Simulation-based variable neighborhood search for optimizing skill assignments in multi-server facilities with inventories

This paper addresses the joint optimization problem of skill assignments and inventory in a multi-skill, multi-server repair facility. Failures of different part types occur according to Poisson processes, and each part type requires a certain repair skill. The repair facility supplies ready-to-install spare parts when available in the inventory, according to the (S−1,S) inventory policy. The repair times follow exponential distributions, with rates dependent on the part type. After repair, the parts are returned to the inventory as ready-to-install spare parts. If the inventory is empty when a failed part arrives, the replacement part is backordered, and a penalty cost is incurred. The objective of the problem is to find an assignment of repair skills to servers and inventory levels that minimize the expected total cost of the system. That is, the costs for servers, the costs to upgrade the skills of servers, and the expected holding and backorder costs. We propose to solve this problem by a simulation-based Variable Neighborhood Search (VNS) approach, in which a Discrete Event Simulation is applied to evaluate the expected backorder and holding costs given the skill assignments. The proposed method is capable of significantly improving the results of a recently published Genetic Algorithm, achieving an average cost reduction of 5.1% in the same running time. Moreover, it is able to find comparable solutions in one fifth of the GA running time.