HIERARCHICAL RULE-BASED ACTIVITY DURATION ESTIMATION By Chris Hendrickson, 1 A. M. ASCE, David Martinelli, 2 and Daniel Rehak 3 ABSTRACT: Activity durations are often estimated by modifying standard work productivities for specific site and job characteristics. Modifications are typically developed from engineering judgment and past experience. In this paper, an explicit hierarchical rule-based framework for making such modifications is investigated. By explicitly formulating estimation rules, the factors felt to influence work productivity can be identified and the accuracy of particular modification rules assessed. Alternative estimation methods such as statistical techniques and a hybrid rule-and-statistical framework are discussed. A prototype expert system for masonry construction duration estimation, MASON, is described and used to illustrate the rule-based estimation approach. Facilities in MASON for explanation and productivity improvement analysis are also described.

INTRODUCTION

The estimation of activity durations is necessary in the preparation of a construction plan and in the application of formal project scheduling methods such as t h e critical p a t h m e t h o d (CPM) or p r o g r a m evaluation research task (PERT) (15,20). Formal project planning a n d scheduling involves the definition of activities, the relationships a m o n g these activities, the resources required by the activities, a n d the activities' durations. This project planning is usually performed in an intuitive a n d u n structured fashion with considerable reliance o n engineering judgment. The process of project planning and, in particular, activity duration estimation has received little systematic attention, even t h o u g h it provides an indispensable input for planning a n d management. Some exceptions to this lack of attention include a prescriptive discussion of good estimating practice by Smith a n d Mandakovic (17) a n d empirical analyses of the accuracy of activity duration estimates by King and Wilson (9) and King, et al. (10). For activity duration estimation, average productivities are usually available as an aid for estimation, b u t these averages must often be modified in light of the special conditions of a job or site. Activity durations are typically estimated as the p l a n n e d quantity of work divided b y the expected productivity. A similar approach m a y be used for activity cost estimation (6). N u m e r o u s estimation h a n d b o o k s (i.e., Refs. 5, 19) provide historical data on averages a n d ranges of work productivities divided into a limited n u m b e r of job-type categories. For example, masonry work productivities might be reported separately for different 'Assoc. Prof., Dept. of Civ. Engrg., Carnegie-Mellon Univ., Pittsburgh, PA 15213. Res. Asst, Dept. of Civ. Engrg., Carnegie-Mellon Univ., Pittsburgh, PA 15213. Assoc. Prof., Dept. of Civ. Engrg., Carnegie-Mellon Univ., Pittsburgh, PA 15213. Note.—Discussion open until November 1, 1987. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on July 17, 1986. This paper is part of the Journal of Construction Engineering and Management, Vol. 113, No. 2, June, 1987. ©ASCE, ISSN 0733-9364/87/00020288/$01.00. Paper No. 21580. 2

3

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masonry thicknesses; types of work, e.g., interior walls, foundations, etc.; and crew compositions. Organizations often maintain historical records to provide similar average productivities relevant to local conditions. However, special job conditions or local variations such as union work rules often require modifications to the average productivities available from historical records. This process of modification relies on considerable expertise, typically without the benefit of computer aids. In this paper, a hierarchical, rule-based approach to estimating activity durations is investigated. The purpose is to propose a model of the process followed by a planner as a means of identifying the factors thought to be important in influencing durations and to allow explicit analysis of the estimation method. For this purpose, a decision tree representation of the estimation problem is employed. This representation can be conveniently implemented as a knowledge-based expert system with domain knowlege expressed as production or "if-then" rules. The expert system MASON illustrates the approach. MASON makes estimates of masonry construction time, and provides a variety of explanation and advisory facilities. MASON is limited to concrete block and brick construction in commercial applications, including related activities, such as installation of flashing, inlets, and other wall components. MASON represents an example of a new type of computer aid that can provide assistance in the construction planning process. Knowledgebased expert systems are computer programs originally developed in the field of artificial intelligence (AI) and designed to reach the level of performance of a human expert in some specialized problem-solving domain (8).. Expert systems have great potential for practical use in ill-structured problem-solving domains in which explicit algorithms do not exist or traditional computer programs provide only restricted problem-solving capabilities. Numerous tasks in the domains of civil engineering and construction fall into these categories and might be assumed by expert systems. Rehak and Fenves (16) provide a review of such potential applications, and some recent conference proceedings (11,18) contain numerous examples of expert system applications in civil engineering. Some applications to construction project monitoring are described by McGartland and Hendrickson (14) and by Levitt and Kuntz (12). In the next section, a hierarchical, rule-based structure for activity duration estimation is described. The following section illustrates the general estimation approach with a description of the MASON expert system. An example application also appears. Next, alternative approaches using statistical techniques are described. HIERARCHICAL, RULE-BASED ACTIVITY DURATION ESTIMATION

