An EOQ model of deteriorating item in imprecise environment with dynamic deterioration and credit linked demand

Abstract In this paper, an inventory model for a deteriorating item with time dependent deterioration has been developed in imprecise environment. For an order more than a fixed label, the supplier offers a credit period for payments per order to his/her retailers, but an interest is charged by the supplier if the payment period exceeds the credit period. The supplier also offers a partial permissible delay in payments even if the order quantity is less than the said fixed label, i.e., the credit period is offered on a fraction of the amount purchased. Due to these facilities, the retailer also offers a fixed partial credit period to his/her customers to boost the demand. Obviously, demand depends on the duration on which the credit period is offered. Depending upon the different types of imprecise inventory costs (fuzzy, rough or fuzzy-rough), different models are developed. Models are formulated as a profit maximization problem with respect to the retailer and depending upon different imprecise parameters, different models are solved. As the optimization of imprecise objectives are not well defined, their expected values are optimized to find an optimal decision for the decision maker (DM). Non-linear optimization problems for different models are solved using a gradient based optimization technique – Generalized Reduced Gradient (GRG) method (using LINGO software). Numerical experiments are performed to illustrate the models and some parametric studies are made.

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