Dynamic modeling and control of supply chain systems: A review
Computers and Operations Research
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As real world supply chain planning always involves uncertainty in demand and various risks, it is a crucial issue for both suppliers and customers. In this research, a mathematic model of supply chain with risk and uncertain demand are established and then solved. The inherent complexity of such a model leads to the solving difficulty in finding exact and integer optimal solutions. Therefore, a fast and acceptable answer becomes urgent when we have to pace up with the competitive business world, even it is only an approximate estimate. Four types of model are discussed in this study, including certain demand without risk, certain demand with risk, uncertain demand without risk, and uncertain demand with risk. After model verification and validation, computer simulations are performed with three selecting policies, namely "low cost first", "random", and "minimum cost path". The results are analyzed and compared, in which the "minimum cost path" is the better policy for node selection in simulation. A general linear programming solver called LINDO was used to find the optimal solutions but took days as the problem size increases, while simulation model obtains an acceptable solution in minutes. For small size problems, numerical examples show that the Mean Absolute Percentage Error (MAPE) between integer simulation solution and mathematical non-integer solution falls into the range of 3.69% to 7.34%, which demonstrates the feasibility and advantage of using simulation for supply chain planning.