A Multi Period Lot-Sizing Model in Three-Echelon Supply Chain by Considering Payment Methods and Joint Replenishment of Inventory Items

Document Type : Original Article


1 M.Sc., Islamic Azad University, Bandar Abbas Branch.

2 Assistant Professor, Islamic Azad University, South Tehran Branch.


Different payment methods and time value of money have a significant impact on the profitability of the supply chain. In many applications, coordinated ordering of items creates savings in the total ordering cost. In this paper, a model is developed that integrates the joint replenishment of inventory items (JRP) and the selection of payment methods into supplier-selection order-allocation problem. Retailer can pay purchasing costs to suppliers and receive the selling price from customers in different payment methods. Three payment methods of cash-in-advance, cash and credit are assumed. In the developed multi-item multi-period model, the negative cash flows are borrowed and positive cash flows are invested. The objective function is maximizing the net future value of retailer’s cash flows. Through a numerical example, it is shown that major ordering is related with the number of selected suppliers but it does not affect the payment methods. In addition, minimum attractive rate of return of the supply chain members affects the selection of payment method and loans.


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