A simulated annealing algorithm for integrated decisions on spare part inventories and cross-training policies in repairable inventory systems

This paper presents a solution methodology for an optimization problem on spare parts inventories and workforce planning in repairable inventory systems. We study the design of a single repair shop that seeks to minimize the cost of repairing multiple failed (repairable) components while assuming that failures for each component are uncertain. We formulate the problem as a stochastic nonlinear integer program in which uncertainty in failures of components is hedged both by holding inventory of spares and by designing an efficient repair process. We improve the efficiency of the repair process by optimizing the workforce capacity and achieving workforce heterogeneity by cross-training. Solving the formulated stochastic program presents many computational difficulties, including the fact that there exist several possible cross-training policies to evaluate and solving the underlying queuing models regarding each cross-training policy may not be tractable. To alleviate these difficulties, we propose a two-stage iterative heuristic algorithm. At the first stage, a simulated annealing algorithm (SA) generates a feasible cross-training policy in which each group of workers is trained for only repairing a subset of the failed component types. In the second stage, workforce capacity and spare parts inventory levels are optimized by a queuing approximation technique and a local greedy heuristic for the generated cross-training scheme at the first stage. The conducted computational experiments show that the proposed two-stage approach achieves lower costs when its results are compared with well-known extreme cross-training policies; i.e., dedicated and full cross-training.