Literature Review on Online Scheduling (Rescheduling)

In the past decades, several works addressed increasingly more complex rescheduling topics, mostly related to uncertainties in the process, rescheduling features, and open-loop and closed-open-loop solutions. Kanakamedala, Reklaitis, and Venkatasubramanian (1994) presented a reactive scheduling problem in multipurpose batch plants in which there are unexpected deviations for unit availabilities and processing times, and employed a bi-level least impact heuristic to reschedule the model. Huercio, Espuna, and Puigjaner (1995) used a heuristic-based rescheduling algorithm to cope with real time disturbances through task start time shifting units’ reassignment. Honkomp, Mockus, and Reklaitis (1999) proposed a framework to validate and evaluate rescheduling strategies under uncertainties such as processing time variations and unit breakdowns. Vin and Ierapetritou (2000) rescheduled a multiproduct batch plant problem within a continuous time formulation considering as disturbances machine breakdowns and rush order arrivals. Vin and Ierapetritou (2001) developed a strategy to improve the scheduling performance and flexibility under occurrence of unexpected events. Méndez and Cerdá (2003) introduced an MILP formulation for a multiproduct batch plant in which rescheduling is performed either under occurrence of unexpected events or to improve a non-optimal schedule. Besides, multiple rescheduling operations, such as reallocation, resequencing, and reordering, could be performed simultaneously. Janak et al. (2006) developed a rescheduling framework to partially reschedule the problem by determining which tasks have been affected or not under unforeseen events such as unit breakdowns and alteration of orders. Adhitya, Srinivasan, and Karimi (2007) proposed a framework to cope with supply chain disruptions in which the procedure of continuously and frequently rescheduling the problem leads to a closed-loop solution.

Kelly and Zyngier (2008) studied a production-chain problem involving a simple reactor and a tank flowsheet in which the inventory gap between the modeled and the real tank could be reduced to zero offset by performing what they called parameter

feedback (gain and/or bias updating). According to these authors, differences between the planned (model) and the real (measured) values in the process do not necessarily result from task execution or operational errors, since the absence of parameter feedback data makes it impossible to distinguish between an inadequate model representation and implementation failure of the problem result. Katragjini, Vallada, and Ruiz (2010) employed three different types of disruptions in a flowshop scheduling problem (arrival of new jobs, machine breakdowns, and release time delays) and developed rescheduling algorithms to find better trade-offs between the quality and the stability of the schedule. Zhuge and Ierapetritou (2012) introduced a closed-loop strategy for the simultaneous integration of scheduling and control, and highlighted the importance of rescheduling not only to handle negative scenarios but also to exploit favorable disturbances in the process. Nie et al. (2014) developed an MILP formulation based on a discrete-time resource task network (RTN) to reschedule a mixed batch/continuous process, which is reformulated in a state-space form and used for continuous rescheduling under process disruption. Kopanos and Postikopoulos (2014) presented a rescheduling approach based on state-space representation, moving horizon framework and multiparametric programming techniques. Lindholm and Nytzén (2014) introduced a bi-level hierarchical approach for a production scheduling problem considering disturbances in the supply of utilities. Du et al. (2015) proposed a time scale bridging framework to integrate closed-loop scheduling and nonlinear control of continuous processes. Gupta, Maravelias, and Wassick (2016) approached rescheduling as an online problem (online scheduling) and showed its benefits even when no disturbances/trigger events occur; therefore, reschedule should be applied whenever new information is available.

Gupta and Maravelias (2016) addressed features of open- and closed-loop scheduling and presented a framework to analyze closed-loop schedules. From an online scheduling perspective, Gupta and Maravelias (2017a) introduced a generic state-space model formulation to routinely handle disturbances and to apply their respective counter-decisions to update the state of the system using parameter feedback. Looking for more efficient closed-loop implementation to properly integrate planning, scheduling and control, Charitopoulos, Papageorgiou, and Dua (2019) introduced a framework based on a rigorous rescheduling mechanism to provide online solutions under dynamic disturbances, which mitigates their impact on operational decisions of

planning and scheduling. Larsen and Pranzo (2019) proposed a generic framework for dynamic scheduling problems in which a solver-simulator-controller approach is employed to a job shop scheduling problem to evaluate when uncertainties become relevant, rescheduling triggering and frequency, and solution quality. Stevenson, Fukasawa, and Ricardez-sandoval (2020) evaluated periodic rescheduling policies using a rolling horizon framework in an industrial-scale multipurpose plant to investigate the effect of plant parameters on the plant performance, and highlighted the importance of addressing rescheduling strategies for industrial applications.

Additionally, Franzoi et al. (2018) addressed an industrial-sized crude oil refinery scheduling problem and introduced an online parameter feedback with data reconciliation integrated within the scheduling cycle to achieve better process determinations. The authors highlighted the importance of properly integrating data to the decision automation core to reduce inaccuracies, to handle uncertainties, and to reduce the gap between optimized determinations and productions. For better performance of industrial operations, high-quality predictive analytics based on near past data (validated, reconciled, estimated, etc.) can determine improved near future predictions, which may be used in decision-making (prescriptive analytics) to correct processes mismatches. This framework relies on better diagnostics to improve predictive analytics (by identifying and correcting mismatches) and prescriptive analytics (by handling inconsistencies and infeasibilities) (MENEZES et al., 2019).

For improved industrial scheduling operations, it is fundamental to properly formulate and optimize the problem. That includes minimizing the plant-model mismatches so that the optimal solution matches the process conditions. Because of the high nonlinear and uncertain nature of most industrial problems, unforeseen events are likely to happen constantly and repeatedly throughout the entire network. That motivates for a continuous optimization cycle, in which the current state of the system is updated, and re-optimizations (rescheduling) are performed. The literature on the topic has been increasingly discussed the importance of rescheduling for process operations, although there are still open questions to be addressed, mostly related to open-loop versus closed-loop methods, rescheduling algorithm or framework, tuning of rescheduling elements or parameters, impacts of disturbances and uncertainties on

the scheduling operations, etc. Some of these topics will be addressed and discussed formulation; and c) open-loop versus closed-loop strategies in the scheduling optimization. In this section, the importance of re-calculation cycles as well as their contribution towards a better scheduling optimization are highlighted.

Due to differences between the data used in the scheduling model and the actual data from the process, there are inconsistencies between what would theoretically be produced (predictions and prescriptions) and what is in fact processed (production).

These disturbances might arise from the arrival of new information, operational deviations (prescriptions versus productions) from manual and automatic procedures, equipment failures and malfunctions, uncertainty on data (mainly information mismatch), etc. More specifically, common examples of disturbances in chemical engineering encompass: a) product demand changes (amount quantities and/or release, and due dates); b) non-updated and untracked or untraced feedstock information (date of arrival, amounts, and properties); c) uncertainty in the flows and properties throughout the process network; d) breakdowns, malfunctions or unplanned maintenance in process units, storage vessels (tanks), and in their connections; e) uncertainty in the raw material (inlets) to product (outlets) yields and properties in complex units (i.e., distillation column). Some of these disturbances are discussed later in this section. In the following, a motivating example illustrates the main concept of rescheduling and underscores the overall benefits that this type of approach brings to the final scheduling solution.

5.3.1 Motivating Example

Let us consider a moving horizon scheduling optimization to be performed daily within the future 5 days, so that the first optimization is carried out from Day 1 to Day 5 and