ALGORITHM FOR SCHEDULING WITH MULTISKILLED ...

ALGORITHM

FOR SCHEDULING WITH MULTISKILLED CONSTRAINED RESOURCES

By Tarek Hegazy,1 Member, ASCE, Abdul Karim Shabeeb,2 Emad Elbeltagi,3 and Tariq Cheema4 ABSTRACT: Scheduling with constrained resources, particularly skilled labor, is a major challenge for almost all construction projects. In the literature, various techniques have been developed to reduce consequent project delay of constrained resources. Most of these techniques assume single-skilled resources and use heuristic rules to decide which activity will receive the resource first and which ones to delay. To improve existing solutions, this paper introduces some modifications to heuristic resource-scheduling solutions, considering multiskilled resources. The proposed approach stores and utilizes information about the resource(s) that can be substituted when there is a shortage in another one. Using this information, less utilized resources can be combined to substitute the shortages in constrained resources during the shortage period, taking into consideration the loss in work productivity. To automate the proposed algorithm, a macroprogram has been written on a commercial scheduling software. An example application is presented to show the improved results of the proposed approach over existing heuristics. The use of the proposed approach as a better resource management tool within the construction industry is then discussed.

INTRODUCTION Two of the most critical challenges facing the construction industry are the limited availability of skilled labor, and the increasing need for productivity and cost effectiveness. These challenges have been discussed by many practitioners and have led researchers to investigate various avenues. One of the most promising solutions to the problem of the shortage of skilled resources has been to develop methods that optimize or better utilize the skilled workers already in the industry (Burleson et al. 1998). Most existing techniques for project scheduling consider a single-skilled resource strategy. As reported in various studies, this strategy has been a contributing factor to many of the inefficiencies in labor utilization, thus bringing substantial costs to projects [e.g., Thomas (1991), Cass (1992), Halpin (1992), and Burleson et al. (1998)]. Multiskilled labor, therefore, has been proposed as one of the solutions (Burleson et al. 1998). This strategy is commonly found in the manufacturing and process industries where some of the labor force is trained to be multiskilled. Various studies have demonstrated the benefits of multiskilled resources. The study by Nallikari (1995), involving Finnish shipbuilding facilities, employed a ‘‘multiskilled work team’’ strategy and found savings of up to 50% in production time. Various multiskill strategies have been explored by Burleson et al. (1998), including a dual-skill strategy, a four-skill strategy, a four-skill-helpers strategy, and an unlimited-skill strategy. The study compared the economic benefits of each strategy in a $70,000,000 construction project to prove the benefits of multiskilling, but did not develop a mechanism for selecting the best strategy for a given project. The study by Brusco and Johns (1998) presented an integer goal-programming model for investigating cross-training, mul1 Asst. Prof. of Constr. Mgmt., Dept. of Civ. Engrg., Univ. of Waterloo, Waterloo, ON, Canada N2L 3G1. E-mail: [email protected] 2 Grad. Student, Dept. of Civ. Engrg., Univ. of Waterloo, Waterloo, ON, Canada N2L 3G1. E-mail: [email protected] 3 Asst. Prof. of Constr. Mgmt., Dept. of Struct. Engrg., Mansoura Univ., Mansoura, Egypt. E-mail: [email protected] 4 Sr. Constr. Mgr., El-Saif Construction Co., Riyadh, Saudi Arabia. E-mail: [email protected] Note. Discussion open until May 1, 2001. 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 August 13, 1999. This paper is part of the Journal of Construction Engineering and Management, Vol. 126, No. 6, November/December, 2000. @ASCE, ISSN 0733-9634/00/0006-0414– 0421/$8.00 ⫹ $.50 per page. Paper No. 21660.

