Determining Activity Durations PDF

CHAPTER F O U R DETERMINING ACTIVITY DURATIONS Once you plan your work, you must work your plan. some instances, an agency, whether public or private, w...

CHAPTER F O U R DETERMINING ACTIVITY DURATIONS Once you plan your work, you must work your plan. some instances, an agency, whether public or private, will need to know the approximate cost of a project before spe- T he development and use of schedules relies heavily on activity durations. Without carefully assigning durations to the various activities, the value of the schedules will be greatly diminished. It is therefore impera- tive that the durations of the various activities be developed cific actions can be initiated. A public agency may require this information prior to holding a bond election. Private owners will need this information in order to know the extent of financing that will be required or the amount of capital that must exist for a project to be feasible. Conceptual with a certain amount of accuracy. The accuracy and useful- estimates are rough approximations of the anticipated costs ness of the schedule will be directly related to the accuracy and are generally prepared by architects, engineers, or other that is inherent in the individual activity durations. There consultants. The preparation of conceptual estimates are several ways that these activity durations can be obtained requires a clear understanding of what an owner wants and a or derived. Some degree of uncertainty is always present good “feel” for the probable costs. whenever project durations are developed. Despite this, a reasonable effort should provide results that will be accept- Detailed Estimates able. Some of these methods will be described. Detailed estimates are generally prepared by contractors prior to submitting bids on competitively bid contracts or ESTIMATING when entering lump-sum or fixed-price contracts. A detailed To determine the probable cost of the project, construction esti- cost estimate includes the costs of materials, labor, equip- mates are prepared before a project is constructed. Thus, an ment, subcontracted work, overhead, and profit. To prepare estimate is, at best, a close approximation of the actual cost. a detailed estimate for a project, the estimator conducts There are many variations in the cost of materials, equipment, a breakdown of the proposed project into the necessary and labor from one locality to another and from one point in operations required to complete the project. To some extent, time to another. Therefore, the cost estimate of a project, even the operations or items appear in the estimate in the order when compared to other similar projects, is unique to that pro- that they will be performed in the project. This reduces the ject. To determine the cost accurately, the estimator should have danger of omitting the costs of one or more operations. an accurate estimate of the quantities of material, equipment hours, and labor hours required to complete a given project. The estimator then applies the proper unit costs to these items. CONDUCTING A DETAILED The soundness of the completed estimate depends on ESTIMATE the following two factors: (1) the accuracy of the quantity The process of conducting a detailed estimate begins with a take-off and (2) the judicious selection of the unit costs and thorough analysis of the various physical quantities that production rates to be used. must be incorporated in the final project. This information is obtained through a detailed quantity take-off. The quan- TYPES OF ESTIMATES tity take-off is generally recorded on a standard sheet that includes information about the various items (numeric Construction estimates may be divided into at least two designation, description, and quantity). This quantity take- different types, depending on the purposes for which they off is then used to develop a detailed cost estimate for the are prepared: conceptual estimates and detailed estimates. prospective project. Costs are generally captured separately for materials, equipment, labor, and subcontracted items. Conceptual Estimates By separating the cost items, it is easier to check to verify Conceptual estimates are generally used by the prospective that all cost categories have been included. During con- owner of a project to determine the approximate cost of a struction, this level of breakdown affords greater control of project before making a final decision to construct it. In expenditures. 45 46 CHAPTER FOUR A project is made up of many activities. Separate take-offs of material can be put in place in a specified time period; are made for each job item, and the take-offs, in general, follow that is, the productivity of labor and equipment for each the same sequence as used to perform the activities. The take-off item must be estimated with accuracy. These values primary elements of work required to complete each activity of productivity may be derived from prior projects com- are tabulated and collected in an orderly and systematic man- pleted by a contractor. In some cases, the estimator may ner. Since virtually all of the take-offs are double-checked, the develop the productivity rates by discussing relevant factors estimator should use care in writing all numbers and notes about a work item with superintendents, project managers, clearly and legibly. (Of course, much of the estimating effort is and other experienced personnel. The estimator may also performed with the use of computers.) decide to obtain rough values of productivity from After the estimate is complete, it is a good practice to published sources. Whenever reference is made to another check the take-off to ensure that no job quantities have been source for production values, the estimator should take care overlooked and that no other obvious errors have