The multiple-job repair kit problem

The repair kit problem is that of finding the optimal set of parts in the kit of a repairman. An important aspect of this problem, in many real-life situations, is that several job-sites are visited before a kit is restocked. In this paper, we present two heuristics for solving the multiple-job repair kit problem. Both heuristics can be used to determine a solution under the service-objective (minimal holding cost for a required job-fill rate) as well as the cost-objective (minimal expected total cost, including a penalty cost for each `broken' job). The `Job Heuristic (JH)' almost always determines the exact optimal solution, as is shown in an extensive numerical experiment. However, it can not (easily) be used in cases where several parts of the same type may be needed on a job, or part failures are dependent, or the number of jobs in a tour varies. The `Part Heuristic (PH)' is simpler and easy to use in these cases also. In fact, it can be applied in a spreadsheet software package, as we illustrate. The numerical experiments show that it s leads to near-optimal solutions (average `cost error' of less than 0.1 per cent). Therefore, the PH is an excellent method for solving repair kit problems in practise.