(626g) A Distributed Optimization Framework for Cooperative Decision Making in Integrated Process Networks

Flexible design and agile operation, enabling rapid response to changing market conditions, has become an increasingly important characteristic of chemical production networks in recent times. A common, but by no means the only, driving force for this is the interaction between chemical processes and a time-varying (due to increasing penetration of renewable energy) electricity market, with chemical processes providing demand response services or being directly electrified. However, within an arbitrarily complex integrated process network comprised of multiple decision making entities, the desired flexibility characteristics of individual facilities and entities often vary. Moreover, decision making entities are typically unwilling to share information about their own models in too much detail with others for fear of exploitation. As such, design and operation decisions are often made at a facility level without coordinating with other entities in the network, leading to suboptimal network-wide decisions.

In this work, we propose an algorithmic framework for cooperative decision making in integrated chemical production networks which uses distributed optimization to ensure only a limited amount of information sharing between decision making entities. It is an extension of recent work, which has shown that network-wide cost savings are possible from coordination of multiple chemical processes, namely when an industrial load with high electricity consumption is able to coordinate operation with its customers [1]. We begin by defining a ``status quo" or reference solution where downstream entities determine their optimal decisions first, and any requirements that these decisions would impose on upstream entities are considered fixed. We then aim to find a new coordinated strategy that can provide network-wide savings with respect to the reference solution, and propose two approaches for solving this problem in a distributed fashion. In the first, a cooperative game based on the reference solution is used, where entities join a coalition such that no entity does worse than their reference solution and network savings are appropriated in a fair manner. We do this through first using the epsilon constraint method paired with the alternating direction method of multipliers (ADMM) to generate a subset of points which are Pareto-optimal with respect to the costs of individual entities and have total network costs less than the reference solution. We then formulate a Nash bargaining problem [2] with proportional fairness constraints [3] to choose one of the Pareto-optimal points and appropriate cost savings fairly. Our second approach finds both the optimal coordinated decisions and distribution of savings in a single problem, using ADMM to solve a Nash bargaining problem with local process models.

To quantify the benefits of both approaches, we present the results of an in-depth computational study which aims to coordinate production schedules within networks of various shapes and sizes. Results suggest that the Pareto approach achieves faster solutions with better objective values when individual operational models are linear due to the fact that the single problem approach inherently attempts to solve a nonlinear, nonconvex problem using ADMM regardless of the local models. However, we show that both approaches are able to obtain operating points which enable savings for all entities with respect to the status quo, and in most cases obtain Nash products within 1-2% of the true optimal value. We conclude by presenting a practical case study which showcases the ability of our framework to also be applied to design problems, considering the design of a fertilizer production network, with three entities who produce hydrogen and nitrogen, ammonia, and urea, respectively.

[1] Allman, A., Zhang, Q. ``Distributed cooperative industrial demand response." Journal of Process Control (86), 2020, 81-93.
[2] Charitopoulos, V.M., Dua, V., Pinto, J.M., Papageorgiou, L.G. ``A game-theoretic optimization approach to fair customer allocation in oligopolies." Optimization and Engineering, 2020, https://doi.org/10.1007/s11081-019-09482-x
[3] Bertsimas D., Farias V.F., Trichakis, N., ``The price of fairness." Operations Research (59)}, 2011, 17–31.