Title: An EOQ model for deteriorating items under credit options

Authors: M. Valliathal; R. Uthayakumar

Addresses: Department of Mathematics, Chikkaiah Naicker College, Erode 638004, Tamil Nadu, India ' Department of Mathematics, Gandhigram University, Gandhigram 624302, Tamil Nadu, India

Abstract: This paper discusses the effects of shortages on an inventory model for deteriorating items with shortages under supplier’s credit linked to maximum inventory level. The proposed model is studied under the replenishment policy, starting with no shortages. The backlogging rate is a non-increasing function of the waiting time up to the next replenishment. The objective of this model is to minimise the total cost of the retailer. Cycle length, maximum inventory level and duration of positive inventory level are taken as the decision variables. Usually, retailers have to face many types of demand for different kinds of goods. In the proposed model, demand is considered as a function of stock and time. The existence and uniqueness of the optimal solutions of the developed models are examined. We propose a solution procedure to find the solution and obtain some managerial results using sensitivity analysis. Numerical examples are presented to determine the developed model and the solution procedure. Sensitivity analysis of the optimal solution with respect to major parameters is carried out.

Keywords: inventories; deteriorating items; shortages; optimisation; partial backlogging; permissible delays; payment delays; EOQ; economic order quantity; credit options; inventory models; supplier credit; inventory levels; replenishment policies; waiting times; total costs; retailers; cycle length; decision variables; demand; stock; time; sensitivity analysis; industrial engineering; systems engineering.

DOI: 10.1504/IJISE.2011.043486

International Journal of Industrial and Systems Engineering, 2011 Vol.9 No.4, pp.455 - 490

Published online: 07 Feb 2015 *

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