(496g) Process Planning Under Uncertainty with Stochastic Inventory Management:

The chemical process industry often constructs large production sites, namely integrated chemical complexes [1] that are composed of many interconnected processes and various chemicals. Integrated chemical complexes allow the chemical production to take advantage of synergies between processes. However, demand uncertainty and supply disruptions or delays may significantly affect tactical decision-making of a chemical complex. Although inventory improves the service by helping deal with demand uncertainty and providing flexibility, excessive inventory can be costly. [2] In addition, a chemical complex usually involves many chemicals, including feedstocks, intermediates and final products, making it a non-trivial task to determine which chemicals should be stored and what would be the optimal inventory level for each of them so as to achieve a certain service level and production target. Since cost-effective and robust inventory and production management can provide a competitive advantage for a company in a highly dynamic market, [3,4] it is of significant importance to integrate the process planning decisions with the stochastic inventory management decisions across the entire chemical complex, and coordinate the activities of purchase, production, inventory and sale to minimize the total cost.

There are several challenges to achieve this goal. The first challenge is how to model the inventory system of a chemical complex, which is more difficult than a multi-echelon inventory system and sometimes involves recycle flows. The second one is how to explicitly account for the supply delay and demand uncertainty in the inventory management and production planning. The third challenge is how to integrate the planning of purchase, production and sale, with inventory control, and how to model the propagation of uncertainties to quantify the internal demand uncertainty of each processes. The last challenge is how to effectively solve the resulting optimization problem that leads to a large-scale nonconvex mixed-integer nonlinear program.

In this paper, we consider the mid-term planning (typically 1- 6 months for process companies) of chemical process networks with integration of stochastic inventory management to deal with supply and demand uncertainty. By using the guaranteed service approach [5-6] to model the time delays in the chemical flows, we capture the stochastic nature of the supply and demand variations, and develop an equivalent deterministic optimization model to minimize the production, feedstock purchase, cycle inventory and safety stock costs. The model takes into account multiple tradeoffs and simultaneously determines the optimal purchases of feedstocks, production levels of processes, sales of final products and inventory levels of all chemicals in the process network. The model also captures the risk-pooling effect1 [7] to allow centralization of safety stock management for chemicals that are consumed/produced in multiple processes. We formulate the model as a mixed-integer nonlinear program (MINLP) with a nonconvex objective function and nonconvex constraints. To solve the problem with modest computational times, a tailored branch-and-refine algorithm based on successive piece-wise linear approximation is developed to for the global optimization. Five industrial-scale examples with up to 38 processes and 28 chemicals are presented to illustrate the application of the model and the performance of the proposed algorithm.

References:

[1] Wassick JM. Enterprise-wide optimization in an integrated chemical complex. Computers & Chemical Engineering. 2009; 33:1950-1963.

[2] Zipkin PH. Foundations of Inventory Management. McGraw-Hill: Boston, MA, 2000.

[3] Grossmann IE. Enterprise-wide Optimization: A New Frontier in Process Systems Engineering. AIChE Journal. 2005; 51:1846-1857.

[4] Varma VA, Reklaitis GV, Blau GE, Pekny JF. Enterprise-wide modeling & optimization ? An overview of emerging research challenges and opportunities. Computers & Chemical Engineering. 2007; 31:692-711.

[5] Graves SC, Willems SP. Optimizing strategic safety stock placement in supply chains. Manufacturing & Service Operations Management. 2000; 2:68-83.

[6] Graves SC, Willems SP. Optimizing the supply chain configuration for new products. Management Science. 2005; 51:1165-1180.

[7] Eppen G. Effects of centralization on expected costs in a multi-echelon newsboy problem. Management Science. 1979; 25:498-501.