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A mathematical model for simultaneous personnel shift planning and unrelated parallel machine scheduling

Maziyar Khadivi, Mostafa Abbasi, Todd Charter, Homayoun Najjaran

TL;DR

This work tackles integrated production and personnel shift planning for unrelated parallel machines under a multi-period horizon where personnel availability varies by time period. It introduces a MILP formulation with a novel discrete 'Positions' resource concept to allocate personnel for both machine setups and processing, and a Two-Step Solution Approach (TSSA) to accelerate solving by first maximizing accepted jobs and then minimizing total production time. The approach is validated on 118 synthetic instances and a real food-processing case, showing the model scales to sizeable problems and offering managerial insights on resource utilization and schedule feasibility. Practically, the method enables scenario analysis for workforce shifts and time-window constraints, guiding decisions that balance operational efficiency with staffing realities.

Abstract

This paper addresses a production scheduling problem derived from an industrial use case, focusing on unrelated parallel machine scheduling with the personnel availability constraint. The proposed model optimizes the production plan over a multi-period scheduling horizon, accommodating variations in personnel shift hours within each time period. It assumes shared personnel among machines, with one personnel required per machine for setup and supervision during job processing. Available personnel are fewer than the machines, thus limiting the number of machines that can operate in parallel. The model aims to minimize the total production time considering machine-dependent processing times and sequence-dependent setup times. The model handles practical scenarios like machine eligibility constraints and production time windows. A Mixed Integer Linear Programming (MILP) model is introduced to formulate the problem, taking into account both continuous and district variables. A two-step solution approach enhances computational speed, first maximizing accepted jobs and then minimizing production time. Validation with synthetic problem instances and a real industrial case study of a food processing plant demonstrates the performance of the model and its usefulness in personnel shift planning. The findings offer valuable insights for practical managerial decision-making in the context of production scheduling.

A mathematical model for simultaneous personnel shift planning and unrelated parallel machine scheduling

TL;DR

This work tackles integrated production and personnel shift planning for unrelated parallel machines under a multi-period horizon where personnel availability varies by time period. It introduces a MILP formulation with a novel discrete 'Positions' resource concept to allocate personnel for both machine setups and processing, and a Two-Step Solution Approach (TSSA) to accelerate solving by first maximizing accepted jobs and then minimizing total production time. The approach is validated on 118 synthetic instances and a real food-processing case, showing the model scales to sizeable problems and offering managerial insights on resource utilization and schedule feasibility. Practically, the method enables scenario analysis for workforce shifts and time-window constraints, guiding decisions that balance operational efficiency with staffing realities.

Abstract

This paper addresses a production scheduling problem derived from an industrial use case, focusing on unrelated parallel machine scheduling with the personnel availability constraint. The proposed model optimizes the production plan over a multi-period scheduling horizon, accommodating variations in personnel shift hours within each time period. It assumes shared personnel among machines, with one personnel required per machine for setup and supervision during job processing. Available personnel are fewer than the machines, thus limiting the number of machines that can operate in parallel. The model aims to minimize the total production time considering machine-dependent processing times and sequence-dependent setup times. The model handles practical scenarios like machine eligibility constraints and production time windows. A Mixed Integer Linear Programming (MILP) model is introduced to formulate the problem, taking into account both continuous and district variables. A two-step solution approach enhances computational speed, first maximizing accepted jobs and then minimizing production time. Validation with synthetic problem instances and a real industrial case study of a food processing plant demonstrates the performance of the model and its usefulness in personnel shift planning. The findings offer valuable insights for practical managerial decision-making in the context of production scheduling.
Paper Structure (14 sections, 34 equations, 9 figures, 4 tables)

This paper contains 14 sections, 34 equations, 9 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature review
  3. Problem definition and basic idea
  4. Mathematical model
  5. Two-step solution approach
  6. Computational experiments
  7. Instance generation and experimental setting
  8. Case study
  9. Results and discussion
  10. Synthetically generated data results
  11. Managerial implications
  12. Case study results
  13. Analysis of personnel shift scheduling
  14. Conclusions

Figures (9)

  • Figure 1: Example of UPMS with personnel availability as a resource constraint
  • Figure 2: Example of "position" concept introduced to the mathematical model
  • Figure 3: Example of connectivity types in the scheduling problem
  • Figure 4: First and second step normalized solution time of model considering influential factors (the solution times of first and second step are represented by the orange and blue line, respectively)
  • Figure 5: Optimality gap of resolved instances model considering influential factors
  • ...and 4 more figures