been to make appropriate modifications to reflect the anticipated made. For unit price contracts, this verification includes conditions. a comparison with the quantities provided in the bid Once the quantities have been priced, an estimate must proposal. However, it is not wise to rely too heavily on these be made for the job overhead and the home-office overhead. listed quantities. Unit price contracts may include work that The job site overhead includes all of those costs that cannot must be done but for which there is no specific pay item. For be attributed to a specific work activity, but that must be example, extensive scaffolding may be required to construct incurred to successfully complete the project. Examples a project, but the owner will probably not allow scaffolding include the cost of maintaining a job pickup truck, the salary to be used as a pay item. of the superintendent, and the cost of an electric generator. To develop a detailed estimate, well-defined costs must Note that these are examples of costs that will continue for be linked to each of the items in the quantity take-off. These the duration of the project and that a longer project dura- costs are easily defined for those activities that will be tion means that higher overhead costs will be incurred for subcontracted. The costs of most materials can also be deter- these items. Some overhead items are “one-time” cost items. mined with some accuracy, as many suppliers quote specific Examples of such cost items include the cost of a layout prices for items that are purchased by a given date. The costs survey, security fence, signs, and mobilization. Of course, of labor and equipment, however, are not as simple to deter- even these may not be one-time costs in all instances. Refer mine. A clear understanding is required of how many units to Table 4.1 for examples of job site overhead items. Table 4.1 Examples of Job Site Overhead Salaries Project manager Superintendent Assistant superintendent Office manager Payroll clerk Safety director Project engineer Field engineer Timekeeper Security watch Party chief Quality control personnel Equipment Costs Trucks Automobiles Cranes Computers Photocopiers Hoists Fax machines Project pickup Scaffolding Mobilization ($/mile) Air compressors Water pumps Water truck Electric generators Welding machine Forklift Temporary Facilities Costs Job office trailer Architect’s field office Janitor service Storage sheds Electric service Water service Tool bins Security fence Signs Lights Temporary toilets Carpenter shed Lavatories File cabinets Temporary Protection and Safety Requirements Fence Canopies Barricades Safety nets Security services Vandalism/theft Alarm system Noise control Fire extinguishers Safety rails Winter protection Summer protection Rain protection Tree protection Safety equipment  Determining Activity Durations 47 Table 4.1 (continued) Engineering Support Services Site survey Project layout Road layout Soil borings Field survey Reporting Expenses CPM schedules Progress reports Certified payrolls Photography Testing and Inspection Concrete Masonry Steel Load Watertight testing Job Cleanup Cutting and patching General housekeeping Disposal and dump charges Dewatering Dumpster fees Taxes and Insurance Truck and auto Public liability Builder’s risk Special risk Sales tax Workers’ compensation Performance bond Social security Communications Costs Telephone/telegraph Loudspeaker Radios Telephone service Permits Building Demolition Sidewalk Blasting Water and sewer fees Expendables (Tools and Consumables Costing Less Than $500) Hammers Blades Bits Shovels Bars Cutters Clamps Fuels Lubricants Welding rods Supplies Stationery File folders Plans Specifications As-built drawings Postage Drinking water Ice Dispensers First aid supplies Cups Other Travel Storage fees Job sign Ads (help wanted) Data processing Petty cash Job parties Temporary roads Community education Home-office overhead must also be allocated to each For example, assume the home-office overhead is $1,000,000 project in some manner. This includes all costs incurred at for 1 year and the total value of all contracts that year is the home office that cannot be attributed easily to one $100,000,000. If the value of one project being bid is project. (See Table 4.2 for examples of this type of overhead.) $20,000,000, then the home-office overhead charged to the There are a variety of philosophies on how these costs are to project is $200,000. More sophisticated allocation methods be charged to a project. Whatever means are employed, the can be devised that take into account the extent that the home-office overhead charged to all of the company projects home office will be involved in a project, such as the number must be a reasonable approximation of the actual costs of worker hours required, or the duration of the project. incurred at the home office. The allocation of home-office For many overhead items, it is essential that an accurate overhead begins with a separate estimate, at the corporate estimate be made of the project duration. Thus, it is impor- level, of the anticipated cost to maintain the home office. tant that some effort be expended on scheduling a project as This cost determination is crucial to any system of overhead the quantity estimate is performed. It is indeed foolish for a allocation. One method of allocation of home-office over- contractor to prepare an estimate without preparing a sched- head to a project is to charge it in proportion to the total ule. Since many of the costs of a project are a direct function value of all projects undertaken within the period of 1 year. of the amount of time required to complete the project, a 48 CHAPTER FOUR Table 4.2 Examples of Home-Office Overhead Salaries Owners President Officers Estimator Engineers Accountant Secretarial staff