Rigorous Unit-Specific Event-Based Model for Short-Term Scheduling of Batch Plants Using Conditional Sequencing and Unit-Wait Times

Abstract

Continuous-time models have evolved as a promising tool for formulating problems related to short-term scheduling. This article presents an analysis, advantages, and limitations of recent models proposed in the literature for shortterm scheduling of batch plants based on unit-specific event-based time representation. The purpose of this study is to generalize and enhance previous unit-specific event-based scheduling models for efficient handling of various issues such as nonsimultaneous material transfers, comprehensive sequencing constraints for handling of different storage policies, unit-wait policies, and utility resources. Accordingly, a rigorous unit-specific event-based model has been proposed that allows for conditional sequencing of each production and consumption task, only if the material produced by a given production task is used by a given consumption task. The proposed approach leads to reduction in number of events, and the model can effectively handle scheduling problems with different storage policies: UIS, FIS, NIS, and ZW. It can can also handle different unit-wait policies. The proposed conditional sequencing concept is also extended for efficient handling of utility resources, thus resulting in further reduction in number of events required compared to the published literature.

Theoretical and computational comparison of continuous‐time process scheduling models for adjustable robust optimization

“…This feature enables the utilization of even fewer intervals in order to achieve the optimal solution. Many such multi‐grid models have been proposed in the literature, either in the form of unit‐specific event‐based models, or in the form of unit slot‐based models . A comprehensive computational comparison of scheduling models across all of the existing categories has been conducted by Shaik et al for the deterministic case.…”

“…Being the first of its kind, the aforementioned model can be characterized by its simplicity and remarkable computational performance at the cost of not modeling a number of problem features that include tasks spanning across multiple event points, real‐time tracking of storage, or support for resources. Later versions of this model overcame these challenges by introducing more involved model formulations. Despite their good performance in the deterministic setting, the improved unit‐specific models were never used in the context of robust optimization due to the fact that they rely on conditional equalities among non‐auxiliary timing variables to model real‐time storage violations and resource consumption.…”

“…In process flow sheets of average complexity, the above limitation typically leads to very conservative solutions, diminishing in this way the benefits of ARO. In fact, for unit‐specific event‐based models that utilize conditional equalities to hedge against real‐time storage violations, the solutions will be of no practical use, as the coefficient matching between unrelated uncertain parameters would give rise to the trivial solution where no task is executed. The above observations lead us to consider exclusively global event‐based models in the comparative study we perform in the context of the multistage ARO framework.…”

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

“…On the other hand, continuous-time models utilize continuous variables to model explicitly the times at which tasks are to be scheduled, allowing for higher time precision and leading to a significant reduction in model size, albeit at the cost of a more complex mathematical representation that may hinder in some cases the ability of the modeler to extend the model towards new settings. The continuous-time models can be further classified into two sub-categories, namely single-grid models, [44][45][46][47][48][49][50][51] and multi-grid models, [52][53][54][55][56][57][58][59][60][61] depending on whether they employ a common or a unit-specific grid to keep track of task timing. The size and computational tractability of each model may vary across different problems and these aspects have been extensively studied in the deterministic literature.…”

Improved Multipopulation Discrete Differential Evolution Algorithm for the Scheduling of Multipurpose Batch Plants

“…Seid and Majozi 21 proposed a unitspecific event-based model with conditional sequence, and production and consumption tasks are aligned conditionally. Vooradi and Shaik 22 proposed a rigorous unit-specific eventbased model by introducing the concept of conditional alignment. Their formulation could effectively handle the nonsimultaneous material transmission and preprocessing and postprocessing unit wait policies.…”