Robust Optimization for a Multi-Product Integrated Problem of Planning and Scheduling under Products Uncertainty
Abstract: This paper presents robust optimization models for a multi-product integrated problem of planning and scheduling (based on the work of Terrazas-Moreno & Grossmann (2011) [1]) under products prices uncertainty. With the objective of maximizing the total profit in planning time horizon, the planning section determines the amount of each product, each product distributed to each market, and the inventory level in each manufacturing site during each scheduling time period; the scheduling section determines the products sequence, start and end time of each product running in each production site during each scheduling time period. The uncertainty sets used in robust optimization model are box set, ellipsoidal set, polyhedral set, combined box and ellipsoidal set, combined box and polyhedral set, combined box, ellipsoidal and polyhedral set. The genetic algorithm is utilized to solve the robust optimization models. Case studies show that the solutions obtained from robust optimization models are better than the solutions obtained from the original integrated planning and scheduling when the prices are changed.
Cite this paper: Chen, M. and Cao, C. (2015) Robust Optimization for a Multi-Product Integrated Problem of Planning and Scheduling under Products Uncertainty. Journal of Applied Mathematics and Physics, 3, 16-24. doi: 10.4236/jamp.2015.31003.
References

[1]   Terrazas-Moreno, S. and Grossmann, I.E. (2011) A Multiscale Decomposition Method for the Optimal Planning and Scheduling of Multisite Continuous Multiproduct Plants. Chemical Engineering Science, 66, 4307-4818. http://dx.doi.org/10.1016/j.ces.2011.03.017

[2]   Papageorgiou, L.G. and Pantelides, C.C. (1996) Optimal Campaign Planning/Scheduling of Multipurpose Batch/Semi- Continuous Plants. 1. Mathematical Formulation. Industrial and Engineering Chemistry Research, 35, 488-509. http://dx.doi.org/10.1021/ie950081l

[3]   Karimi, I.A. and Mcdonald, C.M. (1997) Planning and Scheduling of Parallel Semicontinuous Processes. 2. Short- Term Scheduling. Industrial and Engineering Chemistry Research, 36, 2691-2700. http://dx.doi.org/10.1021/ie9609022

[4]   Grossmann, I.E., Van Den Heever, S.A. and Harjunkoski, I. (2002) Discrete Optimization Methods and Their Role in the Integration of Planning and Scheduling. AIChE Symposium Series, 326, 150-168.

[5]   Lin, X., Floudas, C.A., Modi, S., et al. (2002) Continuous-Time Optimization Approach for Medium-Range Production Scheduling of a Multiproduct Batch Plant. Industrial and Engineering Chemistry Research, 41, 3884-3906. http://dx.doi.org/10.1021/ie011002a

[6]   Erdirik-Dogan, M. and Grossmann, I.E. (2006) A Decomposition Method for the Simultaneous Planning and Scheduling of Single-Stage Continuous Multiproduct Plants. Industrial and Engineering Chemistry Research, 45, 299-315. http://dx.doi.org/10.1021/ie050778z

[7]   Soyster, A.L. (1973) Convex Programming with Set-Inclusive Constraints and Appplications to Inexact Linear Programming. Operational Research, 21, 1154-1157. http://dx.doi.org/10.1287/opre.21.5.1154

[8]   Ben-Tal, A. and Nemirovski, A. (1998) Robust Convex Optimization. Mathematics of Operations Research, 4, 769- 805. http://dx.doi.org/10.1287/moor.23.4.769

[9]   Ben-Tal, A. and Nemirovski, A. (1999) Robust Solutions of Linear Programs. Operation, 25, 1-13.

[10]   Ben-Tal, A. and Nemirovski, A. (2000) Robust Solutions of Linear Programming Problems Contaminated with Uncertain Data. Methematical Programming, 88, 411-424. http://dx.doi.org/10.1007/PL00011380

[11]   Ben-Tal, A. and Nemirovski, A. (2002) Robust Optimization: Methodology and Applications. Math. Program. Ser. B, 92, 453-480. http://dx.doi.org/10.1007/s101070100286

[12]   Lin, X., Janak, S.L. and Floudas, C.A. (2004) A New Robust Optimization Approach for Scheduling under Uncertainty: I. Bounded Uncertainty. Computers & Chemical Engineering, 6, 1069-1085. http://dx.doi.org/10.1016/j.compchemeng.2003.09.020

[13]   Janak, S.L., Lin, X. and Floudas, C.A. (2007) A New Robust Optimization Approach for Scheduling under Uncertainty: II. Uncertainty with Known Probability Distribution. Computers & Chemical Engineering, 3, 171-195. http://dx.doi.org/10.1016/j.compchemeng.2006.05.035

[14]   Verderame, P.M. and Floudas, C.A. (2009) Operational Planning of Large-Scale Industrial Batch Plants under Demand Due Date and Amount Uncertainty. I. Robust Optimization Framework. Industrial & Engineering Chemistry Research, 48, 7214-7231. http://dx.doi.org/10.1021/ie9001124

[15]   Li, J., Verderame, P.M. and Floudas, C.A. (2012) Operational Planning of Large-Scale Continuous Processes: Deterministic Planning Model and Robust Optimization for Demand Amount and Due Date Uncertainty. Industrial & Engineering Chemistry Research, 51, 4347-4362. http://dx.doi.org/10.1021/ie202670a

[16]   Li, Z., Ding, R. and Floudas, C.A. (2011) A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization. American Chemical Society, 50, 10567-10603.

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