Mathematical modeling of inventory cost in a 3-tier supply chain with horizontal cooperation

Abstract

Inventory together with the transport, location of the production factory, and storage represent important factors that influence the performance of a supply chain. It is thus important for organizations to maintain inventory for efficient and smooth running of their operations. Through cooperation, supply chain players at the same level of the market can work jointly to plan and execute supply chain operations, and achieve greater success than when acting in isolation. Accordingly, this work considers a 3-tier supply chain – Supplier, Manufacturer, and Distributor, and it develops a model for minimizing the cost of inventory across the 3-tiers with horizontal cooperation at the post-production inventory end of manufacturing tier only. A constrained mixed integer mathematical program was developed with the objective of minimizing total inventory cost across the three supply chain tiers. A test problem consisting of 3 suppliers, 3 manufacturers, 3 distributors, and 4 products was used to test the model; the resulting mathematical problem was solved using linear programming with and without post-production inventory horizontal cooperation scenarios. It was found that horizontal cooperation was of immense benefit to supply chain players, and offers great cost savings as against individual operation.

Keywords

• Supply chain
• Inventory
• Horizontal cooperation
• Linear programming