The hierarchical, rule-based estimation approach decomposes the estimation problem into component parts in which the higher levels represent attributes that depend upon the details of lower level inferences and calculations. In effect, the estimation problem is represented as loosely coupled subsystems. At each level, inferences and calculations are based on a set of if-then rules or productions. These rules categorize a particular job task and obtain the necessary attributes of the task. Attributes 289 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

such as expected productivity can be inferred, calculated, or obtained externally from a data base or user. One level of decomposition can be represented by an estimation equation or format: fc = ^ nkPk

+*

(1)

nk

where tk is the duration of activity k, in hours or days; qk is the physical quantity of work required for activity k; nk is the number of crews working on activity k; pk is the estimated productivity per crew on activity k, in units of work per hour or day; and dk is the estimated idle or downtime during the activity duration for setup and other activities, in hours or days. With this estimating format, the estimation process decomposes into the specification or estimation of the various factors qk, nk, pk, and dk. Note that various unit conversions may be required to achieve consistency among these various factors so that, e.g., all estimates are made for days or hours of work. Note also that the estimating formula, Eq. 1, is only approximate when uncertainty concerning productivity pk exists. If the expected value of pk is used in Eq. 1, then the calculated duration tk will be (slightly) biased. This is because the mean of a function of random variables is not necessarily equal to the function of the means. Instead of using the expected value of pk in Eq. 1, it would be more accurate to use the expected value of the multiplicative inverse (or l/pk). However, the error in using Eq. 1 from this source is likely to be small in practice. As an example of the procedure, consider a concrete block exterior wall construction activity, k. Two masonry crews have been assigned to the activity, so n t = 2. The productivity of each crew is assessed by considering the work activity and relevant job-site characteristics. The productivity of the activity, pk, has been estimated to be 150 blocks per crew per day for this example. A quantity takeoff for this activity yields the number of concrete blocks required, qk = 2,400. The downtime associated with the activity, dk = 5 crew-days, is the time necessary to complete activity tasks other than laying blocks. The duration can now be calculated using the estimation Eq. 1: h =

2,400 5 + - = 10.5 days y 2(150) 2

K(2)

'

As can be seen, the use of Eq. 1 requires a series of lower level estimates for the various factors. In the estimation of productivity, pk, it may be helpful to employ two distinct stages. First, the maximum expected productivity is estimated for the activity. Next, this maximum productivity may be reduced depending upon various characteristics of the job or site, such as temperature or height. In contrast, downtime estimates dk might simply be made by aggregating various extra items such as anchoring work. More generally, some job attributes might be included as adjustments in the estimates of productivity or in the activity duration itself. For example, weather effects may be imposed at either stage. In contrast, modifications for items such as learning during the activity might best be made 290 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

Activity Duration Estimate

Overall Adjustment (e.g. Learning)

-Quantity of Work -Weather -Number of Crews

Initial Duration Estimation

Productivity Estimate

Down Time Estimate

Productivity Adjustments

Down Time Adjus tments

Ancillary Task Information

Task, Technology and Cite Data

FIG. 1.—Example of Estimation Hierarchy

after an initial duration estimate for the entire activity is made. The adjustment would reflect the fact that productivity on an activity improves after some experience is accumulated. Since the quantity of work affects the extent of the possible adjustment for learning effects, it should be applied after an initial estimation of the activity duration is made. Fig. 1 shows the various stages that might be considered in a duration estimation for masonry work. In this figure, procedural steps are shown in rectangles while data are in ovals. At the bottom level, the maximum productivity is estimated and the various modifications to account for downtime are assessed. At this stage, it is also possible to evaluate the planned work crew for violations of work rules. For example, current union work rules in western Pennsylvania require that masons work in pairs if they are laying 12-in. (30.5-cm) wide block. Consequently, union crews of single masons could be excluded with this size block at this stage. At the next higher level in the estimation hierarchy in Fig. 1, adjustments to standard productivities might be made to account for special characteristics of the site or job. For example, modifications to account for elevation, crew-type, mortar consistency, accessibility, and other factors are made. These modifications typically take the form: If a particular condition exists, then reduce productivity by x%. For example, if highstrength mortar is used, then the productivity might be reduced by 3% of the maximum, depending upon other conditions such as temperature. Note that any subset of the conditions yielding productivity re291 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

