A genetic algorithm for the pooling-inventory-capacity problem in spare part supply systems

We study a pooling-inventory-capacity problem that arises in the design of repair shops for repairable spare part logistic systems. We formulate the problem as a stochastic nonlinear integer programming model and propose a two-stage sequential solution algorithm. At the first stage, a genetic algorithm (GA) generates a set of feasible pooled repair shop design schemes. A pooled design can be viewed and modeled as the union of mutually exclusive and total exhaustive multi-class multi-server queueing systems. Thus, we exploit this fact and optimize each queueing system separately. In the second stage, optimal inventory and capacity levels for each independent system are calculated by using a queueing approximation technique and a local greedy heuristic. Finally, the performed numerical experiments show that proposed two-stage approach achieves high-quality solutions in reasonable time.