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Compu~rs ind. Engng VoL 31, No. 1/2, pp. 229 - 232,1996 Copyright O 1996 El~'vi©r S~en¢© Lid

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LIMITED-RESOURCE ALLOCATION IN CONSTRUCTION PROJECTS

Mostafa M. Khattab I and Ketil S0yland 2

IAssistant Professor, Constr. Management Dept., Univ. of Nebraska, Lincoln, NE 68588 2Graduate Research Asst., Civil. Engr. Dept., Univ. of Nebraska, Lincoln, NE 68588

ABSTRACT

The limited-resource allocation problem arises in many construction projects when there are different limitations on the amount of resources available to the contractor. The scheduling objective is to hold project duration to a minimum while resolving the resource conflict by shifting the activities until the re- source requirements do not exceed the amount of resource available. The objective is to minimize project duration using the resources available and increase the utilization of equipment and labor force available. Numerous computer packages have been developed for limited-resource management. Some of these packages assign priorities to the project activities based on measures obtained from the critical path calculations. The objective of this paper is to demonstrate the major difference between the approach taken by the commercial computer packages and some of the priority ranking procedures developed in some of the heuristic techniques.

INTRODUCTION

The most efficient way to develop a construction schedule is to use computer programs. The contractor's objective is to create the most efficient schedule possible and maximize the usage of the available resources. Scheduling, allocating, and leveling resources for a project can be time consuming unless a computer program is used. In most cases, computer programs give adequate solutions; however, when resource requirements exceed the resources available, the computer programs do not provide the optimum scheduling solutions. When generating a schedule by hand, the scheduler uses his/her experience with similar projects to make decisions concerning time, resources available and cost involved to create a schedule. A set of preprogrammed procedures is used when generating and calculating the schedule using computer software packages like Primavera for Windows. Primavera generates a schedule based on the critical path (CP) calculations and assigns priorities to the project activities based on those CP calculations. These CP calculations are based on unlimited resources available. This paper will show that the default procedures used by Primavera do not consistently give the best solution to the problem. It will also show that there is not one heuristic that will give the optimum solution for all projects, and therefore a set of heuristics has to be used every time a project is going to be scheduled under limited resources.

THEORY AND BACKGROUND

Heuristic Priority Rules

Heuristic rules are used to rank activities when leveling a schedule for a project. There are a large number of different heuristic priority rules proposed. Table 1 lists eight rules proposed by Khattab and Choobineh [1]. The Critical Path Method (CPM)-based group of rules are used in most computer software packages developed for construction project management. Priorities are assigned to the activities based on measures obtained from the critical path calculations. Note that the calculations are made assuming unlimited re- sources are available. This paper will compare the CPM heuristic with priority rule 7 listed in Table 1 by

229

230 19th International Conference on Computers and Industrial Engineering

scheduling and comparing four real projects. When leveling, priority rule 7 gives the activity with highest resource demand the highest priority.

Table 1. Khattab and Choobineh's Proposed Eight Rules

No. Priority Mathematical form

Activity time + time of all sons Activity resource + resource of all sons

Total time of sons

(Activity time + time of all sons) - (total time of parents)

Activity time + time of all sons

Activity time + time of all sons Number of immediate sons

(Time of immediate sons / Resource of immediate sons) Activity resource / Activity time

7 Activity resource

8 Activity time Activity resource

Ri+ Z Rj j c N

~, TjVi je ~F~

(Ti+ Z Tj)-ZTjVi j¢lV~ jeP,

Ti+ ZTjg i j~NE

T,+ Y rj J~tl~i ~.4 "

j~tF,

~. T , / ' 2 to, )~lFi / j~tFi

RiVi

Ti °

T, vl

Where: NFi i o r j Activity index, i=l , 2 ...... n IFi Ti Time required to complete activity i Ri Resource required to complete activity i X i

Set of activities that follow activity i Set of activities that immediately

follow activity i Number of immediate sons

Resource Leveling vs. Resource Allocation

Resource Allocation and Resource I.~veling are the two basic categories for scheduling resources. Re- source allocation is used when there are definite limitations on the resources available. When leveling us- ing resource allocation techniques, both the non-critical and critical activities are shifted with the objective to extend the project duration as little as possible beyond the original critical path length. Resource allocation depends on a list of criteria for how to allocate limited resources within a specific period. The available resources need to be compared to the resource demanded by a given activity. When there are insufficient resources available, the activity has to be rescheduled to free necessary resources. In the case where two activities require the same resources simultaneously and there are insufficient resources to start both activities as planned, the activity with the highest priority will get the scarce resource first. Resource leveling is used when there are enough resources, but the fluctuations of resource usage need to be leveled. The project duration calculated by the critical path initially remains fixed. The leveling process is accomplished by shifting only the non-critical activities within their floats.

