Locating repairshops in a stochastic environment

In this paper we consider a repair shop location problem with uncertainties in demand. New local repair shops have to be opened at a number of locations. At these local repair shops, customers arrive with broken, but repairable, items. Customers go to the nearest open repair shop. Since they want to leave as soon as possible, a (small) inventory of working items is kept at the repair shops. A customer immediately receives a working item from stock, provided that the stock is not empty. If a stockout occurs, the customer has to wait for a working item. The broken items are repaired in the shop and then put in stock. Sometimes, however, a broken item cannot be fixed at the local repair shop, and it has to be sent to a central repair shop. At the central repair shop the same policy with inventory and repair is used. The problem that we focus on, is not only finding locations for the local repair shops, but also minimizing the stock levels at the shops, such that the fraction of customers that can leave the local shops without waiting (the so called fill rate), is above a prespecified level. We assume that the central repair shop is already opened, but that the repair capacity still has to be set. The local repair shops can be opened at a number of locations, which may have different repair capacities. The goal is to minimize the total cost, that is the total cost for keeping the local shops operational, for the transport of items and for the inventory. For this minimizing problem, a local search heuristic with respect to the open locations, repair capacities and inventory levels is presented.