Optimal Ordering Policy for Deteriorating Items with Limited Storage Capacity under Two-Level Trade Credit Linked to Order Quantity by a Discounted Cash-Flow Analysis

Hui-Ling Yang

doi:10.4236/ojbm.2019.72063

Abstract

Nowadays, the supplier often provides cash discount or permissible delay in payments to its retailers, if the order quantity attains a certain amount. Likewise, the retailer also provides a downstream trade credit period to his customers. In practice, as the supplier provides price discounts for bulk purchases, the retailer may purchase more goods than can be stored in its owned warehouse and store the excess quantities in a rented warehouse. Thus, a two-warehouse inventory model is needed to be considered. Further, the cost is usually affected by the present value of time and products deteriorate as time increases. Therefore, this paper develops a supplier-retailer-customer chain inventory model in which 1) two-level trade credit linked to order quantity is considered; 2) storage capacity is limited; 3) the effect of inflation and time value of money by a discounted cash-flow analysis is taken into account. The demand rate is linearly increasing with time and the deterioration rate is constant. Based on the viewpoint of cost minimization, the objective is to find the optimal replenishment cycle and order quantity to keep the present value of the total relevant cost per unit time as minimum as possible. The research shows that in each case discussed, the optimal solution for each case exists uniquely. Finally, numerical examples are provided for illustration and some managerial insights based on the numerical results are also presented.

Highlights

In the classical EOQ model, the supplier often prefers to offer his customers a delay period for payment to attract new customers and promote more sales, especially in the present of economic depression circumstances
The demand rate is linearly increasing with time and the deterioration rate is constant
The supplier offers a permissible delay in payment linked to order quantity, in the the retailer provides a downstream trade credit period to its customers

Summary

Introduction

In the classical EOQ model, the supplier often prefers to offer his customers a delay period for payment to attract new customers and promote more sales, especially in the present of economic depression circumstances. There is no interest charge if the outstanding amount is paid within this permissible delay period. If the payment is unpaid in full by the end of the permissible delay period, interest is charged on the outstanding amount. The policy of granting credit terms adds an additional cost to the supplier as well as an additional dimension of default risk. The literature reviews are described as the following subsections

Papers Related with Permissible Delay in Payment or Two-Level Trade Credit

Assumptions and Notation

Research Models

Theoretical Results

Numerical Examples

Conclusions