Supplier Retailer Inventory Model

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Coordinated production, ordering, shipment and pricing model for supplier-retailer inventory system under trade credit

Abstract
This article focuses on proposing an integrated supplier-retailer inventory model in which supplier and retailer both have adopted trade credit policies, and the retailer receives a lot containing some defective items. The customer’s demand is expressed as a function of time, price and credit period, which is appropriate for the products for which demand increases initially and after sometime it starts to decrease. In order to reduce the holding cost of supplier, the production is considered as one of the decision variable, which is directly proportional to the customer’s demand rate. The aim of this paper is to
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The customer’s demand is expressed as a function of time, price and credit period which is appropriate for the products for which demand increases initially and after sometime it starts to decrease. In order to reduce the holding cost of supplier, the production is considered as one of the decision variable, which is directly proportional to the customer’s demand rate. The aim of this paper is to maximize the joint profit for supplier and retailer. Some numerical examples are demonstrated for validation of the developed mathematical model. Finally, implementing sensitivity analysis on the decision variables by varying the inventory parameters, effective managerial insight are generated which is beneficial for players of supply chain.
2. NOTATIONS AND ASSUMPTIONS:
The mathematical model is developed on the basis of the following notation and assumptions.
2.1 NOTATIONS: The supplier’s production rate per unit at any time t (a decision variable) The retailer’s demand rate per unit at any time t The supplier’s setup cost per order in dollar The retailer’s ordering cost per unit ordered in dollar Transportation cost per delivery in
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Shortages are impermissible. Lot size for seller

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