Abstract
•A general, closed-loop supply chain inventory model is developed.•The decision variables vary from cycle to cycle until the system plateaus.•The solution to the inventory system, if it exists, is unique and global optimal.•All functions and input parameters may change their values for subsequent cycles.•The initial on hand inventory of returned items is tangible, tractable and modelled.
The classical formulation of reverse logistics inventory systems assumes an equal returned amount in all cycles. This assumption necessitates that manufacturing and remanufacturing processes are static in all cycles, i.e. it ignores the impact of the first cycle. This implies that the result of such modelling may not be an optimal policy. Another implicit assumption embedded in the classical formulation is that input parameters remain static indefinitely. In practice, however, it is often desirable that input parameters are adjusted to be responsive to a new policy due to acquired new knowledge. This paper develops a general joint model for production of new items together with remanufacturing of returned items “as good as new” condition. The proposed model focuses on a single production cycle and a single remanufacturing cycle and, as part of its formulation, considers the first time interval. This implies that the decision variables should vary from cycle to cycle until the system plateaus. Adopting this approach ensures a more realistic tractability of the impact of previous cycles, including the first time cycle. The mathematical formulation considers arbitrary functions of time, which allows the decision maker to assess and compare the consequences of a diverse range of time-varying forms by employing a single inventory model. All functions and input parameters may change their values for subsequent cycles and/or periodic review or remain static. A rigorous method is utilised to show that the solution, if it exists, is unique and global optimal. The paper provides illustrative examples that demonstrate the application of the theoretical model in different settings.