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

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.