ductions might exist, so that the node in the decision tree representing modifications is not a simple "AND" or "OR" decision node. At the next higher level in Fig. 1, the quantity, productivity, crew resources, and downtime are combined using Eq. 1 to estimate an initial activity duration. Some of these quantities are input from external sources such as the facility design or a construction planner. Other quantities are calculated from the combination of effects assessed at lower levels. Adjustment factors for learning effects or weather could also be considered at this stage. The basic estimation framework described earlier could be readily modified to develop rules for estimation of optimistic and pessimistic duration times. In essence, the same conceptual framework used to estimate expected duration could be used to estimate optimistic or pessimistic durations. In these cases, separate decision trees might be added to estimate these quantities after estimation of the most likely duration time. Alternatively, rules incorporating modifications to optimistic, most likely, and pessimistic attributes might be added at each level and node in the decision tree (Fig. 1). As noted earlier, it is also possible to alter the order and composition of the various levels included in the estimation hierarchy. Different types of activities might require a different arrangement or number of levels in the tree. For example, if weather effects were of great importance, a separate level to evaluate such impacts might be added. The principle to be adopted in such modifications is to restrict the amount of information that must be passed between levels; this is the reason that learning effects might be considered at the top level as described previously. Another extension to the system would be to include explicit treatment of uncertainties in the estimation process. These uncertainties might arise due to unknown conditions at the site or unforeseeable risks such as adverse weather. For example, a planner might not know the experience level of workers, while the estimation framework could include rules to adjust for different levels of worker experience. Unfortunately, the use of classical methods of probabilistic analysis are difficult to apply in this case due to the large number of different conditions that might be evaluated. Estimating correlations among each of these conditions and potential subsets of conditions might be burdensome, and the assumption of statistical independence may be untenable. However, the use of simplified methods such as fuzzy set evaluations could be readily adopted in this case. Fuzzy sets incorporate the uncertain membership of an element in one or more categories and possess a distinctive set of combination operations. Ayyub and Haldar (3) describe the relevant calculations in this regard. MASON PROTOTYPE EXPERT SYSTEM

To illustrate the hierarchical, rule-based estimation procedure described in the previous section, the expert system MASON was developed (13). MASON is a prototype system applicable to a limited range of all possible masonry activities. It provides facilities for estimating the duration of masonry construction, explaining the various calculations made, and making recommendations for alternative crew compositions 292 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

TABLE 1.—Examples of Maximum Productivity Estimates Masonry unit size (in.) (1)

Condition(s) (2)

Maximum productivity (units/day/mason) (3)

(a) Blocks 8 6 6 12 12 4

4 4 4

None Wall is "long" Wall is not "long" Union labor Nonunion labor Wall is "long" Weather is "warm and dry" or high-strength mortar Wall is not "long" Weather is "warm and dry" or high-strength mortar Wall is "long" Weather not "warm and dry" or no high-strength mortar Wall is not "long" Weather not "warm and dry" or no high-strength mortar (b) Bricks

Support from existing wall 8 8 No support from existing wall 12 Support from existing wall 12 No support from existing wall Note: 1 in. = 2.54 cm.

