Optimizing the troops-to-tasks problem in military operations planning

Abstract

In the planning of military operations, deciding who should do what, where, and when is crucial for the success of the operation. This troops-to-tasks analysis is a project scheduling problem closely related to the well-established resource-constrained project scheduling problem, with many additional characteristics and constraints. The standard resource-constrained project scheduling problem is NP hard. When it comes to the troops-to-tasks analysis, it will vary from case to case whether the problem is solvable mathematically within a practical time frame, and within the memory limits on today’s computers. In this paper we outline the scope of the troops-to-tasks analysis. We present this problem setting, and emphasize its complexity compared to known problems from the literature. We formulate a mathematical model for optimizing the troops-to-tasks analysis in a high intensity land operation on brigade level with supporting resources from the Air Force. This is a small to medium sized operation where the troops-to-tasks problem is solvable mathematically. The model we present in this paper gives us the opportunity to study the characteristics of the problem, and it can serve as a tool in future research, when testing the performance of heuristic solution methods.