The EOQ model – A dynamical system

The paper deals with an inventory model to determine the retailer’s optimal order quantity for similar products. It is assumed that the amount of display space is limited and the demand of the products depends on the display stock level and the initiatives of sales staff where more stock of one product makes a negative impression of the another product. Also, the replenishment rates depend on the level of stocks of the items. The objective of the model is to maximize the profit function by trading off inventory costs, purchasing costs, cost of the effort of sales staff considering the effect of inflation and time value of money by Pontryagin’s Maximal Principles. The stability analysis of the concerned dynamical system has been analyzed. The sensitivity analysis of a suitable example is also carried out.