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Bayesian dynamic scheduling of multipurpose batch processes under incomplete look-ahead information

Taicheng Zheng, Dan Li, Jie Li

TL;DR

The paper tackles dynamic scheduling of multipurpose batch processes under incomplete look-ahead disturbances. It develops a Bayesian dynamic scheduling framework that uses ImpactPropagation to construct local impact variables and Bayesian Networks to update posterior disturbance effects online, guiding rescheduling decisions. A MILP-based schedule generator with warm-start and hierarchical objectives enables robust, flexible replanning, while theoretical results guarantee BN-consistent probabilistic reasoning under independent disturbances. Empirical results across four benchmarks show improved long-term cost and system nervousness relative to periodic rescheduling, highlighting the method’s practical potential and the importance of both when- and how-to-reschedule in incomplete-lookahead settings.

Abstract

Multipurpose batch processes become increasingly popular in manufacturing industries since they adapt to low-volume, high-value products and shifting demands. These processes often operate in a dynamic environment, which faces disturbances such as processing delays and demand changes. To minimise long-term cost and system nervousness (i.e., disruptive changes to schedules), schedulers must design rescheduling strategies to address such disturbances effectively. Existing methods often assume complete look-ahead information over the scheduling horizon. This assumption contrasts with realistic situations where schedulers can only access incomplete look-ahead information. Sticking with existing methods may lead to suboptimal long-term costs and high-level system nervousness. In this work we propose a Bayesian dynamic scheduling method. Our method relies on learning a Bayesian Network from the probability distribution of disturbances. Specifically, the Bayesian Network represents how likely each operation will be impacted by disturbances. During the online execution, when new disturbances become observed, this method updates the posterior distribution and therefore guides the rescheduling strategy. We compare our method with the existing periodic rescheduling strategy (which generates new schedules from scratch at fixed intervals) on four benchmark problems. Computational results show that our method achieves statistically better long-term costs and system nervousness. In the theoretical aspect, we prove that if disturbances are mutually independent, the impact-quantifying variables inherently satisfy the independence assumptions required by Bayesian Networks. As an implication, practitioners can extend the method to other scheduling problems (such as job shop scheduling and continuous processes), given that they define the problem-specific dependencies between operations.

Bayesian dynamic scheduling of multipurpose batch processes under incomplete look-ahead information

TL;DR

The paper tackles dynamic scheduling of multipurpose batch processes under incomplete look-ahead disturbances. It develops a Bayesian dynamic scheduling framework that uses ImpactPropagation to construct local impact variables and Bayesian Networks to update posterior disturbance effects online, guiding rescheduling decisions. A MILP-based schedule generator with warm-start and hierarchical objectives enables robust, flexible replanning, while theoretical results guarantee BN-consistent probabilistic reasoning under independent disturbances. Empirical results across four benchmarks show improved long-term cost and system nervousness relative to periodic rescheduling, highlighting the method’s practical potential and the importance of both when- and how-to-reschedule in incomplete-lookahead settings.

Abstract

Multipurpose batch processes become increasingly popular in manufacturing industries since they adapt to low-volume, high-value products and shifting demands. These processes often operate in a dynamic environment, which faces disturbances such as processing delays and demand changes. To minimise long-term cost and system nervousness (i.e., disruptive changes to schedules), schedulers must design rescheduling strategies to address such disturbances effectively. Existing methods often assume complete look-ahead information over the scheduling horizon. This assumption contrasts with realistic situations where schedulers can only access incomplete look-ahead information. Sticking with existing methods may lead to suboptimal long-term costs and high-level system nervousness. In this work we propose a Bayesian dynamic scheduling method. Our method relies on learning a Bayesian Network from the probability distribution of disturbances. Specifically, the Bayesian Network represents how likely each operation will be impacted by disturbances. During the online execution, when new disturbances become observed, this method updates the posterior distribution and therefore guides the rescheduling strategy. We compare our method with the existing periodic rescheduling strategy (which generates new schedules from scratch at fixed intervals) on four benchmark problems. Computational results show that our method achieves statistically better long-term costs and system nervousness. In the theoretical aspect, we prove that if disturbances are mutually independent, the impact-quantifying variables inherently satisfy the independence assumptions required by Bayesian Networks. As an implication, practitioners can extend the method to other scheduling problems (such as job shop scheduling and continuous processes), given that they define the problem-specific dependencies between operations.

Paper Structure

This paper contains 26 sections, 9 theorems, 70 equations, 10 figures, 4 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Prerequisite
  3. Probabilistic independence
  4. Directed Acyclic Graphs
  5. Bayesian Networks
  6. Problem description
  7. Static aspect
  8. Dynamic aspect
  9. Problem formulation
  10. Dynamic system formulation
  11. MILP formulation
  12. Methodology
  13. Terminologies and notations
  14. Overview
  15. Impact propagation
  16. ...and 11 more sections

Key Result

Lemma 1

Let $\boldsymbol{X}$ be a random vector whose elements are mutually independent under probability distribution $\mathsf{P}$. Let $\boldsymbol{X}_{1}, \cdots, \boldsymbol{X}_{m}$ be random vectors whose elements are disjoint subsets of $\boldsymbol{X}$, respectively. Let also $f_{1}, \cdots, f_{m}$ b

Figures (10)

  • Figure 1: STN representation of a sample multipurpose batch process
  • Figure 2: Illustration of look-ahead information and action sequences
  • Figure 3: Illustration of the ImpactPropagation algorithm
  • Figure 4: Illustration of the propagation function for processing time variations
  • Figure 5: Compilation of computational results. In each subplot, the x-axis represents costs (the value of $c$). The y-axis represents the number of operation changes (the value of $d$). The light blue vertical line represents the value of $c^{*}$. The pink vertical line represents the value of $c^{\infty}$. Each light brown scatter represents a result that is generated by the periodic, completely rescheduling policy. The integer to the top right of a light brown scatter represents the corresponding rescheduling frequency, which is measured in hours. Each light green scatter represents a result that is generated by our Bayesian dynamic scheduling method.
  • ...and 5 more figures

Theorems & Definitions (18)

  • Lemma 1
  • proof
  • Corollary 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • ...and 8 more