustment factors described in the previous section.

4.13 Queues and Resource Bottlenecks

A project manager needs to insure that resources required for and/or shared by numerous activities are adequate. Problems in this area can be indicated in part by the existence of queues of resource demands during construction operations. A queue can be a waiting line for service. One can imagine a queue as an orderly line of customers waiting for a stationary server such as a ticket seller. However, the demands for service might not be so neatly arranged. For example, we can speak of the queue of welds on a building site waiting for inspection. In this case, demands do not come to the server, but a roving inspector travels among the waiting service points. Waiting for resources such as a particular piece of equipment or a particular individual is an endemic problem on construction sites. If workers spend appreciable portions of time waiting for particular tools, materials or an inspector, costs increase and productivity declines. Insuring adequate resources to serve expected demands is an important problem during construction planning and field management.

In general, there is a trade-off between waiting times and utilization of resources. Utilization is the proportion of time a particular resource is in productive use. Higher amounts of resource utilization will be beneficial as long as it does not impose undue costs on the entire operation. For example, a welding inspector might have one hundred percent utilization, but workers throughout the jobsite might be wasting inordinate time waiting for inspections. Providing additional inspectors may be cost effective, even if they are not utilized at all times.

A few conceptual models of queueing systems may be helpful to construction planners in considering the level of adequate resources to provide. First, we shall consider the case of time-varying demands and a server with a constant service rate. This might be the situation for an elevator in which large demands for transportation occur during the morning or at a shift change. Second, we shall consider the situation of randomly arriving demands for service and constant service rates. Finally, we shall consider briefly the problems involving multiple serving stations.

Single-Server with Deterministic Arrivals and Services

Suppose that the cumulative number of demands for service or "customers" at any time t is known and equal to the value of the function A(t). These "customers" might be crane loads, weld inspections, or any other defined group of items to be serviced. Suppose further that a single server is available to handle these demands, such as a single crane or a single inspector. For this model of queueing, we assume that the server can handle customers at some constant, maximum rate denoted as x "customers" per unit of time. This is a maximum rate since the server may be idle for periods of time if no customers are waiting. This system is deterministic in the sense that both the arrival function and the service process are assumed to have no random or unknown component.

A cumulative arrival function of customers, A(t), is shown in Figure 4-6 in which the vertical axis represents the cumulative number of customers, while the horizontal axis represents the passage of time. The arrival of individual customers to the queue would actually represent a unit step in the arrival function A(t), but these small steps are approximated by a continuous curve in the figure. The rate of arrivals for a unit time interval t from t-1 to t is given by:

4.14

While an hour or a minute is a natural choice as a unit time interval, other time periods may also be used as long as the passage of time is expressed as multiples of such time periods. For instance, if half an hour is used as unit time interval for a process involving ten hours, then the arrivals should be represented by 20 steps of half hour each. Hence, the unit time interval between t-1 and t is t = t - (t-1) = 1, and the slope of the cumulative arrival function in the interval is given by:

4.15

The cumulative number of customers served over time is represented by the cumulative departure function D(t). While the maximum service rate is x per unit time, the actual service rate for a unit time interval t from t-1 to t is:

4.16

The slope of the cumulative departure function is:

4.17

Any time that the rate of arrivals to the queue exceeds the maximum service rate, then a queue begins to form and the cumulative departures will occur at the maximum service rate. The cumulative departures from the queue will proceed at the maximum service rate of x "customers" per unit of time, so that the slope of D(t) is x during this period. The cumulative departure function D(t) can be readily constructed graphically by running a ruler with a slope of x along the cumulative arrival function A(t). As soon as the function A(t) climbs above the ruler, a queue begins to form. The maximum service rate will continue until the queue disappears, which is represented by the convergence of the cumulative arrival and departure functions A(t) and D(t).

With the cumulative arrivals and cumulative departure functions represented graphically, a variety of service indicators can be readily obtained as shown in Figure 4-6. Let A'(t) and D'(t) denote the derivatives of A(t) and D(t) with respect to t, respectively. For 0 t t_i in which A'(t) x, there is no queue. At t = t_i, when A'(t) > D'(t), a queue is formed. Then D'(t) = x in the interval t_i t t_k. As A'(t) continues to increase with increasing t, the queue becomes longer since the service rate D'(t) = x cannot catch up with the arrivals. However, when again A'(t) D'(t) as t increases, the queue becomes shorter until it reaches 0 at t = t_k. At any given time t, the queue length is

4.18

For example, suppose a queue begins to form at time t_i and is dispersed by time t_k. The maximum number of customers waiting or queue length is represented by the maximum difference between the cumulative arrival and cumulative departure functions between t_i and t_k, i.e. the maximum value of Q(t). The total waiting time for service is indicated by the total area between the cumulative arrival and cumulative departure functions.

