An EOQ model for three deteriorating items with substitutable and mutual complementary price, stock, and time dependent demand

Abstract

Abstract In this paper, a three-item EOQ model is proposed, where Product 1 is the main item and has a demand that is dependent on the following: its selling price and stock level, the selling price of the mutual complement (Product 2), selling price of its substitute (Product 3), and time. Product 2 has a demand that is dependent on its selling price, the selling price of its complement (Product 1) and time. Product 3 has a demand that is dependent on its selling price, the selling price of its substitute (Product 1) and time. A practical scenario for this model is in the perishable chicken feed supply chain between the supplier of medicines used in chicken feed production and a manufacturer of animal feed. Typical in this node of the supply chain the manufacturer of animal feed may source various medications from the same supplier. Due to certain nutritional specification of the feed formula, some of these medicines must be used together (complementarily), while some of these medicines can be used interchangeably (substitutes). Furthermore, stock availability of these medicines has potential to stimulate their prices, and consequently the demands. The mathematical model presented helps to determine optimal values of the selling prices of the three products and the cycle time that will maximise the total profit. The solution procedure was proposed, followed by numerical example Sensitivity analysis was conducted to assess how the model outputs respond to certain parameter changes. Result obtained from the study indicates that, certain parameter changes on the model have significant impacts on the cycle time, pricing, and the profitability of the inventory system.