A continuous time inventory model for a product recovery system with multiple options

Increasing environmental consciousness, limited availability of natural resources to manufacture new products, recovery quotas to avoid disposal, manufacturers assigned to be responsible for used products, and materials value of components included in returned products are incentives for product recovery. The fact that we now have two possible sources to service demand raises new operational questions. For instance, when is remanufacturing of used and returned products preferred to producing the requirements? Most production and inventory management models for reverse logistics are restricted to stationary demands and returns and do not address seasonal effects and product life cycles. Therefore, we consider a deterministic model with dynamic demands and returns. Then there might exist time periods where returns exceed demands and vice versa. The question has to be answered whether excess returns should be stored for future recovery or disposed of. In our work, there are different demand classes, e.g. different product qualities or different markets. This adds yet another aspect to be examined. It has to be determined for which demand class returns should be used. As a result returns can either be stored for later use for a certain demand class or being used instantly for another class. Demands have to be satisfied either from production or remanufacturing of returned products and returns not needed for recovery may be disposed of. In this paper we determine the optimal production, remanufacturing, and disposal policy for a linear cost model by applying Pontryagin's Maximum Principle.