Clerical Receptionist Roving or general superintendent Equipment Costs Computers Typewriters Photocopiers Fax machines Company vehicles Vehicle operation (gasoline, oil, and maintenance) Idle equipment in the yard Yard and maintenance shop Building or Office Costs Rent, lease, or mortgage costs Building maintenance Furniture and fixtures Real estate taxes Insurance Supplies Stationery Company forms General office supplies Operating Expenses Electric Water and sewer Telephone Postage Insurance: liability, etc. Landscape maintenance Radio Business taxes and licenses Legal and consulting fees Sales promotion, entertainment Custodial services Site investigation costs Study courses Contractor association dues Travel Conventions Other Lost plan deposits Interest expense/finance charges Charitable donations Goodwill expenditures Political donations Licensing fees Company picnic Lost interest on retainage Supervisory training expenses Manuals (software, estimating guides, etc.) reasonably accurate estimate should be made of the project These job items are sufficiently detailed for a quantity duration. This can be accomplished by preparing a schedule take-off to be conducted. However, they do not reflect with with sufficient detail to give meaningful information. sufficient accuracy the work tasks actually required to The example on the following pages consists of a complete the project. It should be evident from the relatively simple evaluation of a basement to be constructed. following activity listing that the estimator has assumed The job items are as follows: that a prescribed sequence of job activities will occur. 䊉 For example, it is assumed that the slab will be placed Mobilization after the concrete walls are completed, as no provision has 䊉 Excavation been included for the costs of forms for the edge of the slab. 䊉 Construct wall footing Thus, it is obvious that the walls will be placed prior to the 䊉 Place granular fill slab and that the concrete walls will function as concrete 䊉 Finish grade (fill) forms. Other sequences may also be identified. 䊉 Erect form wall For scheduling purposes, the following list of job activities 䊉 gives a clearer idea of how the work will be done: Place concrete wall 䊉 Place concrete slab 䊉 Mobilization 䊉 Backfill 䊉 Excavation 䊉 Cleanup 䊉 Wall footing  Determining Activity Durations 49 䊉 Install formwork the work plan could result in considerable cost and time 䊉 Set rebar savings. While some schedulers with a significant amount of 䊉 Place concrete relevant experience might be able to make a good guess 䊉 Strip forms about the amount of time required to perform the work, most of them opt to analyze the operation in detail. The 䊉 Place granular fill duration of such an excavation activity might take several 䊉 Finish grade days or even weeks, but this can only be determined with 䊉 Concrete wall accuracy and confidence with a close look at the operation 䊉 Form one side of form on the N and E walls and the quantities involved. 䊉 Place rebar in N and E walls The determination of the duration of a small task might 䊉 Form second side of form on the N and E walls be made with confidence with only a limited evaluation. For 䊉 Place concrete for N and E walls example, suppose a schedule is being developed for a small, three-story office building. How might the duration be 䊉 Strip forms from N and E walls determined for the clearing and grubbing on the site? 䊉 Form one side of form on the S and W walls Assume the development lot is about an acre in area, with no 䊉 Place rebar in S and W walls trees, debris, or other significant vegetation on the site. How 䊉 Form second side of form on the S and W walls might the duration of the clearing and grubbing be deter- 䊉 Place concrete for S and W walls mined? First of all, perhaps the activity will include the 䊉 Strip forms from S and W walls equipment mobilization, along with the actual clearing and grubbing activity. The scheduler might very well decide to 䊉 Concrete slab allocate 4 days to the duration of the activity based on the 䊉 Set rebar assumption that it might take 2 days to get the equipment 䊉 Place concrete moved to the site. It is assumed that the actual clearing and 䊉 Backfill grubbing will take slightly more than 1 day to complete. 䊉 Cleanup Thus, much of the duration has to do with preparation and, in this case, mobilization. For an activity such as clearing and Note that the pricing of rebar will not vary whether the grubbing, the total cost will generally be fairly modest, but rebar is placed in a sequence of one wall at a time or if it is each site should be evaluated separately. placed in all four walls at the same time. This decision will Suppose the activity on this same small building project have an impact, however, on other costs. For example, if all is the installation of wallpaper on one accent wall in the four walls are formed at the same time, there is no possibility reception area. Since the wall is a small flat area with no for reusing the forms on this project. penetrations and a minimum of electric wall outlets, it is From the quantities that have been estimated, it is possi- assumed that the work can be done in a matter of hours. The ble to determine an anticipated duration for each of the scheduler might very well allow a minimum of 1 day to do work items. To determine such durations requires that the the work, both to allow time to prepare the work area and to productivity estimates are reasonably accurate. The follow- fully mobilize for the work. Essentially no detailed analysis ing pages give examples of how the duration may be derived of this work would be performed. from the quantity estimate when productivity values are On small commercial buildings and residential struc- known. While activity durations can be established without tures, most of the activities will