(448f) Planning Under Uncertainty for Chemical Supply Chains: Stochastic Programming and Risk Management

Global supply chains in the process industries are usually very large scale systems that can be comprised of up to hundreds of or even thousands of production facilities, distribution centers and customers. Due to competition in the global marketplace, process industries are facing increasing pressure to manage their supply chains so as to reduce costs and risks.[1, 2] To achieve this goal, effective mathematical tools for large-scale supply chain optimization, particularly for cost reduction and risk management, have drawn significant attention. [3]

This work is motivated by a real world application originating at The Dow Chemical Company. The main objective is to consider the mid-term planning for a global multi-product chemical supply chain under the uncertainties of customer demand and production reliability. A two-stage stochastic programming model combined with Monte Carlo sampling and the associated statistical methods [4, 5] is proposed to deal with different levels of uncertainty, and it is incorporated into a multi-period planning model that takes into account the production and inventory levels, transportation amounts and modes, times of shipments and customer service levels. In the two-stage framework, the production, distribution and inventory decisions for the current time period are made ?here-and-now? prior to the resolution of uncertainty, while the decisions for the rest time periods are postponed in a ?wait-and-see? mode. In order to solve the resulting large scale industrial sized problems effectively, an algorithm based on the multi-cut L-shaped method [6] is proposed by taking advantage of the problem's decomposable structure. Computational examples are presented to demonstrate the effectiveness of the proposed algorithm.

To assess the potential improvement of using stochastic programming in the supply chain planning process compared with traditional deterministic optimization approaches, we developed a simulation framework that relies on the "rolling horizon" approach. Extensive simulation studies of our real world case study suggest that on average cost savings of 5.70% could be achieved by using the stochastic programming model on a monthly basis.

To explicitly consider the risks included in the global supply chain planning process, we studied five risk management models by using different risk measures, and multi-objective optimization schemes are implemented to establish the tradeoffs between the cost and the risk. A real world case study was presented to demonstrate the effectiveness of the proposed models and algorithms. Computational studies suggest that probabilistic financial risk management model [7] and downside risk management model [8] are more effective in reducing high cost risk compared with the popular variance reduction [9] and variability index management models. [10]

Reference:

[1] Grossmann, I. E., Enterprise-wide Optimization: A New Frontier in Process Systems Engineering, AIChE Journal, 2005, 51, 1846-1857

[2] Shah, N., Process industry supply chains: Advances and challenges, Computers and Chemical Engineering, 2005, 29, 1225-1235

[3] Chopra, S.; Meindl, P., Supply Chain Management: Strategy, Planning and Operation. Saddle River, NJ: Prentice Hall; 2003.

[4] Birge, J.R.; Louveaux, F., Introduction to Stochastic Programming, Springer Verlag, New York, 1997

[5] Shapiro, A.; Homem-de-Mello, T., A simulation-based approach to two-stage stochastic programming with recourse, Mathematical Programming, 1998, 81, 301-325

[6] You, F.; Grossmann, I. E.; Wassick, J. M., Risk Management for a Global Supply Chain Planning under Uncertainty: Models and Algorithms, AIChE Journal, Accepted

[7] Barbaro A. F.; Bagajewicz, M., ?Managing Financial Risk in Planning under Uncertainty?, AICHE Journal, 2004, 50, 963-989

[8] Eppen, G.D.; Martin, R.K., ?A Scenario Approach to Capacity Planning?, Operational Research, 1989, 37, 517-527

[9] Mulvey, J.M.; Vanderbei, R.J.; Zenios, S.A., ?Robust Optimization of Large-Scale Systems?, Operational Research, 1995, 43, 264-281

[10] Ahmed, S.; Sahinidis, N.V., ?Robust Process Planning Under Uncertainty?, Industrial and Engineering Chemistry Research, 1998, 37, 1883-1892