tiskilled resource policies to determine the number of employees in each skill category so as to satisfy the demand for labor while minimizing staffing costs. The model was applied to the maintenance operations of a large paper mill in the United States, where management and union officials agreed on a policy that enables employees to be cross-trained so that they can perform maintenance operations outside their primary area of expertise. The study concluded that the breadth of cross-training (number of skill categories) is more influential on workforce size than the depth of cross-training (level of productivity in each skill category). Although most available studies have successfully demonstrated the benefits of multiskilled labor, no study was found in construction literature that incorporates a structured procedure for scheduling activities using multiskilled resources. Therefore, an attempt is made in this paper to modify existing resource-scheduling heuristics that deal with limited resources, to incorporate the multiskills of available labor, and, accordingly, to improve the schedule. First, existing heuristic solutions that use single-skilled constrained resources are reviewed. Then, a modified heuristic approach is proposed to incorporate multiskilled resources in the solution mechanism. The performance of the proposed approach is then demonstrated using a case study, and the solution is compared with that of a high-end software system that considers multiskilled resources. The benefits of the proposed approach are then discussed along with its potential applicability within the construction industry. SINGLE-SKILL RESOURCE SCHEDULING HEURISTICS Because of its basic assumption of unlimited resources, the traditional critical path method (CPM) of network scheduling often results in a project duration that is unrealistically short. When a resource is limited, however, the daily demand of the resource by the various activities may exceed its availability limit, and thus some activities have to be delayed, causing a delay in project duration. In this case, rescheduling of activities is needed to minimize project delay. One common approach is to prioritize the competing activities, allocate the resources to some activities, and delay the others until the earliest time in which the resource becomes available. The objective of constrained-resource scheduling, therefore, is to reschedule the project activities so that available resources can be efficiently utilized while keeping the unavoidable extension of the project to a minimum.

414 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / NOVEMBER/DECEMBER 2000

Different heuristic solutions for this problem have been introduced by many researchers since the 1960s. Heuristic methods apply a single heuristic rule, or a hierarchy of heuristic rules, to decide the order of resource allocation among competing activities. These heuristic rules are based mainly on activity characteristics. The two most effective and commonly used heuristic rules are the least total-float (LTF) and the earliest late-start (ELS) (Davis and Patterson 1975). These two rules have been proven to provide identical results, with the ELS rule being advantageous compared to the LTF rule (Touran 1991). This is because the value of the late-start derived from the original CPM calculations, unlike the totalfloat, need not to be changed every time an activity is rescheduled due to insufficient resource availability. As such, the ELS rule can be applied with much less computational effort than the LTF rule and, accordingly, has been used as a basis for the developments in this study. Heuristic rules have the advantage of being simple, easy to apply, and can be used for large size projects (Talbot and Patterson 1979). The scheduling process using heuristic rules starts with the project start time, identifying eligible activities according to the network logic, and resolves the overrequirements of resources using a selected set of heuristic rules (Shanmuganayagam 1989). Most commercially available scheduling software provides resource allocation capabilities (sometimes referred to as resource leveling) utilizing proprietary heuristic approaches. Also, in a recent contact with some software vendors, some have indicated that they incorporate multiskill scheduling capabilities in their systems (Table 1). Although the TABLE 1. Systems

Multiskill

Scheduling Capabilities of Software

Software (1)

Single-skill resource scheduling (2)

Multiskill resource scheduling (3)

Artemis Views Autoplan Micro Planner X a Microsoft Project MPS-Team Managment Perception Primavera Project Scheduler 7 Project Workbench SAS/ORa

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Yes Yes No No No Yes No No No Yes

a

Examined from trial version.

details of their implementations were not provided, general information on their multiskill scheduling capabilities were obtained. Manual Procedure: Case Study The heuristic procedure for single-skill resource scheduling is demonstrated on a case study project, obtained from Talbot and Patterson (1979), with 20 activities and six resources with daily availability limits (Table 2). The CPM network of the case study is shown in Fig. 1, indicating a project duration of 32 days, without considering the resource limits (constraints). Applying the single-skill heuristic procedure to consider resource constraints resulted in the manual solution given in Table 3, with a 49-day project duration. In Table 3, columns 1– 10 represent the activities’ data, and columns 11 and 12 are the scheduling decisions made at each cycle. According to the project network of Fig. 1, activities A, B, and D are at the start of the project, and thus they become eligible for scheduling at current time = 0 (beginning of the project), as shown in the first cycle of Table 3. The eligible activities were sorted TABLE 2.

Daily Resource Requirements Duration Activity (days) Predecessors R1 R2 R3 R4 R5 R6 (1) (2) (3) (4) (5) (6) (7) (8) (9) A B C D E F G H I J K L M N O P Q R S T

6 3 4 6 7 5 2 2 2 6 1 2 4 2 3 5 8 2 6 2

— — A — A, B C D A, B G, H F C, E E, G, H I, K F, L L J, M, N O D, O P, R Q

Daily resource limits

FIG. 1.

