Cross-training policies for repair shops with spare part inventories

We study a spare part supply system for repairable spare parts where parallel repair servers may have multiple skills (can repair different failed parts). Demands for the spares occur according to Poisson processes with different rates. The failed spare parts are immediately replaced from the inventory. Otherwise, failed parts are backordered and fulfilled when a spare of the same type becomes available (repaired). The repair servers are heterogeneous and can process certain types of repairables only if they have the necessary skill. In this system, in contrast with the other skill-optimization models, there is a trade-off between adding extra skills to servers (training) or adding extra inventory. In this paper, we formulate a mathematical model to optimize the assignment of skills to servers taking into account inventories for the ready-to-use spares and backorder costs (penalties). To optimize the skill assignments and inventories, we use a hybrid approach combining a Genetic Algorithm (GA) with simulation modeling. The proposed simulation-based optimization heuristic is used for extensive analysis of optimal skill assignments where we show that partial flexibility for repair servers with limited cross-training will lead to lower total system cost.