Study On EOQ Models With Partial Delay In Payments And Varying Demand

The traditional Economic Order Quantity (EOQ) model has been widely applied topractical business, and it is based on the agreement that acceptance of goods and paymentshould be completed synchronously. However, in actual business activities, suppliers oftenadopt the strategy of delay in payments to motivate retailers to order more goods. Andmeanwhile the retailers can earn the additional interest income via rational utilization of theaccumulated sales revenue during the period of delay in payments, and they have to pay acertain interest for the remaining stock beyond the delay in payments period. With thediversification of business operation, suppliers employ various strategies of delay in payments,such as partial of delay in payments, which means that immediate payment is called for acertain percentage of products, contrarily delay in payments for the remaining, and theproportion of delay in payments is depended on the size of the order quantity. Additionallydemand rates of many products take on a dynamic aspect, and for example, demand rate relateson time and inventory level. By considering varying demand rate, this paper will introduce thepartial of delay in payments into the traditional EOQ model.This paper assumes that the supplier offers three kinds of partial delay in paymentstrategies. The longer period of the delay in payments, the greater the more proportion ofimmediate payment. Firstly, under the condition of partial delay in payments and varyingdemand rate, the paper establishes an EOQ model by calculating the interest earns, interestpays and other key indices. And in addition our model is attributed to three existing modelsunder some special situations. Then the retailer’s optimal ordering cycles are determined underthree specific cases, i.e., the demand rate is dependent on the inventory level, the demand rateis a quadratic function of time, and the demand rate is varying exponentially with time. Thereby themaximum average profit is obtained. Finally, numerical examples are given to validate themodels, and the influences of retailer’s profits by different partial delay in payment strategiesare analyzed.