(44e) Modeling and Optimization of Multi-Product Supply Chains

Authors: 
Zavala, V. M., University of Wisconsin-Madison
Martin, M., University of Salamanca
Sampat, A., University of Wisconsin-Madison
Martin, E., University of Salamanca
Multi-product network models are routinely used to evaluate the economic and environmental performance of supply chains and infrastructure networks [1, 2]. Such models are also used to identify optimal resource allocation strategies for strategic planning and to perform optimal network design [3-6]. Several models exist in the literature to deal with different types of systems, constraints, and study areas [7]. Unfortunately, these models are usually developed on a case-by-case basis. The existing lack of coherence between models limits systematic comparisons (benchmarks), collaboration and sharing of data sets, analysis of solution properties, and development of solution algorithms and software implementations.

In this talk, we present optimization formulations for multi-product supply chain networks. The formulations use a general graph representation that considers a set of technologies placed at a set of nodes and under which a set of products undergo transformations. Interactions between products are captured by using a hierarchical graph that maps products at each node using a transformation matrix and that maps network nodes using transportation paths (arcs). The proposed graph abstraction combines modeling concepts from supply chain and infrastructure network modeling. With this, we seek to provide a formal and general representation that can cover a wide range of settings existing in the literature.

We show how to use the framework to compute compromise solutions that resolve geographical and stakeholder conflicts. In particular, we present case studies in which we seek to design supply chains to collect and process organic waste from a large number of farms in the State of Wisconsin to mitigate point phosphorus and methane emissions while minimizing investment and transportation costs.

References:

[1] G. Guillen-Gosalbez and I. E. Grossmann, “Optimal design and planning of sustainable chemical supply chains under uncertainty,” AIChE Journal, vol. 55, no. 1, pp. 99–121, 2009.

[2] F. You, L. Tao, D. J. Graziano, and S. W. Snyder, “Optimal design of sustainable cellulosic biofuel supply chains: Multiobjective optimization coupled with life cycle assessment and input-output analysis,” AIChE Journal, 2012.

[3] Y. Kim, C. Yun, S. B. Park, S. Park, and L. T. Fan, “An integrated model of supply network and production planning for multiple fuel products of multi-site refineries,” Computers and Chemical Engineering, vol. 32, no. 11, pp. 2529–2535, 2008.

[4] S. M. Neiro and J. M. Pinto, “A general modeling framework for the operational planning of petroleum supply chains,” Computers and Chemical Engineering, vol. 28, no. 6-7, pp. 871–896, 2004.

[5] L. G. Papageorgiou, G. E. Rotstein, and N. Shah, “Strategic supply chain optimization for the pharmaceutical industries,” Industrial Engineering Chemical Research, vol. 40, no. 1, pp. 275–286, 2001.

[6] F. You, J. M. Wassick, and I. E. Grossmann, “Risk Management for a Global Supply Chain Planning Under Uncertainty: Models and Algorithms,” AIChE J, vol. 55, pp. 931–946, 2009.

[7] I. E. Grossmann, “Challenges in the new millennium: Product discovery and design, enterprise and supply chain optimization, global life cycle assessment,” Computers and Chemical Engineering, vol. 29, no. 1, pp. 29–39, 2004.