(514h) Capacity Planning of Industrial Gas Plants with Rational Markets Under Demand Uncertainty

Authors: 
Garcia-Herreros, P., Aurubis A.G.
Kandiraju, A., Carnegie Mellon University
Grossmann, I. E., Carnegie Mellon University
Misra, P., Air Products and Chemicals, Inc.
Arslan, E., Air Products and Chemicals, Inc.
Capacity planning under uncertainty is a crucial problem for industrial gases companies due to the significant capital requirements. With dynamic market conditions, it is extremely important for these companies to develop capacity expansion plans based on realistic models. Insufficient capacity may lead to loss of market share and excessive investments in capacity may have a detrimental impact on their economic performance. Uncertainty in future demands and competition among producers to satisfy them, increase the complexity of the capacity planning problem. However, the role of uncertainty and rational decision-makers is fundamental for the success of capacity expansion projects.

Capacity planning for industrial gas producers is a challenging task because expansion plans are highly dependent on market behavior and the future demands [1]. A suboptimal expansion strategy may lead to unnecessary investments or loss of market share. To mitigate the risk associated with uncertain demands and to account for market preferences in the face of competition, a stochastic bi-level MILP optimization model is proposed [4].

The stochastic bilevel MILP optimization model involves an upper level that maximizes the expected Net Present Value (NPV) of an industrial producer, and a lower level that minimizes the expected cost paid by the markets over different demand scenarios. The upper level determines capacity planning decisions, which are modeled with discrete variables; whereas the lower level is a Linear Program (LP) which assigns market demands to competing producers. Our formulation finds a Stackelberg equilibrium between the leading producer and the markets. The producer makes the first move by deciding on the expansion plan, considering the rational responses of the markets in each scenario; then, the markets respond according to their cost minimization criterion. The strong Stackelberg equilibrium is found from the solution of the bilevel optimization problem. In order to solve the capacity planning problem, we reformulate it as a single-level MILP optimization problem. This reformulation leverages the strong duality property of the lower-level LP [2,3]. Uncertainty is considered in scenarios describing different realizations of demand. In this way, the upper level of the bi-level program maximizes the expected NPV obtained from the capacity expansion plan, while the lower level minimizes the cost paid by the markets in different scenarios. The model also accommodates the possibility to distribute capacity among different products and has the flexibility to constrain their production ratios.

The proposed capacity planning model is first implemented on a small illustrative example. The results demonstrate the advantages over its equivalent deterministic formulation. In particular, in the face of large uncertainties in demands, the proposed stochastic model is more conservative in the investments but resulting in a higher expected NPV compared to implementing the deterministic model under conditions of uncertainly. An effective domain reduction strategy developed to solve large-scale problems is demonstrated with an industrial size example. A stochastic bi-level model for capacity planning with non-uniform time periods is also proposed to better handle demand forecasting and to reduce the problem size of the resulting MILP.

[1] Eppen, G.D., R.K. Martin, L.Schrage, 1989. A scenario approach to capacity planning. Operations Research 37 (4), 517â??527.

[2] Garcia-Herreros, P., Misra, P., Arslan, E., Mehta, S., Grossmann, I. E., 2015. A duality-based approach for bilevel optimization of capacity expansion. In: Krist V. Gernaey, J. K. H., Gani, R. (Eds.), 12th International Symposium on Process Systems Engineering and 25th European Symposium on Computer Aided Process Engineering. Vol. 37 of Computer Aided Chemical Engineering. pp. 2021â??2026.

[3] Garcia-Herreros, P; Zhang, L., Misra, P., Arslan, E., Mehta, S., Grossmann, I.E., 2015. Mixed-integer bilevel optimization for capacity planning with rational markets. Computers & Chemical Engineering 86, pp. 33-47.

[4] Ryu, H., V. Dua, E.N. Pistikopoulos, 2004. A bilevel programming framework for enterprise-wide process networks under uncertainty. Computers & Chemical Engineering 28, 1121â??1129

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