Multiple period repair kit problem with a job completion criterion – a case-study

The repair kit problem is concerned with finding an optimal kit of parts and tools to carry for on-site repairs. This choice involves a trade-off between the annual holding cost and a penalty for failing to complete repairs during the first visit. The repair kit problem with job completion criterion tries to find a solution to this trade-off by achieving a predetermined job completion rate (or service level) with minimum holding costs. This formulation of the problem avoids the often difficult definition and calculation of penalty costs. The repair kit problem has been studied in literature for a single period, when restocking is possible between jobs. In the multiple period repair kit problem studied here, restocking of the spare parts is only possible every 12 periods. Other assumptions used in this case study are that failures of the various parts are stochastically independent and that at most one part of each type is used on a given job. This paper describes a case study where the multiple period repair kit problem with a job completion criterion was solved using a knapsack heuristic. First the model for this problem is developed, then numerical results are shown and conclusions drawn.