Generally, the arrival rates A_t = 1, 2, . . ., n periods of a process as well as the maximum service rate x are known. Then the cumulative arrival function and the cumulative departure function can be constructed systematically together with other pertinent quantities as follows:

1. Starting with the initial conditions D(t-1)=0 and Q(t-1)=0 at t=1, find the actual service rate at t=1:

4.19

2. Starting with A(t-1)=0 at t=1, find the cumulative arrival function for t=2,3,. . .,n accordingly:

4.20

3. Compute the queue length for t=1,2, . . .,n.

4.21

4. Compute D_t for t=2,3,. . .,n after Q(t-1) is found first for each t:

4.22

5. If A'(t) > x, find the cumulative departure function in the time period between t_i where a queue is formed and t_k where the queue dissipates:

4.23

6. Compute the waiting time w for the arrivals which are waiting for service in interval t:

4.24

7. Compute the total waiting time W over the time period between t_i and t_k.

4.25

8. Compute the average waiting time w for arrivals which are waiting for service in the process.

4.26

This simple, deterministic model has a number of implications for operations planning. First, an increase in the maximum service rate will result in reductions in waiting time and the maximum queue length. Such increases might be obtained by speeding up the service rate such as introducing shorter inspection procedures or installing faster cranes on a site. Second, altering the pattern of cumulative arrivals can result in changes in total waiting time and in the maximum queue length. In particular, if the maximum arrival rate never exceeds the maximum service rate, no queue will form, or if the arrival rate always exceeds the maximum service rate, the bottleneck cannot be dispersed. Both cases are shown in Figure 4-7.

A practical means to alter the arrival function and obtain these benefits is to inaugurate a reservation system for customers. Even without drawing a graph such as Figure 4-6, good operations planners should consider the effects of different operation or service rates on the flow of work. Clearly, service rates less than the expected arrival rate of work will result in resource bottlenecks on a job.

Single-Server with Random Arrivals and Constant Service Rate

Suppose that arrivals of "customers" to a queue are not deterministic or known as in Figure 4-6. In particular, suppose that "customers" such as joints are completed or crane loads arrive at random intervals. What are the implications for the smooth flow of work? Unfortunately, bottlenecks and queues may arise in this situation even if the maximum service rate is larger than the average or expected arrival rate of customers. This occurs because random arrivals will often bunch together, thereby temporarily exceeding the capacity of the system. While the average arrival rate may not change over time, temporary resource shortages can occur in this circumstance.

Let w be the average waiting time, a be the average arrival rate of customers, and x be the deterministic constant service rate (in customers per unit of time). Then, the expected average time for a customer in this situation is given by: [14]

4.27

If the average utilization rate of the service is defined as the ratio of the average arrival rate and the constant service rate, i.e.,

4.28

Then, Eq. (4.27) becomes:

4.29

In this equation, the ratio u of arrival rate to service rate is very important: if the average arrival rate approaches the service rate, the waiting time can be very long. If a x, then the queue expands indefinitely. Resource bottlenecks will occur with random arrivals unless a measure of extra service capacity is available to accommodate sudden bunches in the arrival stream. Figure 4-8 illustrates the waiting time resulting from different combinations of arrival rates and service times.

Figure 4-8: Illustrative Waiting Times for Different Average Arrival Rates and Service Times

Multiple Servers

Both of the simple models of service performance described above are limited to single servers. In operations planning, it is commonly the case that numerous operators are available and numerous stages of operations exist. In these circumstances, a planner typically attempts to match the service rates occurring at different stages in the process. For example, construction of a high rise building involves a series of operations on each floor, including erection of structural elements, pouring or assembling a floor, construction of walls, installation of HVAC (Heating, ventilating and air conditioning) equipment, installation of plumbing and electric wiring, etc. A smooth construction process would have each of these various activities occurring at different floors at the same time without large time gaps between activities on any particular floor. Thus, floors would be installed soon after erection of structural elements, walls would follow subsequently, and so on. From the standpoint of a queueing system, the planning problem is to insure that the productivity or service rate per floor of these different activities are approximately equal, so that one crew is not continually waiting on the completion of a preceding activity or interfering with a following activity. In the realm of manufacturing systems, creating this balance among operations is called assembly line balancing.