Case Study Data

5 3 2 5 3 4 4 5 3 1 3 3 2 1 5 3 4 5 2 1

2 5 4 4 5 1 1 5 2 5 3 2 2 4 5 2 5 3 4 6

2 2 4 3 2 4 4 4 4 4 2 2 2 4 4 3 4 3 6 2

2 3 2 5 3 9 3 0 3 6 4 8 2 3 6 4 2 3 2 7

7 9 3 5 8 2 9 9 4 7 5 3 4 4 2 7 3 7 3 5

4 6 1 4 0 5 8 1 2 3 1 4 8 1 3 8 4 8 4 2

7

10

10

16

18

13

Case Study Network

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TABLE 3.

Manual Solution for Case Study Using Single-Skilled Resources Resources

Eligible activities (2)

R1 = 7 (3)

R2 = 10 (4)

R3 = 10 (5)

R4 = 16 (6)

R5 = 18 (7)

R6 = 13 (8)

Late start (9)

Duration (10)

0

A B D

5 3 5

2 5 4

2 2 3

2 3 5

7 9 5

4 6 4

0 6 7

6 3 6

Start Delay Delay

6 — —

6

B C D

3 2 5

5 4 4

2 4 3

3 2 5

9 3 5

6 1 4

6 6 7

3 4 6

Start Start Delay

9 10 —

9

C D E H

2 5 3 5

4 4 5 5

4 3 2 4

2 5 3 0

3 5 8 9

1 4 0 1

6 7 9 13

4 6 7 2

Continue Start Delay Delay

10 15 — —

10

D E F H

5 3 4 5

4 5 1 5

3 2 4 4

5 3 9 0

5 8 2 9

4 0 5 1

7 9 10 13

6 7 5 2

Continue Delay Delay Delay

15 — — —

15

E F G H

3 4 4 5

5 1 1 5

2 4 4 4

3 9 3 0

8 2 9 9

0 5 8 1

9 10 13 13

7 5 2 2

Start Start Delay Delay

22 20 — —

20

E G H J

3 4 5 1

5 1 5 5

2 4 4 4

3 3 0 6

8 9 9 7

0 8 1 3

9 13 13 15

7 2 2 6

Continue Start Delay Delay

22 22 — —

22

H J K

5 1 3

5 5 3

4 4 2

0 6 4

9 7 5

1 3 1

13 15 16

2 6 1

Start Start Delay

24 28 —

24

J I K L

1 3 3 3

5 2 3 2

4 4 2 2

6 3 4 8

7 4 5 3

3 2 1 4

15 15 16 17

6 2 1 2

Continue Start Start Delay

28 26 25 —

25

I J L

3 1 3

2 5 2

4 4 2

3 6 8

4 7 3

2 3 4

15 15 17

2 6 2

Continue Continue Delay

26 28 —

26

J L M

1 3 2

5 2 2

4 2 2

6 8 2

7 3 4

3 4 8

15 17 17

6 2 4

Continue Start Delay

28 28 —

28

M N O

2 1 5

2 4 5

2 4 4

2 3 6

4 4 2

8 1 3

17 19 19

4 2 3

Start Start Delay

32 30 —

30

M O

2 5

2 5

2 4

2 6

4 2

8 3

17 19

4 3

Continue Start

32 33

32

O P

5 3

5 2

4 3

6 4

2 7

3 8

19 21

3 5

Continue Delay

33 —

33

P Q R

3 4 5

2 5 3

3 4 3

4 2 3

7 3 2

8 4 8

21 22 24

5 8 2

Start Start Delay

38 41 —

38

Q R

4 5

5 3

4 3

2 3

3 2

4 8

22 24

8 2

Continue Delay

41 —

41

R T

5 1

3 6

3 2

3 7

7 5

8 2

24 30

2 2

Start Start

43 43

43

S

2

4

6

2

3

4

26

6

Start

49

Time (1)

by their late-start values (the criteria used for assigning resources, as shown in column 9). Considering these three activities in their priority order, available resources were enough to start activity A, but the remaining amounts of resources were not enough for either activity B or D. As such, activity A was scheduled to start at time 0 and to end at time 6 (duration = 6 days), whereas activities B and D were delayed until the earliest time at which more resources became available (day 6). At day 6, activity A was finished, and, as such, all of its immediate successors become eligible for scheduling (unless they have other unfinished predecessors), in addition to activities B and D, which were delayed in the previous cycle.

