Samuel Vercraene

Control of a production-inventory system with returns under imperfect advance return information

We consider a production–inventory system with product returns that are announced in advance by the customers. Demands and announcements of returns occur according to independent Poisson processes. An announced return is either actually returned or cancelled after a random return lead time. We consider both lost sale and backorder situations. Using a Markov decision formulation, the optimal production policy, with respect to the discounted cost over an infinite horizon, is characterized for situations with and without advance return information. We give insights in the potential value of this information. Also some attention is paid to combining advance return and advance demand information. Further applications of the model as well as topics for further research are indicated.

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-to-stock 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).

Effects of System Parameters on the Optimal Cost and Policy in a Class of Multidimensional Queueing Control Problems

We consider a class of Markov Decision Processes frequently employed to model queueing and inventory control problems. For these problems, we explore how changes in different system input parameters (transition rates, costs, discount rates etc.) affect the optimal cost and the optimal policy when the state space of the problem is multidimensional. To address a large class of problems, we introduce two generic dynamic programming operators to model different types of controlled events. For these operators, we derive sufficient conditions to propagate monotonicity and supermodularity properties of the value function. These properties allow to predict how changes in system input parameters affect the optimal cost and policy. Finally, we explore the case when several parameters are changed at the same time. The online appendix is available at https://doi.org/10.1287/opre.2017.1600.