Exact and flexible solution approach to a critical chain project management problem

Abstract

An important component in critical chain project management is a scheduling methodology to support resource constraints. Given task duration estimates and precedence relations along with resource designation for each task, one seeks to adhere to a target due date as well as to shorten the estimated makespan. Key are two types of time buffers to absorb potential delays accumulated from preceding tasks, and this makes the problem complex and hard to solve. The “good enough” strategy has been prevalent in research, focusing on the development of heuristic solution methods. There has been only one attempt to minimize estimated makespan, wherein discrete algebra is utilized. The method is, however, inflexible as you must compose a search space. Even the slightest extension requires a major recast of the approach. Hence, we develop a new approach to find an exact optimal solution in an efficient manner. Given a project instance, an optimization problem is constructed as a mixed-integer linear-program, for which an exact solution can be found using an off-the-shelf solver. While the problem is NP hard, larger-scale project instances, including up to 30 tasks, can be solved within a practical time standard. Extension with respect to resource assignment is easily accomplished. Experimental results highlight the significance of the developed framework.