Decision Finish time (11) (12)

After sorting and considering these activities one-by-one, activities B and C could start, whereas activity D was delayed. The process, therefore, was continued at day 9, which is the finish time of activity B (activity C was scheduled to finish at day 10). The third cycle at day 9, as such, included four eligible activities: activity C (continuing until day 10), activity D (delayed from the previous cycle), and two more activities (activities E and H, which immediately follow activity B). Decisions for these activities were made as shown in Table 3, and the process was continued through all of the cycles until all activities were scheduled (project duration = 49 days, a 17day extension beyond the original CPM duration of 32 days).

416 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / NOVEMBER/DECEMBER 2000

FIG. 2.

Multiskill Checking Procedure

Notice that at any cycle, the total amount of resources used by the starting and continuing activities is less than or equal to the resource availability limit. MULTISKILL RESOURCE-CONSTRAINED SCHEDULING Two steps were carried out to modify the described singleskill resource scheduling process to be used for multiskill resource scheduling: (1) Storing the information about the multiskills of resources; and (2) modifying the single-skill procedure to utilize the stored multiskill information. These two steps are discussed in the following subsections. Resource Substitution Rules The ability of a resource (e.g., a steel fixer) to substitute another (e.g., a carpenter) provides a good representation of the multiskill ability of this resource. Certainly, the steel fixer in this case may not be proficient in carpentry, and, as such, his productivity is expected to be less than that of an original carpenter. In some cases, it may take two, three, or any other number of steel fixers to substitute for the productivity of one carpenter. Therefore, a simple representation of the multiskill of resources can be in the form of a substitution rule, as follows: 2 R4 = 1 R2, which means that 2 of resource R4 can be used to substitute a shortage of 1 R2 resource. These 2 R4 resources, as such, can provide the same productivity as a single R2 resource. One important assumption made here is that a rule applies to all members of its resources (e.g., if two steel fixers equal one carpenter, then any two steel fixers can substitute for one carpenter). This assumption becomes reasonable when a training mechanism is implemented for resources to be used in multiskill work assignments. Modified Resource Scheduling Algorithm Having the multiskill information defined in the form of resource substitution rules, it can be used to modify the heu-

ristic procedure by introducing the multiskill checking procedure of Fig. 2. This procedure, instead of delaying an activity due to a shortage in resources, checks to see if enough substitute resources exist to start the activity. The multiskill checking procedure starts, first, by checking if there is one or more rule(s) that can solve the resource conflict. For example, assume a shortage of 2 R1 resources and two substitution rules available (2 R2 = 1 R1; 3 R3 = 1 R1). Then either 4 units of resource R1 or 6 units of resource R3 can substitute for the shortage in the 2 R1 resources. Also, in case the free amount of either resource (R2 or R3) is not enough to substitute for the whole shortage, a combination of resources R2 and R3 together, according to their availability, can be used to substitute for the shortage in R1. When a substitution takes place, the resource pool is adjusted accordingly and the resource scheduling procedure is continued without delaying the activity in question, thus saving project time. If, during the multiskill checking procedure, a resource conflict could not be solved, then the activity will be delayed. Example Application 1 The proposed procedure for multiskill resource scheduling has been applied on the case study with one substitution rule assumed by the writers (2 R5 = 1 R1). The application of the proposed procedure is partly shown in Table 4, resulting in a 39-day project duration, using only one substitution rule. The last column in Table 4 specifies the time when the substitution rule was used. At the beginning of the project (current time = 0), the only eligible activities were A, B, and D, which were sorted by their late-start values (column 9). Considering these three activities in order, activity A could start, and, accordingly, not enough resources will be available for either activity B or D. As such, activity A was started at time 0 and could end at time 6 (duration = 6 days). Before delaying activities B and D, the multiskill checking procedure of Fig. 2 was applied using the substitution rule (2 R5 = 1 R1). Accordingly, activity B could start at time 0 because the shortage of 1 R1

JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / NOVEMBER/DECEMBER 2000 / 417

TABLE 4.