Example 4-15: Effect of a crane breakdown

Suppose that loads for a crane are arriving at a steady rate of one every ten minutes. The crane has the capacity to handle one load every five minutes. Suppose further that the crane breaks down for ninety minutes. How many loads are delayed, what is the total delay, and how long will be required before the crane can catch up with the backlog of loads?

The cumulative arrival and service functions are graphed in Figure 4-9. Starting with the breakdown at time zero, nine loads arrive during the ninety minute repair time. From Figure 4-9, an additional nine loads arrive before the entire queue is served. Algebraically, the required time for service, t, can be calculated by noted that the number of arrivals must equal the number of loads served. Thus:

A queue is formed at t = 0 because of the breakdown, but it dissipates at A(t) = D₂(t). Let

from which we obtain t = 180 min. Hence

The total waiting time W can be calculated as the area between the cumulative arrival and service functions in Figure 4-9. Algebraically, this is conveniently calculated as the difference in the areas of two triangles:

so the average delay per load is w = 810/18 = 45 minutes.

Example 4-16: Waiting time with random arrivals

Suppose that material loads to be inspected arrive randomly but with an average of 5 arrivals per hour. Each load requires ten minutes for an inspection, so an inspector can handle six loads per hour. Inspections must be completed before the material can be unloaded from a truck. The cost per hour of holding a material load in waiting is $30, representing the cost of a driver and a truck. In this example, the arrival rate, a, equals 5 arrivals per hour and the service rate, x, equals 6 material loads per hour. Then, the average waiting time of any material load for u = 5/6 is:

At a resource cost of $30.00 per hour, this waiting would represent a cost of (30)(0.4)(5) = $60.00 per hour on the project.

In contrast, if the possible service rate is x = 10 material loads per hour, then the expected waiting time of any material load for u = 5/10 = 0.5 is:

which has only a cost of (30)(0.05)(5) = $7.50 per hour.

Example 4-17: Delay of lift loads on a building site

Suppose that a single crane is available on a building site and that each lift requires three minutes including the time for attaching loads. Suppose further that the cumulative arrivals of lift loads at different time periods are as follows:

6:00-7:00 A.M.	4 per hour	12:00-4:00 P.M.	8 per hour
7:00-8:00 A.M.	15 per hour	4:00-6:00 P.M.	4 per hour
8:00-11:00 A.M.	25 per hour	6:00P.M.-6:00 A.M.	0 per hour
11:00-12:00 A.M.	5 per hour

Using the above information of arrival and service rates

1. Find the cumulative arrivals and cumulative number of loads served as a function of time, beginning with 6:00 AM.
2. Estimate the maximum queue length of loads waiting for service. What time does the maximum queue occur?
3. Estimate the total waiting time for loads.
4. Graph the cumulative arrival and departure functions.

The maximum service rate x = 60 min/3 min per lift = 20 lifts per minute. The detailed computation can be carried out in the Table 4-2, and the graph of A(t) and D(t) is given in Figure 4-10.

4.14 References

1. Bourdon, C.C., and R.W. Levitt, Union and Open Shop Construction, Lexington Books, D.C. Heath and Co., Lexington, MA, 1980.
2. Caterpillar Performance Handbook, 18@+(th) Edition, Caterpillar, Inc., Peoria, IL, 1987.
3. Cordell, R.H., "Construction Productivity Management," Cost Engineering, Vol. 28, No. 2, February 1986, pp. 14-23.
4. Lange, J.E., and D.Q. Mills, The Construction Industry, Lexington Books, D.C. Heath and Co., Lexington, MA, 1979.
5. Nunnally, S.W., Construction Methods and Management, Prentice-Hall, Englewoood Cliffs, NJ, 2nd Ed., 1987.
6. Peurifoy, R.L., Construction Planning, Equipment and Methods, 2nd Edition, McGraw-Hill, New York, 1970.
7. Tersine, R.J., Principles of Inventory and Materials Management, North Holland, New York, 1982.