400 430 370 190 300 480

430 370 320

1,000 750 700 550

and technologies. The system is implemented in the OPS5 programming language (4,7). As currently implemented, MASON employs a "backward-chaining" problem-solving approach in which evaluation of particular attributes or quantities is expressed as a system goal to be satisfied (13). For example, an important system goal is to estimate an activity duration. Before this can be accomplished, subgoals associated with productivity and downtime estimation must be accomplished. These in turn require evaluation of more limited subgoals, which would be associated with the various nodes in Fig. 1. MASON could also have been implemented as a forward-chaining system based on job characteristics or using a semantic net. Knowledge included in the MASON system was originally developed from interviews with a professional mason and a supporting laborer. The two experts had nearly 70 years of commercial construction experience between them. Direct interviews were supplemented with records of actual productivities and downtime experienced by the two experts over a number of years. As an example of the knowledge included in MASON, Table 1 contains the estimated maximum productivities that might be achieved un293 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

TABLE 2.—Examples of Adjustments to Maximum Productivities

Input (1) Crew type Crew type Supporting labor Supporting labor Mortar type Elevation Elevation Elevation Visibility Temperature Temperature Brick texture

Condition(s) (2) Crewtype is nonunion Job is "large" Crew type is union Job is "small" ' 2 masons for each laborer per crew High-strength mortar used Warm/dry weather expected Steel-frame building Exterior wall Insufficient support labor Solid-masonry building Exterior wall Union labor Solid-masonry building Exterior wall Nonunion labor Block is not covered Temperature is below 45° F Temperature is above 85° F Bricks are baked high Weather cold or moist

Adjustment magnitude (% of max) (3) 15 10 20 10 3 10 7 12 7 7 10 10

Note: 45° F = 7.22° C; 85° F = 29.44° C. der various conditions. These maximum productivities would be modified by site conditions as necessary at the next higher level in the estimation hierarchy. Table 2 contains a subset of possible modifications of this type. Each row in Tables 1 and 2 would be represented in the system as one or more rules. For example, row 1 in Table 1 indicates a maximum productivity of 400 Units per day per mason while working with eight-in. block. This expression can be represented as an if-then rule: IF the maximum productivity assessment is desired AND eight inch block is to be used on the activity THEN the maximum productivity on the activity is 400 units per day per mason AND a maximum productivity assessment is no longer desired This rule can be expressed as the following production in OPS5: (p find-max-prod-8-inch {(goal "name find-maximum-productivity "status desired) (goal)} (unit "type block "thickness 8) 294 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

{(activity "maximum-productivity nil) (activity)} —» (modify (activity) "maximum-productivity 400) (modify (goal) "status not-desired) ) Note that the various conditions shown in Tables 1 and 2 might be complementary or mutually exclusive. In the latter case, control restrictions might be imposed to prohibit mutually exclusive modifications from being attempted. If more than one productivity reduction condition is imposed for a particular job, the reduction percentages are added to approximate the overall effect. In addition to the estimation procedures, MASON also includes a series of rules intended to make recommendations concerning appropriate crew compositions and technologies. These recommendations are based on a strategy of overcoming the reductions imposed on the maximum productivity due to site conditions or crew composition. In essence, if a particular rule was used to modify (reduce) the productivity, then a recommendation that would reverse this modification might be possible. For example, if there are too few laborers assigned to the crew, then a rule reduces the productivity accordingly. However a recommendation to add more laborers to the crew can be made, yielding an improvement in productivity. This recommendation could be expressed in an OPS5 production as: (p recommend-more-laborers {(reduction-rule "name lack-of-labor "improvement (improvement) "status not-recommended) (rule)} (crew "masons (masons) "laborers (laborers)) —> (bind (needed-labor) (compute (masons)//2 - (laborers))) (write You can increase the productivity on this activity by| (improvement) units per day per mason if| (needed-labor) |laborers were added to| each crew. | Would you like to add| (needed-labor) |laborers to each crew?|) (modify (rule) "status recommended) ) Upon each recommendation, the user may respond " y e s " t 0 accept, thus implementing the recommendation, " n o " to reject it, or "why" to be given an explanation of why the suggested recommendation will lead to the estimated improvement. The appropriate explanation of a recommendation depends on the job and activity conditions and may vary from session to session. If the user has asked why, he will again be given the option of accepting or rejecting the recommendation following the explanation. If the user wishes to accept the recommendation, the productivity and the resulting activity duration is adjusted for the improvement. If it is rejected, the productivity remains the same. 295 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

TABLE 3.—Comparison of Observed and MASON Estimated Work Productivities Masonry material (in.) (1) Face brick 12 x 8 x 16 block

8P x 8 x 16 block

4 x 8 x 16 block

Observed daily productivity (2)

MASON estimated daily productivity (3)

Percentage error (4)