take only a few days. For a detailed estimate, it is not prudent to do so without at least example, the roofing on a building can be estimated with considering the basic assumptions that were made about considerable accuracy. The scheduler might determine that how the construction operations would be accomplished. the new roofing system can be installed in 2.5 days. The first Basically, the estimate should form the foundations on reaction might be to round up the computed value of the which the schedule is actually based. Ignoring the estimating duration to about 3 or even 4 days. This added time might be assumptions may very well result in inaccuracies in the needed to accommodate the mobilization of the roofing crew, computed durations. include the installation of the roofing materials, and allow for cleanup/demobilization. The scheduler could also think about productivity ESTIMATING DURATIONS performances on past projects and thus make the duration To a large extent, the method used to establish the duration estimates without actually performing any detailed analysis. of an activity will depend on the size, in terms of time For example, the drywall installation duration might be consumption, of the activity and the amount of accuracy determined with minimal computations. This might be that is required. For example, the excavation of 375,000 done if the scheduler can visualize the work actually being cubic yards of material on a large dam would be considered done at a given pace. Perhaps the drywall on a prior project a significant activity as considerable resources would be was installed by a work crew at a rate of four rooms per day. involved. Such an activity would warrant considerable If the proposed building is similar to the past project being investigation. Even some seemingly minor alterations in referenced, a rough estimate might be made about the 50 CHAPTER FOUR duration. If the new building has 30 rooms, the duration can use this information to determine the duration. In the might logically be stated as being about 8 days (30/4 = 7.5). first example, assume the work task involves hand excavation An increase in crew size can result in shorter durations just on a relatively small project with no viable means of using as reductions in the crew size will result in longer durations. heavy equipment. The volume of material to be excavated On the short duration activities just described, a signifi- consists of 9 cubic meters (11.8 cubic yards). The budgeted cant percentage of the time was devoted to allowances for amount and the hourly costs are known, and from this, the mobilization. While mobilization may not be a major task minimum duration can be determined. If the duration is for the members of some trades, they must still arrive on the exceeded, the cost of the activity will also overrun the bud- job site at the appropriate time. Most building projects get. The calculation of the duration is as follows: involve many subcontractors. It would not be realistic to Quantity of excavation = 9m3 (determined in the estimate) expect each subcontractor to be on the job site at a precisely designated time. If a subcontractor is told to be on site Budgeted amount = $950 (provided in the budget) at noon on a particular day but is unable to begin work Hourly cost per worker: $33.20 (includes general because another crew has not yet completed its work, that conditions and overhead L 50 percent) subcontractor’s crews are unlikely to wait while other sub- contractors finish their tasks. What is even worse, that Cost rate = budgeted cost/quantity of earth = $950/9 m3 subcontractor’s crews may not be assigned to show up the = $105.56/m3 next day. It is costly for a subcontractor to be on a project at a stated time and then not be able to begin work. Thus, it is Production rate = cost rate/hourly cost generally a good idea to allow some time to transition = $105.56/m3/$33.20/hr = 3.18 hr/m3 smoothly from one activity to another, especially when Excavation time = production rate * quantity different specialty contractors are involved. This will allow = 3.18 hr/m3 * 9 m3 = 28.6 hr time to contact the subcontractors to inform them of the specific needs of the project for their services. If one worker is employed, duration = 3.6 days (use 4 days) But how is the duration determined if the scheduler has If two workers are employed, duration = 1.8 days (2 days) no experience with a particular work item? Probably the first step that most would take is to ask someone with experience. In this example, the production rate was determined For example, the scheduler can talk with the estimator or the from the estimated quantity of material, the amount job superintendent. The job superintendent should have a very budgeted, and the cost of labor. Obviously, if the estimated good idea of how the work plan is to be put into effect. The values were in error, the production rates would also be in only note of caution here is that superintendents are often very error. Presumably, the estimator used the production rates to optimistic about what they can accomplish in a given period of derive the appropriate costs to be used in the estimate or time. They often fail to include the transition time between budget. activities. With experience, one can assess the need for modify- The scheduler might use the production rates directly ing or adjusting the duration estimates provided by others. rather than determine the production rates that must be If the firm has no individuals to contact concerning the achieved to finish an activity within the budget. The follow- duration of a specific activity, one might use reference guides ing example assumes that the production rates for erecting that give productivity estimates for various tasks. Use refer- 47 square meters (506 sq. ft.) of concrete formwork are