Stochastic Mixed-Integer Programming for a Spare Parts Inventory Management Problem

The German Armed Forces provide an operation contingent to support the  North Atlantic Treaty Organization (NATO) Response Force (NRF). For short deployments (e.g., one month), the NRF troops can bring with them a tightly constrained "warehouse" of spare parts. To ensure optimal use this warehouse, we developed the computer program "The OPtimization of a Spare Parts INventory" (TOPSPIN) to find an optimal mix of spare parts to repair a set of systems. Each system is composed of several parts, and it can only be used again in the mission if all broken parts are replaced. Due to the stochastic nature of the problem, we generate scenarios that simulate the failure of the parts. The backbone of TOPSPIN is a mixed-integer linear program that determines an optimal, scenario-robust mix of spare parts. Using input data provided by the German Logistikzentrum (RealData.xlsx), we analyze how many scenarios need to be generated in order to determine reliable solutions. A further data set (SimData.xlsx) was generated with random data, having a similar structure as the real data set. Using these two data sets, we analyze the composition of the warehouse over a variety of different weight restrictions, and we examine the number of repairable systems for different values of this bound.