Application of perturbation analysis to multiproduct capacitated production-inventory control

We consider a multiproduct periodic review system with a capacity constraint and no setup cost. The optimal stationary control policy for such a system is characterized by a complex switching curve, which is usually computationally intractable. We tackle the infinite horizon case by proposing a linear approximation to the optimal switching curve. In order to determine the settings of the parameters in the linear approximation, we apply perturbation analysis in a stochastic approximation algorithm. We consider a randomly chosen test example and provide numerical results for the approximation algorithm and compare them to computational results using dynamic programming. Our algorithm is computationally very efficient-orders of magnitude faster than the truncated dynamic programming solution, and provides a satisfactory solution to the test problem.