well ence guides with some degree of caution. These guides are documented. In this example, the budgeted amount is not generally conservative in their estimates, but they can be essential to deriving a duration. very helpful if no other resources are available. Note that Quantity of forming = 47 m2 each project has unique characteristics and that the reference guides cannot be expected to anticipate all the nuances that Production rate = 1.8 hr/m2 (obtained from historical data) exist in project differences. One contractor stated that if a Forming time = production rate * quantity bid were prepared solely with the use of costs derived from = 1.8 hr/m2 * 47 m2 = 84.6 hr reference guides, the firm would never win a contract. This may reflect the conservative nature of reference cost data. If one worker is employed, duration = 10.6 days (use11days) Before using published reference materials, it is best to If two workers are employed,duration = 5.3 days (5 or 6 days) explore company files for relevant information. The histori- cal data on past company projects can be a very valuable If three workers are employed, duration = 3.5 days (4 days) resource for the scheduler. Where detailed information is If four workers are employed, duration = 2.6 days (3 days) desired, this is perhaps the scheduler’s best resource. When historical data are used, the information of Note that durations are generally recorded in terms of primary interest will be the productivity rates. That is, the whole days. This need not be done, especially with the use of scheduler will want to know the number of units of work computers, which can readily handle fractions of days. accomplished in a given unit of time (generally hours). A Rounding up to whole integer values does add some conser- couple of examples will help demonstrate how the scheduler vatism to the duration estimate and is often preferred. Some  Determining Activity Durations 51 judgment must be exercised whenever activity durations are possible to defer the large payment for the item. The project determined. manager should also try to anticipate some rework and the loss of some time due to inspections. Efforts may be expended to minimize these adverse impacts. SCHEDULING ISSUES While determining activity durations is important, it is also important to consider the actual scheduling of the activities. FACTORS INFLUENCING When using a schedule to control a project, a decision must CHOICE OF ACTIVITY be made about the use of float. Float is the leeway that is assigned to various activities in a network. This leeway may SCHEDULES be effectively manipulated by a project manager. A very basic Scheduling should satisfy various constraints that may approach is to use either an “early start” or a “late start” be imposed by the contract or by specific needs of the schedule. In an early-start schedule, all of the available float firm. As noted earlier, the sequencing of activities depends of each activity remains controllable, while in a late-start on a variety of constraints or considerations. In developing schedule, the float of each activity has been reduced to 0. In a the network logic, primary focus is placed on physical late-start schedule, all activities are critical. constraints. Other constraints (resource, environmental, An early-start schedule has obvious advantages in that management, safety, etc.) are not necessarily used to order many activities are not critical. In a late-start schedule, on the activities. Instead, these constraints are simply noted and the other hand, all flexibility has been removed from the net- left to be introduced at a later stage of the planning and work. In spite of the shortcomings of the late-start schedule, scheduling process. contractors may be inclined to use them. This is particularly To the extent possible, activity start times are estab- true if the owner is perceived as “owning” the float. The lished such that the resulting schedule reflects these noted early-start schedule has a disadvantage in that resources may constraints. For example, if two activities require the same not be consumed in a uniform fashion on the project. The piece of equipment and have similar start times, it may be same disadvantage exists on late-start schedules. The obvi- possible to set the scheduled start times of the two activities ous ideal solution probably lies in a compromise between so that they do not overlap. Of course, the opportunities for the two types of schedules. By starting with an early-start accommodating these constraints are subject to available schedule, problems might be identified that can be resolved float and the implications of start times presented earlier. simply by making use of available float. A more detailed discussion of scheduling procedures is pre- The early-start and the late-start schedules may be used sented in the chapter on resource allocation and leveling. to predict the cash flow requirements on the project. In a An additional consideration is that of materials delivery cash flow diagram, one would see that the area between the and storage. Staggering deliveries can reduce job site conges- early-start schedule and the late-start schedule forms an tion and simplify coordination efforts on site. Delaying envelope of money over a period of time. This “lazy S-curve” material deliveries can also take the pressure off when there presents the full range of options open to the project is limited storage space. In most cases, it is wise to base the manager. The S-curve could also contain actual cost data as material inflow rate on the available storage space and the compared to the predicted. This would show at a glance the rate of installation. The schedule should reflect any signifi- magnitude of the various costs that are being incurred. It cant concerns related to materials. must be