19th International Conference on Computers and Industrial Engineering 231

Primavera Software

Primavera for Windows (P3) was used for scheduling and leveling the projects considered in this paper. A brief description follows on how P3 levels a project. Note that P3 first schedules and calculates the Critical Path. P3 needs the following data to level a project: Start Dates, End Dates if a fixed end project, normal and maximum resource usage (money, labor, equipment), and resource usage for each activity. There are several options to select before leveling a project. The most important options are described in the Primavera Reference Manual [2].

ii , i ~ E . - . . Jb ,~

s ~

, ~ l t N ". Nm.4im ¢om~aia~l \ J . i am n a m ~ a i m K I

SthNkdo ~ ~ o ~

i+iiii iiii!ililili+

i ~ ~ ....................................... I ................ . ~ : ~ .......................

':i v.~,Jh,~

i

Fig. 1. Primavera Resource Leveling Options

! DISCUSSION OF RESULTS

To compare P3 for Windows with priority rule number 7, four real projects were scheduled. The projects varied in size, complexity and resource availability. Each project was scheduled using information given from the contractors involved in the project.

Priority Rule using Primavera

To use the priority rule with P3 we assigned each activity a number from "1" to "10" by defining an extra field using the command "activity codes". This number reflects the activities total resource need. The ac- tivities using the highest number of "man hours" are assigned the number "1". When leveling the project the "priority rule" has to be selected as the first priority. Second priority was chosen to be "total float".

Comparison of the projects

Depending on the preference and experience of the scheduler, the projects could be leveled based on any of the resources used with the project. The four projects considered in this paper were leveled based on the resource "general labor". The comparison between the CPM-based rule P3 uses and the Priority role are charted in Fig. 2. The data indicate that the priority rule performs significantly better than the CPM- based rule. Project 1, for example, shows that with a resource level of 5 people the priority rule gives a completion date 18 days (as indicated on the graph) earlier than the CPM-based rule. With a resource level of 6 the priority rule gives completion of the project 30 days earlier than the CPM-based rule. Note that for all the projects the priority rule performs better than P3 when there are resource limitations. Also, P3 does not give the user the option to specify the minimum resource level needed to schedule an activity and therefore this is not taken to account when leveling the projects.

232 19th International Conference on Computers and Industrial Engineering

Project 1: Lincoln Northeast High School Project 2: First Data

570 ' --

5 2 0 - :ii 510 "

5OO 4 5 6 7 8 15

Re~xJrce L e ~ (labor)

~ 260 . . . . .

24O

~0 7 8 9 10 11 12 13 14 15 16 17 18

Rs~u~'ce Lev~ (Labor)

Project 3: Southeast Community College Project 4: Dr. Gewain Office Building

i ~ . . . . . . . . . . . . . . . . . . . . . . . . . ~ 45- 35- 40- 50.

: J i ~ 20-

1 5 -

~ o ~ i

3OO

8 9 10 11 12 13 14 15 16 17 18 19 20 Resource Lev~ (Lal~)

16

- ,~ , i I -

-,ii~!iiii - _ iii~i!i _

~!i i!il

17 18 Resource Level (Labor)

19 20

Fig. 2. Graphical presentation of the Resource Level vs. Project Duration. (Note: scale is not identical in the four plots.)

CONCLUSIONS

The priority rule performed significantly better than the CPM-based rule when leveling the four projects considered in this paper. The priority rule performed best when leveling projects with resource limitations. Other priority rules might perform better when other constraints govern the project. The experienced user of a scheduling software would not accept the default leveling procedure given by Primavera. The scheduler would need to level the project using different heuristics in order to find the best solution, which is a time consuming task. It would be advantageous to any project manager to have a computer software equipped with the option of testing the behavior of his/her project under limited resources using a set of priority rules that would result in the best duration possible for the project. This will eliminate the time consuming process of testing each rule individually.

REFERENCES

Khattab, M., and F. Choobineh (1991). .A New Approach for Project Scheduling with a Limited Resource. Int. J. Prod. Res. 29 (1) 185-198.

Primavera Systems, Inc. (1993). Primavera for Windows User Manual. Easa, S.M. Resource Leveling in Construction by Optimization. Journal of Constr. Engr. and Manage-

ment. 11___55 (2) 302-316. Chang, T.C., W.C. Ibbs and K.C. Crandall. Network Resource Allocation with Support of a Fuzzy

Expert System. Journal of Constr. Engr. and Management. 116, (2) 239-260.