Single-manufacturer and multi-retailer supply chain model with pre-payment based partial free transportation

¹ Department of Mathematics, The University of Burdwan, Burdwan 713104, India
² Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh 202002, India

^* Corresponding author: aakbarshaikh@gmail.com

Received: 9 February 2020
Accepted: 5 April 2021

Abstract

In this paper, a supply chain model between a manufacturing firm and a group of retailers has been developed. Manufacturing firm produces simultaneously both perfect and imperfect items which are separated by screening process. Then the perfect items are transferred to the retailers’ showroom/warehouse located in different places and a part of imperfect items are repaired by rework process. Retailers receive the products from the manufacturer with paying partial pre-payment to ensure the replenishment of order. On the other hand, the manufacturer provides partial free transportation facility to the retailers due to pre-payment. The corresponding problem has been formulated mathematically as a profit maximization problem and then solved it analytically. As an illustration of this supply chain model, three numerical examples have been considered and solved. Finally, post optimality analyses have been carried out to investigate the effects of changes of different parameters on the optimal policy.