kept in mind that the expenditure of money does In other situations the scheduler may be faced with not necessarily imply that progress is being made or that a balancing the relative uncertainties inherent in any con- specific amount of profit has been earned. It is merely an struction project. While one can anticipate these problems indication of total project expenditures. to occur during the life of a construction project, it is Once a schedule has been developed, the scheduling of nonetheless desirable to develop as realistic a schedule as certain activities should be examined. For example, major possible. Arrangements made for materials’ deliveries, sub- activities should be examined to determine the time of the contractor start dates, contract-specified milestone dates, year in which they are scheduled to occur. This helps man- and the like suggest that the initial schedule is important. agement anticipate the need for certain precautionary Selecting scheduled dates, therefore, may include a consid- measures, including those guarding against the effects of eration of the likelihood that the assumptions of the network rain, snow, temperature extremes, high winds, and poor soil model will not hold true. An activity may, for example, be problems. To respond to this information, management may considered likely to experience problems that will extend its decide to winterize a portion of the project in order to stay duration. In such a case, this activity might be scheduled on schedule. The schedule may also help the project toward its early start to minimize the chance of project delay. manager anticipate problems caused by delayed shop draw- Subsequent activities might be set to later-scheduled starts so ing approvals, delays in material deliveries, the expiration of that arrangements made for the start of these activities would labor agreements, and deficiencies in the cash position on be less likely to be altered. An alternative, of course, would be the project. A poor cash position may be handled by sched- to increase the duration of the initial activity to account for uling particularly expensive noncritical activities as late as the amount of delay that might be expected. 52 CHAPTER FOUR Weather and the Schedule and the project can be completed with fewer revisions of the network. If the weather activity is early in the schedule, Weather considerations or other contingencies may be essentially all activities will be scheduled later than they incorporated into a schedule in the manner just described. would normally occur. That is, the accuracy of the schedule The weather-dependent activity would be scheduled earlier will probably suffer if the weather activity is inserted early and succeeding activities later. Alternatively, the durations of and no adverse weather occurs; that is, early start times for weather-dependent activities could be increased prior to activities will be scheduled as if it is certain that the adverse proceeding with the network calculations. The amount by weather will occur early in the project. which the activity’s duration would be increased would be One other weather-related scheduling consideration based on the likelihood that a delay would occur as well as is whether the contract is administered on the basis of the extent of the delay. For example, if history indicated that working days or calendar days and how weather affects rainfall could be expected 10 percent of the time (1 out of 10 the definition of working days. (This issue of how weather days) during the period this activity would occur, then the is handled in contracts is addressed further in the next duration would be increased by 10 percent. This activity chapter.) weighting to accommodate adverse weather conditions is often a preferred approach. It should be noted that weather is a more serious consideration for the scheduler when the Uncertainty in Duration Estimates contract stipulates that the contract duration reflects the When most network schedules are developed, the activity impact of adverse weather. durations are assumed to be fixed at a particular duration Another method of weather inclusion is to insert one or estimate. While this approach is a standard practice, there is a more specific activities into the network labeled as weather fundamental flaw with this method of activity duration delays. These activities would be inserted into activity chains estimation. The flaw is not fatal and is certainly defendable in that contain weather-dependent activities. One drawback of that any other approach would make the solution of the this technique is that schedule monitoring is made more network very unwieldy. Nonetheless, it is important to difficult because the extra activities make the schedule have a good appreciation of the true meaning of a duration appear to be artificially tight (containing less float). If a estimate, which requires at least a rudimentary understanding weather activity is added to the network, should this appear of probability and statistics. early or late in the project? The decision of the actual place- Table 4.3 gives information on the probabilities associ- ment of the weather activity is not a trivial or arbitrary one. ated with certain estimates as defined in terms of standard A stronger case can probably be made for placing the deviation. The values in the table show the amount of the weather activity at the end of the network. In this way, if no area under the bell-shaped curve that extends to the right of adverse weather is encountered, the schedule remains intact the mean a specified number of standard deviations. When Table 4.3 Area Under a Standard Normal Curve x = the number of standard The area under the curve (as shown deviations to the right of in the table) always includes the the mean portion containing the mean. X x 0 