Multiskill Scheduling of Example Application 1

Resources

Eligible activity (2)

R1 = 7 (3)

A B D

5 3⫺1 5

2 5 4

2 2 3

2 3 5

7 9⫹2 5

4 6 4

0 6 7

6 3 6

Start Start Delay

3

A D

5 5⫺3

2 4

2 3

2 5

7 5⫹6

4 4

0 7

6 6

6

D C E H

5 2 3 5

4 4 5 5

3 4 2 4

5 2 3 0

5 3 8 9

4 1 0 1

7 6 9 13

⭈ ⭈

⭈ ⭈

⭈ ⭈

⭈ ⭈

⭈ ⭈

⭈ ⭈

⭈ ⭈

⭈ ⭈

36

S T

2 1

4 6

6 2

2 7

3 5

4 2

Time (1) 0

R2 = 10 R3 = 10 R4 = 16 R5 = 18 R6 = 13 Late start (4) (5) (6) (7) (8) (9)

resource (a total of 8 were required for activities A and B, whereas only 7 were available) could be substituted for by 2 free R5 resources. Notice here that the substitution information of activity B is shown in columns 3 and 7 of Table 4. In column 3, the shortage in 1 R1 resource was subtracted, wheres 2 R5 resources were added to column 7. This approach made it possible to maintain a total amount of used resources at any cycle that is less than or equal to the resource availability limit. After scheduling activity B, the multiskill checking procedure was used for activity D, but failed to resolve the conflict in resources R1, R2, R5, and R6, thus delaying activity D until the earliest time that more resources became available (day 3). At day 3, activity B was finished, and the eligible activities were A (continued from the previous cycle) and D (delayed from the previous cycle). After sorting and considering these activities one-by-one, activity D could start only after the given substitution rule was applied. Accordingly, the shortage of 3 R1 resources could be covered by 6 R5 resources. The process was then continued through all of the cycles until all activities were scheduled (project duration = 39 days). As shown, using just one rule of substitution resulted in a 10-day saving in project duration (from 49 to 39 days). The manual process described above undoubtedly indicates the benefit of utilizing the multiskills of resources to minimize project duration. It also shows that the calculations add little computational burden on the scheduling process. Once the multiskill scheduling procedure is finished, the calculation table can be used to read the multiskill strategy that specifies when, how long, and what resource substitutions should take place. Table 4, for example, shows the strategy used in example 1 as follows: • Two of the free R5 resources are to join R1 resources in the period from time 0 to time 3, to help in activity B. • Six of the free R5 resources are to join R1 resources in the period from time 3 to time 6, to help in activity D. • Two of the free R5 resources are to join R1 resources in the period from time 26 to time 28, to help in activity P. • Four of the free R5 resources are to join R1 resources in the period from time 31 to time 33, to help in activity R. Example Application 2 The proposed approach is capable of dealing with more complex resource substitution rules. To demonstrate this capability, five substitution rules were assumed and applied to the case study at hand. The five substitution rules are as follow:

• • • • •

2 2 2 2 2

R5 R4 R5 R4 R6

Duration (10)

Decision Finish time (11) (12)

Substitution rule (13)

