A fuzzy framework for coordinating pricing and inventory policies for deteriorating items under retailer partial trade credit financing

• A fuzzy EOQ model under a two-level trade credit policy has been proposed.
• Selling price dependent demand rate which is imprecise in nature is considered.
• Imprecise cost and interest parameters are considered.
• Theoretical results have been framed to characterize the optimal solutions.
• An algorithm is designed to identify the optimal solutions.

In this paper, we proposed a generalized economic order quantity (EOQ) – based inventory model using a trade credit policy in a fuzzy sense. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer, in turn, partially provides customers a permissible delay period N. This study considers fuzzy EOQ model to allow for: (1) selling price dependent demand rate which is imprecise in nature, (2) a profit maximization objective and (3) an imprecise holding cost, ordering cost, purchasing cost, interest earned and interest charged rate. Besides, the cases N ⩽ M and N ⩾ M are explored thoroughly. The objective function for the retailer in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method. For the defuzzified objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined.