(530b) Robust Planning and Scheduling for Processes with Equipment Degradation

Process planning and scheduling frequently assumes perfect equipment availability and performance. In reality, equipment degradation can cause deteriorating process performance or equipment failure if maintenance is not carried out frequently enough. Process performance and equipment availability are therefore dependent on the selected maintenance strategy. Furthermore, the rate at which equipment health degrades may be partially random and affected by the selected operating strategy. Process scheduling and planning are both known to be hard problems. Integrating them and including effects of maintenance and uncertain equipment degradation is therefore challenging.

Multiple authors have addressed planning and scheduling with equipment degradation by proposing integrated process and maintenance models which explicitly incorporate unit degradation, e.g. [1–4]. Most of these works assume deterministic relationships between degradation, process performance, operating variables, and/or time. In contrast, the field of Condition-based maintenance (CBM) has attracted significant attention in recent years by using data-informed, stochastic degradation models to infer equipment health, albeit mainly at unit level [5]. We argue that properly accounting for equipment degradation requires new integrated process and maintenance planning and scheduling models which exploit the more sophisticated data-driven stochastic degradation models developed in CBM.

To this end, we show how Lévy type models [6], a class of stochastic processes commonly used for degradation modelling in CBM, can be incorporated into a MILP scheduling and/or planning model using the Lappas and Gounaris [7] adjustable robust optimization approach. Robust optimization has been applied to scheduling and planning by multiple authors, e.g. [7-9], but it has not been applied, to the best of our knowledge, to uncertainty in equipment degradation. We account for effects of the operating strategy on degradation by allowing the Lévy models parameters to depend on a set of discrete operating modes. As demonstrated by Li and Li [10], selecting an appropriate uncertainty set size in robust optimization is challenging and may be treated as its own optimization problem. We describe the uncertainty set size through a single parameter which we optimize by solving the robust MILP model repeatedly. Since this model can be computationally expensive, we propose using Bayesian optimization, which is known to work well for low dimensional problems with expensive to evaluate objective functions. Bayesian optimisation can also manage the noise introduced when some of the MILP sub-solves cannot be solved to optimality in a reasonable amount of time.

We furthermore propose a cheap way of estimating probabilities of equipment failure. We generate data regarding the relative frequency of occurrence of operating modes by solving a short-term scheduling model repeatedly. This data can be used to construct a Markov chain from which a large number of long-term schedules can be generated cheaply. These schedules are not necessarily feasible in the original problem but can be used to obtain a good estimate of equipment failure probabilities.

We apply our framework to an integrated planning and scheduling model recently proposed by Biondi et al. [3] with explicit treatment of unit degradation for the state-task-network (STN) originally developed by Kondili et al. [12]. We demonstrate that robust optimization is capable of trading of equipment availability and cost of maintenance for a number of STN instances and we show that Bayesian optimization can be used to optimize the uncertainty set size in a computationally efficient way.

[1] N. I. Zulkafli and G. M. Kopanos, “Integrated condition-based planning of production and utility systems under uncertainty,” J. Clean. Prod., vol. 167, pp. 776–805, 2017.

[2] S. Liu, A. Yahia, and L. G. Papageorgiou, “Optimal Production and Maintenance Planning of Biopharmaceutical Manufacturing under Performance Decay,” Ind. Eng. Chem. Res., vol. 53, no. 44, pp. 17075–17091, 2014.

[3] M. Biondi, G. Sand, and I. Harjunkoski, “Optimization of multipurpose process plant operations: A multi-time-scale maintenance and production scheduling approach,” Comput. Chem. Eng., vol. 99, pp. 325–339, 2017.

[4] C. G. Vassiliadis and E. N. Pistikopoulos, “Maintenance scheduling and process optimization under uncertainty,” Comput. Chem. Eng., vol. 25, no. 2–3, pp. 217–236, 2001.

[5] S. Alaswad and Y. Xiang, “A review on condition-based maintenance optimization models for stochastically deteriorating system,” Reliab. Eng. Syst. Saf., vol. 157, pp. 54–63, 2017.

[6] D. Applebaum, “Lévy processes-from probability to finance and quantum groups,” Not. Am. Math. Soc., vol. 51, no. 11, pp. 1336–1347, 2004.

[7] N. H. Lappas and C. E. Gounaris, “Multi-stage adjustable robust optimization for process scheduling under uncertainty,” AIChE J., vol. 62, no. 5, pp. 1646–1667, 2016.

[8] Z. Li, R. Ding, and C. a Floudas, “A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization,” Ind. Eng. Chem. Res., vol. 50, no. 18, pp. 10567–10603, 2011.

[9] C. Ning and F. You, “Data-driven robust MILP model for scheduling of multipurpose batch processes under uncertainty,” 2016 IEEE 55th Conf. Decis. Control., 2016.

[10] Z. Li and Z. Li, “Optimal robust optimization approximation for chance constrained optimization problem,” Comput. Chem. Eng., vol. 74, pp. 89–99, 2015.

[11] D. R. Jones, M. Schonlau, and W. J. Welch, “Efficient Global Optimization of Expensive Black-Box Functions,” J. Glob. Optim., vol. 13, pp. 455–492, 1998.

[12] E. Kondili, C. C. Pantelides, and R. W. H. Sargent, “A general algorithm for short-term scheduling of batch operations—I. MILP formulation,” Comput. Chem. Eng., vol. 17, no. 2, pp. 211–227, 1993.