6 3 —

2 R5 = 1 R1

Continue Start

6 9

2 R5 = 1 R1

6 4 7 2

Continue Start Delay Delay

9 10 — —

⭈ ⭈

⭈ ⭈

⭈ ⭈

⭈ ⭈

26 30

6 2

Continue Start

39 38

= = = = =

1 1 1 1 1

⭈ ⭈

R1 R2 R4 R5 R5

The manual solution of this example application is shown in Table 5. The first two cycles are similar to those in Table 4. Afterward, the process was continued at the third cycle (day 6) which included four eligible activities: activity D (continuing until day 9); and three more activities: C, E, and H. Activity C could start since enough resources were available. As such, activities C and D consumed a total of 7, 8, 7, 7, 8, and 5 of resources R1–R6, respectively. Now, considering activity E, its resources are checked one-by-one. Activity E requires 3 of R1 resource, but none was available because all 7 R1 resources were used in activities D and C. The multiskill checking procedure was then used and a substitution rule (2 R5 = 1 R1) was applied to utilize 6 free R5 resources to replace the missing 3 R1 resources. Accordingly, the substitution amount of 3 was subtracted from column 3, and at the same time, an amount of 6 was added to R5 (column 7). Using this substitution, the total amount of the R5 requirement becomes 22 (5 for activity D; 3 for activity C; 8 originally required for activity E; and 6 for the substitution), thus leaving a shortage of 4 in resource R5 (limit is 18). To substitute for the missing R5 resources, a search through available rules reveals that rule 2 R6 = 1 R5 could be used and will require the use of 8 free R6 resources. Adding these 8 to the resource requirements of R6 makes a total of 13, which is the resource availability limit of R6, thus making the substitution possible. Once the assignment conflict of R1 is resolved through the two nested rules, the process was continued with R2, which also exhibited a shortage of 3 that was substituted by the rule 2 R4 = 1 R2. Activity E could then start. Moving to activity H, the substitution rules did not solve the conflicts in R1, R2, R3, R5, and R6, and thus it was delayed until the earliest time at which more resources became available (day 9). It is noted that at the beginning of a new cycle (e.g., at time 9), all the resource substitutions that took place at the previous cycle are released so that the activities can be scheduled using the original resources. The fourth cycle at day 9 included four eligible activities: C and E (continued from previous cycle until days 10 and 13, respectively); H (delayed from previous cycle); and one more new activity (G). The resources used by activities C and E were 5, 9, 6, 5, 11, and 1 for R1–R6, respectively. Activity G could start because the available substitution rules could solve the conflicts in R1 (4 of R5 substituted for 2 of R1) and R5 (8 of R4 plus 4 of R6 substituted

418 / JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / NOVEMBER/DECEMBER 2000

TABLE 5.

Time (1) 0

Eligible activity (2)

Multiskill Scheduling of Example Application 2

Resources R1 = 7 R2 = 10 R3 = 10 R4 = 16 (3) (4) (5) (6)

R5 = 18 (7)

R6 = 13 Late start (8) (9)

Duration (10)

Decision Finish time (11) (12)

A B D

5 3⫺1 5

2 5 4

2 2 3

2 3 5

7 9⫹2 5

4 6 4

0 6 7

6 3 6

Start Start Delay

3

A D

5 5⫺3

2 4

2 3

2 5

7 5⫹6

4 4

0 7

6 6

6

D C E H

5 2 3⫺3 5

4 4 5⫺3 5

3 4 2 4

5 2 3⫹6 0

5 3 8⫹6⫺4 9

4 1 0⫹8 1

7 6 9 13

9

C E G H

2 3 4⫺2 5

4 5 1 5

4 2 4 4

2 3 3⫹8 0

3 8 9⫹4⫺6 9

1 0 8⫹4 1

10

E G F H

3 4 4 5

5 1 1 5

2 4 4 4

3 3 9 0

8 9 2 9

11

E F H

3 4 5

5 1 5

2 4 4

3 9 0

13

F H K

4 5⫺2 3

1 5 3

4 4 2

F I K L

4 3 3⫺3 3

1 2 3 2

I J L

3 1 3

17

J L M

18

Substitution rules (13)

