Optimal lot sizing for a production-recovery system with time-varying demand over a finite planning horizon

In this paper, a recovery inventory system in which a product is remanufactured by the original equipment manufacturer is considered. The remanufacturing process brings used products up to quality standards that are as rigorous as those of new products. The planning horizon is finite and the demand rate is time varying. For satisfying the demand, there are two options: either new items are produced or the used items are repaired back to an 'as new' condition, before being sold again. The returned products are a fraction of the demand and they are stored in the recoverable stocking point (recoverable inventory). At the beginning of the planning horizon, the demand is satisfied by new manufacturing lots of unequal size. When the production stops, the demand is satisfied by remanufacturing lots of unequal size (used products are recovered at a fixed rate) and the intervals between multiple production and repair runs are of unequal length and variable. The aim of this study is the determination of these time intervals, which leads to the formulation of a special optimization problem. The solution of this problem enables the determination of the newly produced and remanufactured quantities that minimize the total cost over the planning horizon. Also a simple procedure is proposed which relies on the decoupling of the problem into two sub-problems and determines the optimal time point of switching from a manufacturing activity to a remanufacturing one.