Title: Designing retailer's replenishment policies for non-instantaneous deteriorating items under fuzzy costs

Authors: M. Valliathal; R. Uthayakumar

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

Abstract: In this paper, we discuss retailer's optimal replenishment policies for non-instantaneous deteriorating items with partial backlogging under inflation over a finite horizon. The backlogging rate is a decreasing function of the waiting time up to the next replenishment. The objective of this model is to minimise the total cost of the retailer which includes the setup cost, holding cost, shortage cost and the opportunity cost due to lost sales. Here the total cost, time durations and the optimum number of replenishment are taken as decision variables. In the practical situation, it is not always possible that all the cost components in the total cost are known and have definite values. For reality, the cost components involved in the total cost of the retailer are fuzzified to a certain extent. Triangular fuzzy numbers are used to represent the mentioned costs. Signed distance method is used to defuzzify the triangular fuzzy numbers. Numerical examples are given to illustrate the model.

Keywords: inventory modelling; fuzzy modelling; non-instantaneous deterioration; retailing; inflation; shortages; triangular fuzzy numbers; signed distance; defuzzification; deteriorating items; replenishment policies; backlogging rate.

DOI: 10.1504/IJSOM.2012.050139

International Journal of Services and Operations Management, 2012 Vol.13 No.4, pp.415 - 440

Published online: 23 Aug 2014 *

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