6 3 —

2 R5 = 1 R1

Continue Start

6 9

2 R5 = 1 R1

6 4 7 2

Continue Start Start Delay

9 10 13 —

2 R5 = 1 R1 2 R6 = 1 R5 2 R4 = 1 R2

6 9 13 13

4 7 2 2

Continue Continue Start Delay

10 13 11 —

2 R5 = 1 R1 2 R4 = 1 R5 2 R6 = 1 R5

0 8 5 1

9 13 10 13

7 2 5 2

Continue Continue Delay Delay

13 11 — —

8 2 9

0 5 1

9 10 13

7 5 2

Continue Start Delay

13 16 —

9 0 4

2 9⫹4 5

5 1 1

10 13 16

5 2 1

Continue Start Delay

16 15 —

2 R5 = 1 R1

4 4 2 2

9 3 4 8

2 4 5⫹6 3

5 2 1 4

10 15 16 17

5 2 1 2

Continue Start Start Delay

16 17 16 —

2 R5 = 1 R1

2 5 2

4 4 2

3 6 8⫺1

4 7 3⫹2

2 3 4

15 15 17

2 6 2

Continue Start Start

17 22 18

2 R5 = 1 R4

1 3 2

5 2 2

4 2 2

6 8 2

7 3 4

3 4 8

15 17 17

6 2 4

Continue Continue Delay

22 18 —

J M N O

1 2 1 5

5 2 4⫺1 5

4 2 4 4

6 2 3⫹2 6

7 4 4 2

3 8 1 3

15 17 19 19

6 4 2 3

Continue Start Start Delay

22 22 20 —

20

J M O

1 2 5

5 2 5

4 2 4

6 2 6

7 4 2

3 8 3

15 17 19

6 4 3

Continue Continue Delay

22 22 —

22

O P

5 3⫺1

5 2

4 3

6 4

2 7⫹2

3 8

19 21

3 5

Start Start

25 27

25

P Q R

3 4 5

2 5 3

3 4 3

4 2 3

7 3 2

8 4 8

21 22 24

5 8 2

Continue Start Delay

27 33 —

27

Q R

4 5⫺2

5 3

4 3

2 3

3 2⫹4

4 8

22 24

8 2

Continue Start

33 29

29

Q S

4 2

5 4

4 6

2 2

3 3

4 4

22 26

8 6

Continue Start

33 35

33

S T

2 1

4 6

6 2

2 7

3 5

4 2

26 30

6 2

Continue Start

35 35

15

16

for 6 of R5). It is worthwhile to note that the shortage of 6 R5 resources was covered by two resources (8 from R4 and 4 from R6) because no single resource was enough to cover the whole shortage amount. As such, this feature of combining underallocated resources ensures maximum utilization of available resources and distinguishes the proposed procedure from existing heuristic methods. To continue the present cycle at time 9, activity H was delayed because the available substitution rules still could not solve the conflicts in R1, R2, R3, R5, and R6. The process was continued through all of the cycles (Table 5) until all activities were scheduled (project

2 R4 = 1 R2

2 R5 = 1 R1

2 R5 = 1 R1

duration = 35 days; only 3 days extension beyond the original CPM duration of 32 days). MULTISKILL SCHEDULING AUTOMATION Implementing the proposed multiskill scheduling procedure on commercial scheduling software simplifies the implementation process and provides project managers with an automated tool to improve the results of their familiar software. In this study, Microsoft Project software (Microsoft Project 98) is selected for the implementation of the proposed multiskill

JOURNAL OF CONSTRUCTION ENGINEERING AND MANAGEMENT / NOVEMBER/DECEMBER 2000 / 419

FIG. 3.

Gantt-Chart of Example 2

Project software (Fig. 3). To demonstrate the capabilities of MURSA, the case study at hand was input to Microsoft Project software to perform CPM analysis. When MURSA was activated, the form shown in Fig. 4 appeared to allow the user to enter the substitution rules among all resources. Afterward, MURSA starts the scheduling process and calculates the scheduled start and finish dates of each activity and modifies the original CPM analysis. For the case study at hand, the modified schedule is shown in Fig. 3. Once the multiskill scheduling procedure was complete, the user can view the resource substitution strategy that applies to each activity, as shown in Fig. 5, or view the resource profile of any resource on an Excel worksheet to confirm that all resource overallocations were resolved by MURSA. FIG. 4.

Defining Multiskilled Resources

RESULTS AND COMPARISON

FIG. 5.

Resources Substitution Report (Example 2)

scheduling procedure because of its ease of use and programmability features. Using the macrolanguage of Microsoft Project, the procedure was coded and then used to schedule the case study under different rules of substitution. The results and a comparison with the solutions provided by one commercial scheduling software that use multiskilled resources (SAS/OR), are shown in the next section. The developed program is named MUltiskill Resource Scheduling Algorithm (MURSA) and involved large programming effort in coding the multiskill scheduling procedure and developing a user-friendly interface. To facilitate the use of MURSA, a simple toolbar interface was used on Microsoft

A comparison was made between the results (project duration) obtained by using MURSA on the case study and the results obtained from a software program (SAS/OR), incorporating multiskill scheduling capabilities. The SAS/OR system was selected because of its being a high-end system with sophisticated resource management capabilities. Without considering the given resource constraints, the total project duration, determined by simple CPM analysis, is 32 days for MURSA and SAS/OR. Considering the given resource constraints and single-skilled resources, a project duration of 49 days was obtained from both programs, using the ELS heuristic rule. Multiskilled resources with one substitution rule (2 R5 = 1 R1) were then used and a project duration of 39 days was achieved by MURSA, as described earlier, and a duration of 47 days was obtained from SAS/OR. Multiskilled resource scheduling with five substitution rules, on the other hand, reTABLE 6.

