Multiproject scheduling: Analysis of scheduling strategies under unequal delay penalities

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 385 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. 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. 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.