Effect of deteriorating items and promotional effort factor in fuzzy instantaneous replenishment model

Abstract This paper presents a stylized model for analyzing the effect of deteriorating items and the promotional effort in a fuzzy optimal instantaneous replenishment model for a finite planning horizon. Accounting for holding costs and ordering costs have traditionally been the case when modelling inventory systems in a fuzzy environment. These imprecise parameters, which are defined on a bounded interval on the axis of real numbers and the physical characteristics of stocked items, dictate the management and control of inventory policies. This paper postulates on some of these costs, the promotional effort cost. Thus a modified fuzzy EOQ (FEOQ) model with a promotional effort factor is introduced. It assumes that a percentage of the on-hand inventory is wasted due to deterioration and it is considered as an enhancement to the EOQ model to determine the optimal promotional effort and the replenishment quantity so that the net profit is maximized. Through the theoretical analysis, the necessary and sufficient conditions for the existence and uniqueness of the optimal solutions are proved and the concavity of the fuzzy net profit function is established. A computational algorithm using the LINGO 13.0 software is developed to find the optimal solution. The results of the numerical analysis enable decision-makers to quantify the effect of promotion policy on optimizing net profit for the retailer and reduce inventory wastage due to deterioration . Finally, a sensitivity analysis of the optimal solution with respect to the major parameter is also conducted. In terms of profit maximization, fuzzy decision making is shown to be superior to crisp decision making without the promotional effort.

[1]  M. Pattnaik,et al.  AN ENTROPIC ORDER QUANTITY MODEL WITH FUZZY HOLDING COST AND FUZZY DISPOSAL COST FOR PERISHABLE ITEMS UNDER TWO COMPONENT DEMAND AND DISCOUNTED SELLING PRICE , 2008 .

[2]  A. Goswami,et al.  An EOQ Model for Deteriorating Items with Time Varying Demand and Costs , 1996 .

[3]  M. Hariga.  Optimal EOQ Models for Deteriorating Items with Time-Varying Demand , 1996 .

[4]  Mohamad Y. Jaber,et al.  Effect of deteriorating items on the instantaneous replenishment model , 1999 .

[5]  Fred Raafat,et al.  Survey of Literature on Continuously Deteriorating Inventory Models , 1991 .

[6]  M. Pattnaik,et al.  A Fuzzy Arithmetic Approach for Perishable Items in Discounted Entropic Order Quantity Model , 2011 .

[7]  Yu-Chung Tsao,et al.  Dynamic pricing, promotion and replenishment policies for a deteriorating item under permissible delay in payments , 2008, Comput. Oper. Res..

[8]  Diwakar Gupta,et al.  Joint product durability and lot sizing models , 1995 .

[9]  Jim Freeman,et al.  Inventory Control and Management , 1992 .

[10]  Edward A. Silver,et al.  Lot sizing for a product subject to obsolescence or perishability , 1994 .

[11]  M. Pattnaik.  An Entropic Order Quantity (EnOQ) Model with Post Deterioration Cash Discounts , 2011 .

[12]  A. Goswami,et al.  An EOQ Model for Deteriorating Items with Linear Time-dependent Demand Rate and Shortages under Inflation and Time Discounting , 1995 .

[13]  A Non-Random Optimization Approach to a Disposal Mechanism Under Flexibility and Reliability Criteria , 2011 .

[14]  M. Pattnaik.  Entropic Order Quantity (EnOQ) Model under Cash Discounts , 2011 .

[15]  Radivoj Petrovic,et al.  EOQ formula when inventory cost is fuzzy , 1996 .

[16]  S. K. Goyal,et al.  Recent trends in modeling of deteriorating inventory , 2001, Eur. J. Oper. Res..

[17]  Nita H. Shah,et al.  LITERATURE SURVEY ON INVENTORY MODELS FOR DETERIORATING ITEMS , 2000 .

[18]  M. Pattnaik.  An Entropic Order Quantity Model (EnOQ) under Instant Deterioration of Perishable Items with Price Discounts , 2010 .

[19]  M. Pattnaik.  A Note on Non Linear Optimal Inventory Policy Involving Instant Deterioration of Perishable Items with Price Discounts , 2011 .

[20]  P. K. Tripathy,et al.  Optimal Disposal Mechanism with Fuzzy System Cost under Flexibility & Reliability Criteria in Non-Random Optimization Environment , 2009 .

[21]  Adrijit Goswami,et al.  Production lot-size model with fuzzy production rate and fuzzy demand rate for deteriorating item under permissible delay in payments , 2006 .

[22]  Angappa Gunasekaran,et al.  An integrated production-inventory-marketing model for deteriorating items , 1995 .

[23]  Moncer Hariga,et al.  Economic analysis of dynamic inventory models with non-stationary costs and demand , 1994 .

[24]  M. Hariga.  An EOQ Model for Deteriorating Items with Shortages and Time-Varying Demand , 1995 .

[25]  G. Padmanabhan,et al.  EOQ models for perishable items under stock dependent selling rate , 1995 .