Retailer Inventory Model

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

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

Figure (i) Retailer’s Inventory Level and Interest earned

On the basis of the available possibilities as shown in the figure (i), there are three cases, This case comprises of collection of all the payment of sales items at time , from the customers by the retailer. But the supplier’s payment is done only after the end of credit period, , So, the retailer is not supposed to pay any of the above stated opportunity costs. And the retailer’s sales revenue is utilized to earn interest at a rate of and thus the retailer’s earned per unit time is, And Opportunity Cost per unit time is . This case explains that, the supplier is paid by the retailer at the period , the time after the retailer sold all the items and before the time that the retailer collects all returns. Specifically, the retailer cannot receive the payment instantly after the delivery of all the items to the customers, but pays off the supplier at the due date, and has to bear an opportunity cost during the time interval at a rate of . Therefore, the retailer’s opportunity cost per unit time is ,