An integrated model for production, inventory and distribution problem with direct shipment

The necessity of reducing costs and inventory along supply chain has made production-distribution coordination a key point. In this paper, we develop an integrated production-inventory-distribution model for two stages supply chain with multiple plants and distribution centres, over multiple time periods which each plant can produce multiple products and utilise direct shipments between plants and distribution centres (DC). The model is formulated as mixed integer programming (MIP) with objective function to minimise total costs that consist of setup cost, production cost, inventory cost, and transportation cost. We compare the solution obtained from integrated model with decoupled model to determine the value of coordination. Numerical experiment on 24 test problems showed that the cost reduction obtained from coordination ranged between 0.5%-16.3%. Sensitivity analysis is used to obtain problem parameters that will affect the effectiveness of the integrated model, such as number of plants, number of time periods, and production capacity.