# A Production-Inventory Model for a Deteriorating Item Incorporating Learning Effect Using Genetic Algorithm

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Advances in Operations ResearchVolume 2010 2010, Article ID 146042, 26 pages

Research Article

Department of Mathematics, National Institute of Technology, Durgapur, West Bengal 713209, India

Department of Computer Science, Prabhat Kumar College, Contai, Purba- Medinipur, West Bengal 721401, India

Received 20 November 2009; Revised 3 June 2010; Accepted 5 July 2010

Academic Editor: Frédéric Semet

Copyright © 2010 Debasis Das et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Demand for a seasonal product persists for a fixed period of time. Normallythe -finite time horizon inventory control problems- are formulated for this typeof demands. In reality, it is difficult to predict the end of a season precisely. It isthus represented as an uncertain variable and known as random planning horizon. In this paper, we present a production-inventory model for deteriorating items inan imprecise environment characterised by inflation and timed value of money andconsidering a constant demand. It is assumed that thetime horizon of the business period is random in nature and follows exponentialdistribution with a known mean. Here, we considered the resultant effect of inflationand time value of money as both crisp and fuzzy. For crisp inflation effect, thetotal expected profit from the planning horizon is maximized using genetic algorithmGA to derive optimal decisions. This GA is developed using Roulette wheelselection, arithmetic crossover, and random mutation. On the other hand when theinflation effect is fuzzy, we can expect the profit to be fuzzy, too! As for the fuzzyobjective, the optimistic or pessimistic return of the expected total profit is obtainedusing, respectively, a necessity or possibility measure of the fuzzy event. The GA wehave developed uses fuzzy simulation to maximize the optimistic-pessimistic returnin getting an optimal decision. We have provided some numerical examples andsome sensitivity analyses to illustrate the model.

Author: Debasis Das, Arindam Roy, and Samarjit Kar

Source: https://www.hindawi.com/