4.15 Problems

1. Using the relationship between the productivity index and job size in Example 4-1, determine the labor productivity for a new job requiring 350,000 labor hours under otherwise the same set of work conditions.
   
   
2. The potential labor hours available for a large energy complex were found to be 5.4 million hours. The non-productive activities expressed in thousands of labor hours were:
   1. 360 for holidays and strikes
   2. 1,152 for absentees
   3. 785 for temporary stoppage
   4. 1,084 for indirect labor

   Determine the productive labor yield after the above factors are taken into consideration.

3. Labor productivity at job site is known to decrease with overtime work. Let x be the percentage of overtime over normal work week. If x is expressed in decimals, the productivity index I as a function of the percentage of overtime is found to be:
   
   Find the value of the index I for x = 0, 0.1, 0.2, 0.3, 0.4 and 0.5 and plot the relationship in a graph.
   
   
4. Labor productivity for a complex project is known to increase gradually in the first 500,000 labor hours because of the learning effects. Let x be the number of 100,000 labor hours. The labor productivity index I is found to be a function of x as follows:
   
   Find the value of the index I for x = 0, 1, 2, 3, 4 and 5 and plot the relationship in a graph.
   
   
5. The probabilities for different delivery times of an item are given in the table below. Find the expected delivery date of the item. Also find the lead time required to provide an expected delivery date one day less than the desired delivery date.

   t	p(t)	Pr{T t}
   12	0.05	0.05
   13	0.10	0.15
   14	0.25	0.40
   15	0.35	0.75
   16	0.15	0.90
   17	0.10	1.00

6. A power shovel with a dipper of two cubic yard capacity has a standard operating cycle time of 80 seconds. The excavated material which has a swell factor of 1.05 will be disposed by a dump truck with an 8 cubic yard capacity at a dump site 6 miles away. The average speed of the dump truck is 30 mph and the dumping time is 40 seconds. Find the daily standard production rates of the power shovel and the dump truck if both are operated 8 hours per day. Determine also the number of trucks needed daily to dispose of the excavated material.
   
   
7. The power shovel in Problem P6 has a daily standard production rate of 720 cubic yards. Determine the job site productivity and the actual cycle time of this shovel under the work conditions at the site that affect the productivity as shown below:

   Work conditions at site	Factors
   Bulk composition	0.972
   Soil properties and water content	0.960
   Equipment idle time for breaks	0.750
   Management inefficiency	0.750

8. Based on the information given for Problems P4-6 and P4-7, find the job site productivity of a dump truck, assuming that the only factors affecting work conditions are 0.85 for equipment idle time and 0.80 for management efficiency. Also find the number of dump trucks required.
   
   
9. A Power shovel with a dipper of 1.5 cubic yard capacity has a standard operating cycle time of 60 seconds. The excavated material which has a swell factor of 1.08 will be disposed by a dump truck with a 7.5 cubic yard capacity at a dumpsite 5 miles away. The average speed of a dump truck is 25 mph and the dumping time is 75 seconds. Both the power shovel and the dump truck are operated 8 hours per day.
   1. Find the daily standard production rate of the power shovel.
   2. Find the daily standard production rate of the dump truck and number of trucks required.
   3. If the work conditions at the site that affect the productivity of the shovel can be represented by four factors F₁ = 0.940, F₃ = 0.850 and F₄ = 0.750, determine the job-site productivity and the actual cycle time.
   4. If the work conditions at the site affect the productivity of the dump truck can be represented by three factors F₁ = 0.952, F₂ = 0.700 and F₃ = 0.750, determine the job site productivity of the dump truck, and the number of dump trucks required.
   
   
10. Suppose that a single piece of equipment is available on a site for testing joints. Further, suppose that each joint has to be tested and certified before work can proceed. Joints are completed and ready for testing at random intervals during a shift. Each test requires an average of ten minutes. What is the average utilization of the testing equipment and the average wait of a completed joint for testing if the number of joints completed is (a) five per hour or (b) three per hour.
    
    
11. Suppose that the steel plates to be inspected are arriving steadily at a rate of one every twelve minutes. Each inspection requires sixteen minutes, but two inspectors are available so the inspection service rate is one every eight minutes. Suppose one inspector takes a break for sixty minutes. What is the resulting delay in the arriving pieces? What is the average delay among the pieces that have to wait?
    