1 2 3 4 5 6 7 8 9 0.0.5000.5040.5080.5120.5160.5199.5239.5279.5319.5359 0.1.5398.5438.5478.5517.5557.5596.5636.5675.5714.5754 0.2.5793.5832.5871.5910.5948.5987.6026.6064.6103.6141 0.3.6179.6217.6255.6293.6331.6368.6406.6443.6480.6517 0.4.6554.6591.6628.6664.6700.6736.6772.6808.6844.6879 0.5.6915.6950.6985.7019.7054.7088.7123.7157.7190.7224 0.6.7258.7291.7324.7357.7389.7422.7454.7486.7518.7549 0.7.7580.7612.7642.7673.7704.7734.7764.7794.7823.7852 0.8.7881.7910.7939.7967.7996.8023.8051.8078.8106.8133 0.9.8159.8186.8212.8238.8264.8289.8315.8340.8365.8389 1.0.8413.8438.8461.8485.8508.8531.8554.8577.8599.8621 1.1.8643.8665.8686.8708.8729.8749.8770.8790.8810.8830  Determining Activity Durations 53 Table 4.3 (continued) x 0 1 2 3 4 5 6 7 8 9 1.2.8849.8869.8888.8907.8925.8944.8962.8980.8997.9015 1.3.9032.9049.9066.9082.9099.9115.9131.9147.9162.9177 1.4.9192.9207.9222.9236.9251.9265.9279.9292.9306.9319 1.5.9332.9345.9357.9370.9382.9394.9406.9418.9429.9441 1.6.9452.9463.9474.9484.9495.9505.9515.9525.9535.9545 1.7.9554.9564.9573.9582.9591.9599.9608.9616.9625.9633 1.8.9641.9649.9656.9664.9671.9678.9686.9693.9699.9706 1.9.9713.9719.9726.9732.9738.9744.9750.9756.9761.9767 2.0.9772.9778.9783.9788.9793.9798.9803.9808.9812.9817 2.1.9821.9826.9830.9834.9838.9842.9846.9850.9854.9857 2.2.9861.9864.9868.9871.9875.9878.9881.9884.9887.9890 2.3.9893.9649.9898.9901.9904.9906.9909.9911.9913.9916 2.4.9919.9920.9922.9925.9927.9929.9931.9932.9934.9936 2.5.9938.9940.9941.9943.9945.9946.9948.9949.9951.9952 2.6.9953.9955.9956.9957.9959.9960.9961.9962.9963.9964 2.7.9965.9966.9967.9968.9969.9970.9971.9972.9973.9974 2.8.9974.9975.9976.9977.9977.9978.9979.9979.9980.9981 2.9.9981.9982.9982.9983.9984.9984.9985.9985.9986.9986 3.0.9987.9987.9987.9988.9988.9989.9989.9989.9990.9990 the mean is selected, the number of standard deviations to subcontracted activities on a building project. One of the the right of the mean is 0.0 and the area to the left of this activities is related to the masonry work, and the other point is 0.5, or 50 percent of the total area. If the area is relates to laying carpet. Both subcontractors were asked to sought for a point that is one standard deviation to the right estimate the time to allow for their work. The estimate from of the mean, the area is determined to be 84.13 percent of the masonry contractor was 28 days, and the estimate from the total area (see Table 4.3). Thus, it can be said that with a the carpet installer was 23 days. When asked how they duration estimate of one standard deviation beyond the arrived at these durations, both said that they had data on mean, there is an 84.13 percent chance of completion in the seven prior projects that were similar to the one being allotted time. With two standard deviations, the estimate of constructed. The masonry contractor considered such the area to the left is found to be 97.72 percent of the total factors as the number of bricks, the number of window area. Examine Table 4.3 and develop a clear understanding openings, the number of doorways, the number of corners of the way the above-mentioned percentages were derived. in the structure, and various other features. The carpet Let’s first consider what is meant by the value that is installer considered room regularity, size of rooms, access to assigned to an activity duration. This will be demonstrated the work areas, and other features. The specific project data by considering the time durations for two different that they used to make their estimates are shown as follows: Masonry Data Carpet Data Project # Duration (Dur) (Dur-Mean)2 Duration (Dur) (Dur-Mean)2 1 14 36 18 4 2 17 9 21 1 3 27 49 19 1 4 16 16 22 4 5 18 4 17 9 6 25 25 22 4 7 23 9 21 1 Sum 1 = 140 Sum 2 = 148 Sum 1 = 140 Sum 2 = 24 Mean1 = 20 (Sum 2/n -1)1/2 = 4.97 Mean1 = 20 (Sum 2/n-1)1/2 = 2 n = 7 Std. Dev. = 5 (approx.) n = 7 Std. Dev. = 2 54 CHAPTER FOUR Note that the average duration of performing the work exceeded? Referring to Table 4.3, find the number of standard on previous projects was 20 days for both specialty contrac- deviations that include 95 percent of the area under the curve. tors. Yet the average value is not the duration they quoted. To From the table, it can be interpolated that the number use the average duration would mean that the estimated dura- of standard deviations is 1.645 for a confidence of 95 per- tion would be too small in many instances. So how did these cent. Thus, the estimate that we would be well advised to use firms come up with the duration estimates of 28 days and 23 is 144.8 or 145 hours (130 + 1.645 [9 hours]). days? This is where the standard deviation about past project While contractors may not generally go through this data is helpful. In this example, let’s assume that the subcon- rigorous type of statistical approach, the essence of their tractors would want to give an estimate that will not be under- logic is essentially the same. Contractors must compute a stated in 95 percent of the cases, meaning that we want a high realistic duration or have a very good intuitive sense of the level of confidence that the estimate is not too small. If the appropriate estimate to be used. estimate of 20 days had been given, the contractors would When the durations for the various activities are consid- have a level of confidence of 50 percent that sufficient time ered from the perspective of probability and statistics, it had been allowed to perform the work (see Table 4.3). If the should be clear that the durations attached to many activities masonry contractor’s estimate had been 25 days (essentially represent best guesses. A contractor will view an activity one standard deviation beyond the mean), the confidence with a duration of 8 days as being one that will be completed would increase to 84 percent. To be 95 percent confident that in the vicinity of 8 days, but it