An economic order quantity model with reverse logistics program

The economic order quantity (EOQ) model has evolved greatly over past decades on the strength of incorporating realistic factors. In recent times, interest has been geared towards studying the effect of reverse flow of products into inventory system. In practice, businesses may operate return policy (and may reuse products and material) in an effort to increase customer loyalty and recover assets. In this paper, a reverse logistics EOQ model is studied. The inventory problem of when to order and how much quantity to order when there is reverse flow of items into the system is addressed in the form of profit maximisation. To find the optimal solution of the model (a nonlinear maximisation problem), the Karush-Kuhn-Tucker (KKT) conditions for the objective function are presented and the square-root formulae for the firm's order size and price are derived. A simple algorithm is proposed for a search of the optimal solution. To illustrate the applicability of the model, some numerical examples are given. Finally, sensitivity analyses are carried out on several key parameters in order to gain some useful insight.