    
12. Suppose that three machines are available in a fabrication ship for testing welded joints of structural members so that the testing service rate of the three machines is one in every 20 minutes. However, one of the three machines is shut down for 90 minutes when the welded joints to be tested arrive at a rate of one in every 25 minutes. What is the total delay for the testing service of the arriving joints? What is the average delay? Sketch the cumulative arrivals and services versus time.
    
    
13. Solve Example 4-17 if each lift requires 5 minutes instead of 3 minutes.
    
    
14. Solve Example 4-17 if each lift requires 6 minutes instead of 3 minutes
    
    
15. Suppose that up to 12 customers can be served per hour in an automated inspection process. What is the total waiting time and maximum queue with arrival rates for both cases (a) and (b) below:

    	(a)	(b)
    6-7:00 am	0	0
    7-8:00	25	10
    8-9:00	25	10
    9-10:00 am	25	15
    10-11:00 am	25	15
    11-12:00 am	10	10
    12-1:00 pm	8	15
    1-2:00 pm	0	15
    2-3:00 pm	0	10
    3-4:00 pm	0	10
    4-5:00 pm	0	10
    After 5 pm	0	0
    Total number of arrivals	118	120

16. For the list of labor characteristic qualities in Section 4.3 (beginning with Quality of Work and ending with Diversity), rate your own job performance on the three point scale given.

4.16 Footnotes

2. Rosefielde, Steven and Daniel Quinn Mills, "Is Construction Technologically Stagnant?", in Lange, Julian E. and Daniel Quinn Mills, The Construction Industry, Lexington Books, 1979, pg. 83. (Back)

3. This example was adapted with permission from an unpublished paper "Managing Mega Projects" presented by G.R. Desnoyers at the Project Management Symposium sponsored by the Exxon Research and Engineering Company, Florham Park, NJ, November 12, 1980. (Back)

4. See R.L. Tucker, "Perfection of the Buggy Whip," The Construction Advancement Address, ASCE, Boston, MA, Oct. 29, 1986. (Back)

5. For more detailed discussion, see D.G. Mills: "Labor Relations and Collective Bargaining" (Chapter 4) in The Construction Industry (by J.E. Lang and D.Q. Mills), Lexington Books, D.C. Heath and Co., Lexington, MA, 1979. (Back)

6. This example was adapted from Stukhart, G. and Bell, L.C. "Costs and Benefits of Materials Management Systems,", ASCE Journal of Construction Engineering and Management, Vol. 113, No. 2, June 1987, pp. 222-234. (Back)

7. The information for this example was provided by Exxon Pipeline Company, Houston, Texas, with permission from the Alyeska Pipeline Service Co., Anchorage, Alaska. (Back)

8. This example was adapted from A.E. Kerridge, "How to Develop a Project Schedule," in A.E. Kerridge and C. H. Vervalin (eds.), Engineering and Construction Project Management, Gulf Publishing Company, Houston, 1986. (Back)

9. For further details on equipment characteristics, see, for example, S.W. Nunnally, Construction Methods and Management, Second Edition, Prentice-Hall, 1986 (Back)

10. See Paulson, C., "Automation and Robotics for Construction," ASCE Journal of Construction Engineering and Management, Vol. 111, No. CO-3, 1985, pp. 190-207. (Back)

11. This example is adapted from Fred Moavenzadeh, "Construction's High-Technology Revolution," Technology Review, October, 1985, pg. 32. (Back)

12. This and the following examples in this section have been adapted from E. Baracco-Miller and C.T. Hendrickson, Planning for Construction, Technical Report No. R-87-162, Department of Civil Engineering, Carnegie Mellon University, Pittsburgh, PA 1987. (Back)

13. This model used the INSIGHT simulation language and was described in B.C. Paulson, W.T. Chan, and C.C. Koo, "Construction Operations Simulation by Microcomputer," ASCE Journal of Construction Engineering and Management, Vol. 113, No. CO-2, June 1987, pp. 302-314. (Back)

14. In the literature of queueing theory, this formula represents an M/D/1 queue, meaning that the arrival process is Markovian or random, the service time is fixed, only one server exists, and the system is in "steady state," implying that the service time and average arrival rate are constant. Altering these assumptions would require changes in the waiting time formula; for example, if service times were also random, the waiting time formula would not have the 2 shown in the denominator of Eq. (4.27). For more details on queueing systems, see Newell, G.F. Applications of Queueing Theory, Chapman and Hall, London, 1982. (Back)