Raw material order allocation problem using mixed integer linear programming and simulation

This study aims to provide a conceptual model and to develop a mathematical model to determine order allocation in multi products, multi suppliers, multi carriers, and multi periods problem under uncertainty. The conceptual model describes the connection between related variables. The problem is formulated in mixed integer linear programming (MILP) model. MILP model objective function is to minimize supply chain costs which are purchasing cost, ordering cost, inventory holding cost, carrier cost, late delivery penalty cost, and low-quality penalty cost. In order to illustrate the applicability of the MILP model, a real-world case in cement industry is demonstrated. Based on historical data, the most common uncertainty factor is supplier delivery performance and product quality. Those factors are experimented in MILP model using Monte Carlo simulation. The integration between MILP model and Monte Carlo simulation shows that the proposed model resulted a global optimum solution.