Optimizing Field Repair Kits Based on Job Completion Rate

A formulation is presented for obtaining the optimal kit of parts and tools for on-site equipment repairs, based on the fraction of jobs which can be completed from the contents of the kit. This formulation generalizes previous approaches in that part demands need not be independent and various numbers of parts as well as multiple part types per job may be required. It is shown that the formulation is a special case of Balinski's "selection problem" and thus can be solved by maximal flow/minimal cut network algorithms.