EOQ Models for Imperfect Quality Items with Varying Demand and Allowable Proportionate Discount in Fuzzy Environment

Abstract

newlineIn every manufacturing organization inventory plays the role of lifeblood. From newlineproduction to distribution and then finally to customers, the role of inventory is newlineincomparable. Hence, without the proper management of inventory related problems found newlinein different organizations it becomes very difficult to take right decisions on when to newlineorder , how much to order and where to store , which are directly related to issues like newlineprofit from the products and the goodwill of customers. In the competition business world newlineevery company tries to attract the customer so that they can sustain in market for all times newlineto come. Whatever extra effort the companies may give at the time of the production the newlineproduced items cannot be 100 per cent perfect. Automatically both retailers and customers newlinereceive the products that are not also free from defects. So, appropriate measures are to be newlinetaken to maintain the goodwill at every stage. Earlier researchers have given emphasis on newlinethe fixed rate of discount on the imperfect items present in each lot. So, in the present thesis newlineimportance is given on the proportationate discounts on the defective items under the newlineconsideration of different conditions introduced for the parameters involved in the model newlineproblems. newlineThis dissertation examines the inventory models for items with imperfect quality newlinewith allowable proportionate discount. In inventory management, the economic order newlinequantity (EOQ) model plays an important role. From the early decades of 19th century the newlineEconomic Order Quantity (EOQ) models have been used in the area of inventory newlinemanagement. But several EOQ models contain some unrealistic assumptions like all newlineproduced lots are of good quality, all received items are not deteriorating in course of time, newlinea description of parameters of the models are considered to be certain (not fuzzy) and no newlinerole of learning on parameters. newlineIn this thesis, we developed different types of inventory models and with their newlinecorresponding fuzzy models such as without and with shortages, without and with learning, newlinetwo ware house model, two types of quality items, deteriorating items with imperfect newlinequality by introducing the proportionate discount for the defective items present in each lot. newlineIn all types of models each lot having some percentage of defects. To obtain the total profit, newlinea 100% screening is conducted for the lot and the allowable proportionate discount newlinevii newline(estimated) is introduced for the defective items. In case of the fuzzy inventory models the newlinedefective rates are taken to be fuzzy with the allowable proportionate discount for the newlinedefective items present in each lot, where the total profit per unit time is derived in fuzzy newlinesense. The fuzzy EOQ models are derived by using the triangular fuzzy numbers for the newlinedefective rates and the fuzzy models are defuzzified by using the signed distance method. newlineIn the present work we have analyzed the impact of learning on optimal solution of newlineinventory problem when its effect is introduced for the defective items present in each lot, newlinethe holding cost and the ordering cost. The solutions for maximizing the fuzzy total profits newlineper unit time have been derived for all developed models. Finally, numerical examples are newlineprovided to illustrate all the developed models. The sensitivity analysis and graphical newlinerepresentations are also performed to observe the effect of the number of shipments on the newlineorder quantity and the total profits of the models.