Comparison of Results Project Duration (days)

Scheduling (1)

SAS/OR (2)

MURSA (3)

With no resource constraints, using CPM With single-skilled resource constraints With multiskilled resource constraints (one rule) With multiskilled resource constraints (five rules)

32 49 47 47

32 49 39 35

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sulted in a project duration of 35 days with MURSA, whereas SAS/OR did not improve its 47-day duration. Table 6 summarizes these results, which obviously reveal the powerful capabilities of MURSA as it reduced the delay in project duration by up to 80% when using the five rules of substitution, as opposed to only 12% by SAS/OR. Based on an investigation of the reasons behind the less efficient results of SAS/OR, it was revealed that the multiskill procedure of SAS/OR has two shortcomings: (1) It applies resource substitutions to the whole activity duration, not the shortage period only as MURSA does; and (2) it uses one resource to substitute for the shortage, not a combination of resources as MURSA does. Based on these findings, a telephone contact was made with the technical support of the other software systems to reveal that they all exhibit either one or both shortcomings.

Although multiskilled resource utilization strategy has many potential benefits, North American labor unions have mixed opinions about it. In Canada, the Christian Labor Association of Canada, for example, favors multiskilled workers and allows an employee to do more than one kind of work if he/she is qualified. In the United States, on the other hand, the American Federation of Labor-Congress of Industrial Organizations and Building Trades Council unions oppose the use of multiskilled labor strategy as it may lead to jurisdictional disputes. In various other countries around the world, the use of multiskilled labor strategies, including training, is under the full authority of project managers who can use it to improve site productivity and reduce cost (Cheema 1998). In North America, therefore, some cooperation with union organizations is still needed to regulate and arrive at acceptable multiskilled labor agreements before this strategy can be fully utilized.

COMMENTS AND DISCUSSION ON UNION IMPACT

SUMMARY AND CONCLUSIONS

The model presented in this paper has been demonstrated to work effectively on the example application. Various experiments were also conducted on various other problems with different skill substitutions and MURSA performed well. For interested readers, MURSA can be downloaded from the first writer’s Web page at 具www.civil.uwaterloo.ca/tarek典 under the title ‘‘Free Educational Software.’’ The main characteristics of MURSA that makes it an efficient system for multiskill constrained resource scheduling include the following: • It permits the user to specify any number of substitution rules among resources. • It uses the most common heuristic rule for resource-constrained scheduling (ELS). • It allows underallocated resources to combine so that enough substitute resource can relieve the overallocation in other resources, thus minimizing project delay. • It releases the resources used in the substitution as soon as the shortage is ended. • It has been implemented on a commercial scheduling software that is customary to many practitioners in construction. • It provides the user with a detailed report of how many units of each resource are used to substitute for another and the substitution period. Various additional experiments can be conducted on the proposed algorithm, including the following: • Considering the use of priority factors if more than one resource can substitute for the shortage in another resource (i.e., two rules can be applied). • Considering resource cost into account to minimize the cost of the substitution. • Investigating the use of the proposed approach in multiproject scheduling. • Investigating the use of a heuristic rule such as ‘‘longest activity duration,’’ rather than the ELS rule used in this paper. In this manner, resources will be given to longer activities first, and substitutions will likely be applied to shorter ones, thus reducing work disruptions.

This research provided an effective enhancement to common heuristic approaches for resource-constrained scheduling, utilizing the multiskills of available resources. A structured manual approach was presented. The major benefit of the proposed approach is its ability to utilize the underallocation of one resource to resolve an overallocation of another, thus saving project time and cost. A computer program was developed to automate the proposed approach and to provide a good interface and reporting capabilities. To prove its effectiveness, a comparison between results of the developed program and a commercial software was presented. The developed program showed a much better performance and achieved a significant reduction in project duration of the case study used. The resource management benefits of the proposed approach are perceived to encourage project managers to put multiskill strategies into their project planning processes. APPENDIX.

REFERENCES

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