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(701d) Robust Optimization for Production - Distribution Coordination of Industrial Gases Supply-Chains Under Uncertainty

Authors: 
Zamarripa, M., Carnegie Mellon University
Grossmann, I., Carnegie Mellon University
Lotero, I., Air Liquide
Gopalakrishnan, A., Air Liquide
Besancon, B., Air Liquide
Singh, T., American Air Liquide

An industrial gases supply-chain coordinates production and distribution decisions at multiple plants or depots while satisfying several customer demands. Plants operate air separation units, which feature high electricity consumption to produce gaseous and liquid products. Detailed distribution is required to coordinate pipeline demands for gaseous products and truck availabilities for liquid products. Multiple depots are considered as the source of the trucks, then trucks visit the plants, and finally the trucks distribute the product to the customers. In order to ensure customer storage replenishments, the product can also be purchased form alternative sources. Additionally, detailed inventory management has been developed by considering the storage tanks and the consumption profile for each day at the customer location. The replenishment is then coordinated with the production and storage levels at the production plants. At the supply-chain level, production and distribution decisions must be coordinated to fulfill several customer demands, local demands, and guarantee a safety stock in the inventory levels while minimizing the overall cost. Fixed customer demands based on forecast data or consumption profiles are usually considered, but, it is often the case that these parameters are unknown or characterized using several scenarios, upper and lower levels, probability functions, etc.

When large scale problems are studied and recourse actions are expensive or unrealistic, the robust optimization approach becomes an important tool to obtain feasible solutions for all the uncertainty sets under consideration1. This work further elaborates on a mixed-integer linear programming (MILP) formulation to minimize the overall cost of production and distribution of industrial gases supply-chains.2Given the uncertain demands we propose to characterize a closed box demand uncertainty set reformulating: i) a robust counterpart to analyze the worst case scenario; ii) the robust counterpart considering budgets of uncertainty, in which budgets of uncertainty have been proposed to compute the tradeoff between robustness and expenses of the solutions.

This work proposes two reformulations of the deterministic MILP production-distribution coordination model to consider demand uncertainty for large-scale industrial gases problems. In the first approach the deterministic model has been reformulated in to a robust counterpart to consider the worst case approach. The second approach obtains the robust counterpart considering budgets of uncertainty that constrain the number of realizations of the worst case scenario3. Budgets of uncertainty reduce the robustness, but they yield more realistic solutions and provide flexibility to the decision makers. The main objective is to minimize the total cost of production and distribution of liquid products under demand uncertainty.

[1] Bertsimas D., Thiele A. (2006). A Robust Optimization Approach to Inventory Theory. Operations Research. (54), pp. 150-168.

[2] Marchetti, P. A., Gupta, V., Grossmann, I. E., Cook, L., Valton, P. M., Singh, T., Li, T., and André, J. (2014). Simultaneous Production and Distribution of Industrial Gas Supply-Chains. Computer and Chemical Engineering. (69), pp. 39-58.

[3] Zhang, Q., Grossmann, IE., Heuberger, C.F., Sundaramoorthy, A., Pinto J.M. (2015). Air separation with cryogenic energy storage: Optimal scheduling considering electric energy and reserve markets. (61),  pp. 1547-1558.