900 820 243 202 187 307 307 279 338 321

980 840 190 190 181 332 332 289 310 310

8.89 2.44 21.81 5.94 3.21 8.14 8.14 3.58 8.28 3.43

Note: 1 in. = 2.54 cm. In its current state, MASON does not include provisions for estimating optimistic or pessimistic duration times or for evaluating uncertain data. These provisions could be added, although the accuracy of the resulting estimates would have to be carefully assessed. Inclusion of "fuzzy" uncertainties in inferences (3) is also possible; most expert system frameworks include explicit provisions for uncertainty calculations of this type. As an illustration of the type of accuracy from the estimates provided by the MASON system, Table 3 contains some comparisons between the actual productivities and MASON's estimates for a series of masonry construction tasks. This data was provided by a masonry subcontracting firm in western Pennsylvania. All of the figures pertain to activities on a two-story school building constructed in the summer of 1985. The activities vary in location, materials, crew structure, and other factors. For the nine tasks included in the comparison, the average percentage error was 8%. These results were obtained without any other calibration or adjustment of the MASON system beyond the interviews with our experts. Further development of the system might include adjustment of the rules or numerical values included in the system after comparing observed activity durations with those estimated by MASON, as illustrated in Table 3. EXAMPLE APPLICATION OF MASON

To illustrate the operation of MASON and the hierarchical approach to duration estimation, this section contains a sample estimation session with MASON. Note that MASON provides duration estimates through an assessment of the productivity and downtime inefficiencies at both the project and activity levels. The system queries the user and determines if possible productivity impacts or downtime events exist that could have a bearing on the duration. In such cases, the user is usually asked follow-up questions in order to make assessments of these impacts and events. Thus, a session with MASON includes input, recommendation, and explanation phases as well as the estimation of durations and pro296 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

ductivities. In what follows, user responses are italicized, and menubased queries from MASON are omitted; notes are in bold. Welcome to MASON. What is the name of the job? Martinelli's What type of job is it? Steel-frame Is this job large or small? large Is this an addition for an existing building? no What would you like to call this activity? first What is the expected temperature level during this activity? Low (under 50° F) . . . and the precipitation level? High (More sophisticated input control would omit this question for interior jobs.) Where on the job is this activity located? Interior-Wall How many crews are you putting on this activity? 1 How many laborers are on each crew? 2 . . . and how many masons? 6

Are you using union or nonunion labor? union I need to know how many openings there are? 9 Will this wall be insulated? no What type of material is being laid? Block . . . and how many orders of this material were placed? 1 What thickness of block was ordered for this activity [inches]? 4 inch Will high strength mortar be used? no 297 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

J i ;

What type of finishing will be placed over the block? Drywall What is the average length-of the wall-s [feet]? 50 Will FIRST take place on more than one floor? [yes, no] no On what floor will FIRST take place? [0 for foundation] 4 What is the average width of the opening-s [feet]? 2 . . . and the height? 3 How much area is to be covered [sq-ft]? 10000 How will strap anchors be attached to steel? Shoot with Hildy-Guns Input is now complete. THE DURATION OF ACTIVITY: FIRST IS 16.4 DAYS THE PRODUCTIVITY IS 176.0 UNITS PER DAY PER BRICKLAYER THE TOTAL DOWNTIME IS 5.7 DAYS Would you like recommendations to improve productivity? yes You can increase the productivity on FIRST by 32.0 BLOCK per bricklayer per day if at least 1 laborers are added to each crew. Would you like to increase the number of laborers by 1? why Supporting laborers are needed to mix mortar, keep the bricklayer stocked, as well as assist him in laying out corners, etc. If there are more than 2 bricklayers for every laborer, then it is said that the laborers cannot keep up and that the bricklayers will have to slow down. Also, because FIRST is on the 4 floor, the added labor is necessary to efficiently transport the materials and tools to the high elevation activity site. Because you plan to use 6 bricklayers, I recommend that you add 1 laborers to each crew. By doing this, the bricklayers will not have to be delayed. You can increase the productivity on FIRST by 32.0 BLOCK per bricklayer per day if at least 1 laborers are added to each crew. Would you like to increase the number of laborers by 1? yes 298 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

