Optimisation on a constrained integrated supply chain for multiple steel products with investment and freight cost discount

This paper intends to help the reader to understand a new inventory control model for steel products. This model introduces a steel marketing supply chain between a manufacturer and a merchant with multiple steel products. The purpose of this work is to influence a price discount on backorder for the merchant, ordering cost reduction and setup cost reduction, proceeding with the cogitation of discount on freight cost. We hold the freight cost to be a function of the order's quantity, and it is to be in the format of all-unit-discount costs. We thus assimilate freight costs into the system comprehensively and straightforwardly and have worked out the optimal solution procedures for working with the posed inventory model. A numerical example and sensitivity analyses are also carried out to demonstrate the study's implementations and performances.