(368f) Tactical Planning and Scheduling of Flexible Process Networks Under Uncertainty with Stochastic Inventory

In order to take advantage of the synergies that exist between processes and also ensure maximum flexibility, the chemical process industry often constructs large production sites composed of many interconnected processes and chemicals [1]. But, on the other hand, the risks associated with demand uncertainty and supply disruptions may significantly affect tactical decisions made by a chemical complex. Although inventories can serve as buffers in dealing with demand and supply uncertainties, excessive inventory can be costly [2]. In addition, a chemical complex usually involves many chemical states, including feedstocks, intermediates, and final products. Thus, it is of significant importance to determine which chemicals should be stored and what is the optimal inventory level for each of them so as to achieve a certain service level and production target [3]. A body of research closely related to this work is the multi-echelon stochastic inventory theory, which is originally developed for the supply chain management. By using the guaranteed service approach, one is allowed to model the inventory allocation across the entire system [4-6]. However, the application of the stochastic inventory management policy is not limited to the optimization of supply chain configurations. You and Grossmann [3] integrated this approach with the tactical planning of chemical complexes under supply and demand uncertainty. Though problems like how to model chemical process networks involving recycle flows and how to model the propagation of uncertainties to quantify internal demands are addressed in their work, only a set of dedicated processes are considered. However flexible processes that are able to perform different production schemes are quite common in industries, because these processes exhibit flexibility with both raw materials and products, thus improving the robustness and economic performance of the entire chemical complex [1]. It is known that ignoring the effects of changeovers may lead to infeasible schedules or suboptimal solutions [7]. Thus, it is desirable to take into account the detailed scheduling when making tactical decisions. Furthermore, the planning and scheduling are closely related to the stochastic inventory, because the production timings would have great impacts on the order processing delays. This results in an aggregated problem involving the integration of planning, scheduling and stochastic inventory management. The simplest approach is to formulate a single simultaneous model, while how to solve the aggregated problem efficiently remains a challenge

In this work, we approach this challenge from the following aspects. To capture the stochastic nature of the demand variations and supply delays, we use the guaranteed service time approach. To address the detailed scheduling problem, we employ the cyclic scheduling policy. We propose a single MINLP model that simultaneously determines the scheme selections, production schedules, purchases, sales, production/consumption amounts and working and safety inventory levels. This model exhibits multiple tradeoffs among variables from all decision levels, thus seamlessly integrate the planning, scheduling and stochastic inventory management. While this basic model contains multi-linear and concave terms, which would be computationally intractable for large-size problems, we reformulate the model to an MINLP with only square root and linear terms by exploiting the problem properties and using general linearization methods. In order to obtain global optimal solutions with modest computational times, we further develop a tailored branch-and-refine algorithm based on successive piecewise linear approximations. Also, inspired by the work of Dogan and Grossmann [7], novel symmetry breaking cuts are added to eliminate the degeneracy of the assignment configurations, which in turn greatly accelerate the computation. Three examples with up to 16 processes and 25 chemicals are presented to illustrate the application of the model and its computational performance. To examine the responsiveness issues[8] of chemical complexes, we present approximated Pareto-optimal curves to reveal the trade-offs between the total cost and inventory versus the maximum guaranteed service times to the markets by solving a series of instances. The results show that the more responsive the process network needs to be, the higher cost and more inventory it will have.

References

[1]        L. C. Norton and I. E. Grossmann, "Strategic-Planning Model for Complete Process Flexibility," Industrial & Engineering Chemistry Research, vol. 33, pp. 69-76, Jan 1994.

[2]        F. Q. You and I. E. Grossmann, "Design of responsive supply chains under demand uncertainty," Computers & Chemical Engineering, vol. 32, pp. 3090-3111, Dec 2008.

[3]        F. Q. You and I. E. Grossmann, "Stochastic Inventory Management for Tactical Process Planning Under Uncertainties: MINLP Models and Algorithms," Aiche Journal, vol. 57, pp. 1250-1277, May 2011.

[4]        S. C. Graves and S. P. Willems, "Optimizing the Supply Chain Configuration for New Products," Management Science, vol. 51, pp. 1165-1180, Aug 2005.

[5]        F. Q. You and I. E. Grossmann, "Integrated Multi-Echelon Supply Chain Design with Inventories Under Uncertainty: MINLP Models, Computational Strategies," Aiche Journal, vol. 56, pp. 419-440, Feb 2010.

[6]        F. Q. You and I. E. Grossmann, "Mixed-Integer Nonlinear Programming Models and Algorithms for Large-Scale Supply Chain Design with Stochastic Inventory Management," Industrial & Engineering Chemistry Research, vol. 47, pp. 7802-7817, Oct 2008.

[7]        M. Erdirik-Dogan and I. E. Grossmann, "A decomposition method for the simultaneous planning and scheduling of single-stage continuous multiproduct plants (vol 45, pg 299, 2006)," Industrial & Engineering Chemistry Research, vol. 46, pp. 5250-5250, Jul 2007.

[8]        F. Q. You and I. E. Grossmann, "Balancing Responsiveness and Economics in Process Supply Chain Design with Multi-Echelon Stochastic Inventory," Aiche Journal, vol. 57, pp. 178-192, Jan 2011.