# Trade Credit Policies for Supplier, Manufacturer, and Retailer: An Imperfect Production-Inventory System with Rework

## DOI:

https://doi.org/10.5614/j.math.fund.sci.2022.54.1.5## Keywords:

holding cost, imperfect production, net profit, rework, supply chain, trade credit policy## Abstract

In this study, we developed a trade credit policy for a three-layer supply chain consisting of a supplier, a manufacturer and a retailer. We propose an optimal production rate and selling price for the manufacturer and the retailer under an imperfect production system. The suggested coordination policy optimizes the profit of each supply chain member. Two models were formulated for two real-life strategies respectively. The first one is a collaborative (integrated) system and the second one is a Stackelberg leadership system. Both strategies were analyzed for various credit periods, respectively offered by the supplier to the manufacturer, by the manufacturer to the retailer, and by the retailer to the customers, by considering price-sensitive demand and a certain replenishment rate. Finally, we concluded which strategy will be better for inventory management under the given restrictions in the form of propositions. The concavity property for the net profit function was established with respect to the selling price and the production rate, which was also described graphically and analyzed by numerical examples.

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