Multiproject scheduling: Analysis of scheduling strategies under unequal delay penalties
Authors: Kurtulus Ibrahim 
Published: October 2002

The multiproject scheduling problem is investigated under the assumption that delays corresponding to different projects carry different penalties. Five penalty functions are introduced that simulate typical business behavior. These are: 1) assigning the highest penalty to the project requiring the greatest amount of resources; 2) assigning the highest priority to the longest project; 3) assigning the highest priority to the project requiring the least amount of resources; 4) assigning the highest priority to the shortest project; and 5) random assignment. Justification for each case is provided.

Two powerful project summary measures were used to generate the test problems. The first measure, average resource load factor (ARLF), identifies whether the location of the peak requirement of all (i.e., combined) resources is in the first or second half of the project's critical path. If each resource is expressed in terms of dollars, then ARLF identifies the location of the peak cash requirement. Since in practice the choice of the scheduling strategy is influenced by the location of the peak cash requirement, performance of the scheduling strategies is analyzed with respect to values of this measure. The second measure, average utilization factor (AUF), calculates the ratio of resource requirements to availabilities. It is shown that problems tested must have different AUF values in order to be classified different for purposes of experimental design. Thus a factorial model of the form, y = Strategy + Penalty + ARLF + AUF + ϵ was used to generate 385 problems, each requiring 2 to 4 resources, containing 3 to 5 projects and 34 to 63 activities.

The computer program used in the study is based on a parallel method of scheduling in which priorities of the activities are determined when the activity is considered for scheduling. Ten scheduling strategies are tested. Some important ones are: 1) to schedule the shortest activity first; 2) to schedule the activity with minimum slack first; 3) to schedule the activity with maximum work content first (i.e., from the project with highest work content); 4) to schedule the shortest activity from the shortest project first; and 5) to schedule the activity with maximum penalty first. Shortest activity first and minimum slack first are popular strategies introduced by other researchers.

Using number of times ranked first as our criterion, scheduling the activity with maximum penalty first provides the best results followed by the strategy of scheduling the activity with maximum work content. But when these results are analyzed with respect to existence of a very expensive project (i.e., dominance) in the problem, performance of the maximum penalty strategy improves. When the overall results are analyzed with respect to values of ARLF, a different picture emerges. Then the strategy of scheduling the activity with the highest penalty first provides the best results if the peak requirement is early. When the peak requirement is toward the middle of a project's unconstrained critical path, scheduling the activity with the highest work content provides the best results. When the peak requirement is late in a project's life, scheduling the shortest activity from the shortest project is the best strategy to adopt. These findings were tested for statistical significance by using nonparametric testing procedures and were found to be significant.