Your increase in the number of laborers in each crew is confirmed. You can increase the productivity on FIRST by 41.0 units per day per mason if high strength mortar is used. Do you wish to switch to high strength mortar? why When working with regular strength mortar in the cool and damp conditions expected for activity FIRST, the block does not set as fast. This situation has significant impact on productivity when using 4 inch block. This is because the thinner 4 inch block is, in general, more difficult to balance than blocks of other thicknesses. You can increase the productivity on FIRST by 41.0 units per day per mason if high strength mortar is used. Do you wish to switch to high strength mortar? Revised duration estimation is complete. THE DURATION OF ACTIVITY: FIRST IS 13.2 DAYS THE PRODUCTIVITY IS 249.0 UNITS PER DAY PER BRICKLAYER THE TOTAL DOWNTIME IS 5.7 DAYS Would you like to know the factors considered in calculating the productivity?

ves

The low temperatures expected for this activity has given rise to a 12% (of the maximum) reduction in the productivity. This example illustrates the interactive, explanatory characteristics of MASON that would be quite useful in application. Graphic displays to improve interaction and more sophisticated input control to avoid unnecessary questions would enhance the usefulness of the system. ALTERNATIVE APPROACHES TO ACTIVITY DURATION ESTIMATION

The hierarchical, rule-based approach used in MASON and described in a previous section is only one of many different approaches that might be adopted for estimation purposes. In this section other alternatives are described. First, the various combinations of conditions described for the MASON system could be expressed as an extremely large table in which individual entries represent the expected productivity for a particular combination of job-site conditions. Individual entries in the table could be estimated by standard statistical techniques such as averaging productivities on comparable jobs. Unfortunately, the number of table entries would be extremely large. Even in the prototype state of MASON, well over 1,000 different job conditions would result in different productivity estimates. As a result, complete enumeration would be bur299 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

densome, and sufficient numbers of comparable observations would be difficult to obtain for estimation purposes. Moreover, adding a new factor is much easier in an expert system due to the separation of knowledge and control mechanisms. Of course, the reliance on a single-level, tabular representation of job conditions may be a model of the actual estimation process employed by an expert. In this circumstance, an expert might look for patterns of conditions and immediately synthesize an appropriate productivity figure. In contrast, the writers have proposed a model in which different components of the process are explicitly examined and assessed by means of rules. This explicit decomposition has the advantage of facilitating the assessment of particular modifications. Another approach to the activity duration problem would be to represent the essential characteristics of the task by means of a limited number of parameters and to fit a functional model to this set of parameters. This functional estimation procedure is often accomplished using ordinary least squares regression (1,2). Variations in job-site characteristics not represented by the various explanatory parameters would be treated as irreducible random "noise" in this approach. Similar conceptual statistical estimation models are available for activity cost estimates (6). In theory, consideration of actual job conditions should improve estimates. An advantage of an estimation system such as MASON in this regard is that much of the work associated with preparing a detailed estimate is assumed by the program. Of course, barring complete validation of a hierarchical, rule-based estimation model, it could be that a simpler, parametric model might be just as accurate due to the influence of various uncertainties or inaccuracies in judgment on the part of experts or the expert system developer. Also, a hybrid approach may be useful in which a hierarchical, rulebased approach develops some preliminary sets of appropriate attributes or factors, and these are then employed in a parametric statistical study. Alternatively, parametric models might be estimated and inserted into a hierarchical, rule-based structure at one or more nodes. In this case, the statistical estimation model simply takes the place of a set of rules. As experience and evidence accumulate, this latter approach may be advantageous. CONCLUSIONS

In this paper, a hierarchical, rule-based approach to the estimation of activity durations is described, This framework provides a means of decomposing an estimation problem into related subproblems and formalizing the means by which various job conditions are assessed. A prototype expert system implementation of this estimation procedure was described and some relevant knowledge summarized for the domain of commercial masonry construction. A useful extension of the work described here would be to develop a general expert system framework that could quickly accommodate alternative decision trees and new if-then rules to provide an estimation aid for a wide range of activities. 300 Downloaded 14 Jun 2012 to 128.237.190.83. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org

ACKNOWLEDGMENTS

The writers would like to t h a n k Ernest Brady a n d Thomas Martinelli for lending their expertise in the development of MASON. Financial support for this research from the National Science Foundation (Grant MSM-8503400) is also gratefully acknowledged. APPENDIX.—REFERENCES

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