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Domain-Independent Dynamic Programming and Constraint Programming Approaches for Assembly Line Balancing Problems with Setups

Jiachen Zhang, J. Christopher Beck

Abstract

We propose domain-independent dynamic programming (DIDP) and constraint programming (CP) models to exactly solve type-1 and type-2 assembly line balancing problem with sequence-dependent setup times (SUALBP). The goal is to assign tasks to assembly stations and to sequence these tasks within each station, while satisfying precedence relations specified between a subset of task pairs. Each task has a given processing time and a setup time dependent on the previous task on the station to which the task is assigned. The sum of the processing and setup times of tasks assigned to each station constitute the station time and the maximum station time is called the cycle time. For type-1 SUALBP, the objective is to minimize the number of stations, given a maximum cycle time. For type-2 SUALBP, the objective is to minimize the cycle time, given the number of stations. On a set of diverse SUALBP instances, experimental results show that our approaches significantly outperform the state-of-the-art mixed integer programming models for SUALBP-1. For SUALBP-2, the DIDP model outperforms the state-of-the-art exact approach based on logic-based Benders decomposition. By closing 76 open instances for SUALBP-2, our results demonstrate the promise of DIDP for solving complex planning and scheduling problems.

Domain-Independent Dynamic Programming and Constraint Programming Approaches for Assembly Line Balancing Problems with Setups

Abstract

We propose domain-independent dynamic programming (DIDP) and constraint programming (CP) models to exactly solve type-1 and type-2 assembly line balancing problem with sequence-dependent setup times (SUALBP). The goal is to assign tasks to assembly stations and to sequence these tasks within each station, while satisfying precedence relations specified between a subset of task pairs. Each task has a given processing time and a setup time dependent on the previous task on the station to which the task is assigned. The sum of the processing and setup times of tasks assigned to each station constitute the station time and the maximum station time is called the cycle time. For type-1 SUALBP, the objective is to minimize the number of stations, given a maximum cycle time. For type-2 SUALBP, the objective is to minimize the cycle time, given the number of stations. On a set of diverse SUALBP instances, experimental results show that our approaches significantly outperform the state-of-the-art mixed integer programming models for SUALBP-1. For SUALBP-2, the DIDP model outperforms the state-of-the-art exact approach based on logic-based Benders decomposition. By closing 76 open instances for SUALBP-2, our results demonstrate the promise of DIDP for solving complex planning and scheduling problems.
Paper Structure (29 sections, 4 theorems, 22 equations, 6 figures, 8 tables, 1 algorithm)

This paper contains 29 sections, 4 theorems, 22 equations, 6 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Main contributions.
  3. Outline of the paper.
  4. Background
  5. Problem Definition and Notation
  6. State-of-the-art MIP Model for SUALBP-1
  7. State-of-the-art MIP Model for SUALBP-2
  8. State-of-the-art Exact Approaches for SUALBP-1 and SUALBP-2
  9. Constraint Programming
  10. Domain-Independent Dynamic Programming
  11. CP Models for SUALBP-1 and SUALBP-2
  12. CP model for SUALBP-1
  13. CP model for SUALBP-2
  14. DIDP Models for SUALBP-1 and SUALBP-2
  15. DIDP model for SUALBP-1
  16. ...and 14 more sections

Key Result

Theorem 1

Term (5e-i) is a valid lower bound of the number of additional stations to be used at the current state.

Figures (6)

  • Figure 1: Illustration of dual bound (5e-i).
  • Figure 2: Illustration of dual bound (11e-i).
  • Figure 3: Ratio of instances solved to optimality over time for SUALBP-1
  • Figure 4: Ratio of instances over primal integral for SUALBP-1
  • Figure 5: Ratio of instances solved to optimality over time for SUALBP-2
  • ...and 1 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4