### Title: Optimal replenishment decisions in the EPQ model for deteriorating items with fuzzy cost components under retailer partial trade credit financing

Authors: Gour Chandra Mahata

Addresses: Department of Mathematics, Sitananda College, Nandigram, Purba Medinipur 721631, West Bengal, India

Abstract: In this paper, a realistic inventory model with imprecise inventory cost components have been formulated for deteriorating items under trade credit policy within the economic production quantity framework. It assumes that the retailer maintains a powerful position and can obtain full trade credit offered by supplier yet retailer just offers the partial trade credit to his/her customers under the replenishment rate is finite. Under these conditions, we model the retailer|s inventory system as a cost minimisation problem to determine the retailer|s optimal inventory policy. We derive the expressions for the annual total inventory cost for the retailer both in the crisp and fuzzy sense. The annual total variable inventory cost in the fuzzy sense is defuzzified using graded mean integration representation method and it has been proved that there exists a unique optimal cycle time to minimise the annual total variable cost for the retailer. In addition, two theorems and three algorithms are developed to efficiently determine the optimal ordering policies for the retailer. Some previously published results of other authors will be special cases of this paper. Finally, numerical examples are given to illustrate the theorems and obtain a lot of managerial insights from numerical examples.

Keywords: EPQ; economic production quantity; fuzzy inventory models; graded mean integration; fuzzy costs; annual costs; total costs; variable costs; fuzzy coefficients; cost coefficients; partial trade credit; optimal decisions; replenishment decisions; deteriorating items; credit financing; imprecise costs; inventory costs; cost components; retailers; full trade credit; suppliers; customers; replenishment rates; cost minimisation; inventories; optimal cycle times; ordering policies; operational research.

International Journal of Operational Research, 2011 Vol.12 No.4, pp.363 - 389

Published online: 14 Feb 2015 *