The multiple-job repair kit problem

Abstract

The repair kit problem is that of finding the optimal set of partsin the kit of a repairman. An important aspect of this problem, inmany real-life situations, is that several job-sites are visitedbefore a kit is restocked. In this paper, we present twoheuristics for solving the multiple-job repair kit problem. Bothheuristics can be used to determine a solution under theservice-objective (minimal holding cost for a required job-fillrate) as well as the cost-objective (minimal expected total cost,including a penalty cost for each `broken' job). The `JobHeuristic (JH)' almost always determines the exact optimalsolution, as is shown in an extensive numerical experiment.However, it can not (easily) be used in cases where several partsof the same type may be needed on a job, or part failures aredependent, or the number of jobs in a tour varies. The `PartHeuristic (PH)' is simpler and easy to use in these cases also. Infact, it can be applied in a spreadsheet software package, as weillustrate. The numerical experiments show that it s leads tonear-optimal solutions (average `cost error' of less than 0.1 percent). Therefore, the PH is an excellent method for solving repairkit problems in practise.logistics;inventory;repair kit problem