is recognized that the duration the duration will not be too small, the estimate must be 1.645 could be more or less. Owners may view durations a bit dif- standard deviations beyond the mean, or about 28 days for the ferently. The owner on a project may view the duration of 8 masonry work (20 + 1.645 * 5 = 28.2). Similarly, the days as implying that the duration will not exceed 8 days. carpet installer used the same logic and came up with a While these viewpoints may not seem to be drastically differ- duration of 23 days (20 + 1.645 * 2 = 23.3). The carpet ent, they could be the source of much conflict on a project. installer had less scatter in the past project durations, as is For example, the issue of float ownership becomes a serious evidenced by the smaller standard deviation of 2. The desired matter on some projects. If the owner owns the float, an estimate should bear a realistic value of the duration that does activity with a duration of 8 days had best not exceed that not generally understate the duration. This is where statistics duration. If the contractor exceeds that duration, there may can be valuable. be a cost associated with it. Contractors may very well argue The most relevant information needed to make an that, since the durations are “fuzzy,” it is inappropriate for estimate with confidence is the mean and the standard the owner to seize the float. The contractor likes to utilize deviation. The standard deviation implies the amount of float without the owner’s interference. variability that exists in a collection of numbers. In our case, the average was 20 days for both contractors, and the standard deviations were 5 days and 2 days, respectively. FINAL COMMENTS In our example, we assumed that the various estimates are The duration estimates for activities can be determined by essentially normally distributed, similar to a bell curve. If various methods. At the root of many of these estimates is either subcontractor’s estimate had been 20 days, it should the quantity take-off. Another key piece of information is be apparent that there is only a 50 percent chance of achiev- the production rate associated with the installation of those ing this duration. These are not desirable odds. On the other quantities. The quantity take-off is project specific, while the hand, if 98 percent confidence was desired, the duration production rate is relatively constant for that particular type estimates would be about 30 and 24 days, respectively, for of activity. Despite the computations associated with the the masonry and carpet work. activity durations, it must be recognized that these are essen- Consider another similar problem. The amount of time to tially best guesses and should not be regarded as absolute set the flatwork (sidewalk) forming on a project is to be deter- values. Some deviation from the estimated durations is to be mined. The data on past projects indicate that the duration has expected. Allowances may have to be made for the impact of a mean of 130 worker hours and a standard deviation of 9 adverse weather conditions and for other factors, such as the hours. What estimate should be used if we are to have a 95 per- accommodation of small tasks that are not specifically cent confidence that the estimated duration will not be included in the schedule. Review Problems that for this simple type of structure, the production rate for erecting scaffolding is 0.002 hours per square 1. Scaffolding is to be constructed on all faces of a six-story foot of building surface area. If 10 workers (working building in order for major masonry rehabilitation 8-hour days) are assigned to do the entire scaffolding work to be performed. The exposed surface area of the erection, what duration (in working days) should be exterior walls of the building has been estimated to be used for this activity? Round up your answer to the 432,000 sq. ft. Historical records of the company show nearest whole integer day.  Determining Activity Durations 55 2. Tiles (6⬙ by 6⬙) can be installed at a rate of 50 per worker 5. A masonry facade consisting of 3,800 square feet is to hour. The floor of a large lobby area (80 ¿ by 40 ¿ ) is to be be constructed for a building. The total cost per covered with these tiles. If three workers are assigned to worker hour is estimated to be $31.50, and the total this task, what duration (to the nearest whole day) estimated cost of the labor for this task is $10,500. should be assigned to this activity? Assuming 8-hour work days and a crew of six workers, 3. Historic records show that the mean duration of an how many days should be allowed to complete this activity is expected to be 8 days with a standard devia- task? What is the production rate that the crew must tion of 2.4 days. What duration should be used if there attain to keep the project on schedule and within the is to be a 95 percent confidence that the duration will budget? not be exceeded? What is the probability that the dura- 6. Based on historical weather data, a particular project is tion will actually exceed 10 days? expected to be impacted by six adverse weather days. 4. The task of framing a building has been estimated to Using one of the procedures described in this chapter, take an average of 25 days with a standard deviation of make the appropriate allowance for adverse weather and 4 days. What duration should be used if there is to be a solve the network for the basic scheduling information. 90 percent confidence that the duration will not be For each activity, show the computed value of early exceeded? What is the probability that the duration will start, early finish, late start, late finish, total float, and actually exceed 23 days? free float. B E G Dur = 7 Dur = 9 Dur = 4 A C F I 1 Dur = 1 Dur = 4 Dur = 6 Dur = 2 D H Dur = 6 Dur = 5 This page intentionally left blank