Optimal control of a production-inventory system with product returns and two disposal options

We consider a production-inventory system facing stochastic product returns that can either be disposed upon arrival or placed in a serviceable inventory, where serviceable products can be disposed at any time. In an M/M/1 make-tostock queue setting, we establish that the optimal control policy is a threshold policy with three policy parameters and we derive closed-form results for the optimal thresholds and costs. For several situations, we establish that either the disposal upon arrival (DUA) option or the disposal of serviceable products (SD) option is sufficient to achieve optimality. We also present numerical examples for which it is useful to have both disposal options. Moreover, we explore four extensions for which the two options are complementary (limited secondary market, manufacturing start-up cost, Markov modulated demand and positive remanufacturing lead time).