An EPQ model of substitutable products under trade credit policy with stock dependent and random substitution

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THEORETICAL ARTICLE

An EPQ model of substitutable products under trade credit policy with stock dependent and random substitution P. Majumder1 • U. K. Bera1 • M. Maiti2 Accepted: 7 May 2020  Operational Research Society of India 2020

Abstract Many retailers are trying to attract more customers by offering the different offers to compete for market share. The offer of the similar items implies that the items may be substitutable type. Now a day two equally priced mutually substitutable products are arranged in the similar place such as Coke and Pepsi colas, Colgate and Close up, Progresso soups and Campbell etc. It is usually seen that a large amount of products (tooth paste, perfume, fruits, baked foods, vegetables, etc.) displayed in the market sometimes influenced the customers to purchase more product because of its stock, diversity, and brightness. Hence the items with more stock are preferable by the customers. In a simple meaning demand of one item is positively related to the displayed stock of the item and negatively infected by the stock of other item. In this research work, we are considering the demand of two substitute items. Since the items are substitutable, in case of a stock-out for one of them, a known fraction of its demand can be satisfied by using the stock of the other product. Demand of two substitutable items depends upon the inventory level. Substitutions among random customers are one of the realistic topics. In this paper for the first time we construct an EPQ model of substitutable items under trade credit with stock dependent substitutions and substitutions among random customers. The aim of this research work is to determine the relevant profit of each item. A real life numerical example is set to illustrate this model. Finally the model was solved by LINGO 13.0 software. Managerial insights and implications are also discussed. Keywords EPQ model  Substitute items  Deterioration  Budget

& P. Majumder [email protected] U. K. Bera [email protected] M. Maiti [email protected] Extended author information available on the last page of the article

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1 Introduction From twentieth century inventory problems have been studied in deterministic environment by a number of researchers. For instance one may refer to Van Eijs [53], Chen [6], Sun and Queyranne [49], etc. Different types of uncertainty such as randomness [18], fuzziness [27, 44] and roughness [9] are common in any real life situation. Several mathematical methods are available to solve the problems with these above said uncertainties. Since last two decades, the inventory problems with permissible delay in payment have been considered extensively by a number of researchers. In this expect Goyal [10] established the first economic ordered quantity model with constant demand considering trade credit policy. After that Aggarwal and Jaggi [1] extended Goyal’s [10] model in view of deteriorating items. Huang [16, 17] first established two inventory models wi