The Value of Resource Flexibility in the Resource-Constrained Job Assignment Problem

We consider the problem of minimizing project duration in an environment where each project activity can be executed by a number of different flexible resources. The capabilities of the flexible resources are modeled using a binary activity-resource matrix A called the availability matrix. Activity durations are known deterministically. We develop tight lower bounds and a variety of heuristics accompanied with extensive computational tests regarding their performance. It is shown that our algorithms consistently perform near optimally. Using these heuristics, we perform experiments on the effect of operating flexibility on project duration, where resource flexibility is measured by the number of resources available per activity, and the form of the availability matrix A. Our experiments lead to important managerial guidelines regarding the role of resource flexibility on project duration. For instance, it is found that when the flexible capabilities of the resources are evenly distributed across the activities, small improvements in resource flexibilities provide nearly the same benefits in project duration as a system of fully flexible resources