The Repair Kit Problem Revisited

The repair kit problem is concerned with finding an optimal kit of parts and tools to carry for on-site repairs. The choice of a kit involves evaluating two attributes—an annual holding cost and a penalty for failing to complete repairs. We present a unifying approach for the repair kit problem which demonstrates that a monotone sequence of optimal kits exists for several parameterizations of the objective function combining the two attributes. We analyze the structure of the Pareto set of the convex hull of the kits in the attribute space and show the relationship between the extreme points of these Pareto sets and the optimal kits. Decomposition and various monotonicity properties of the repair kit problem yield some computational simplifications in generating optimal kits.