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A hybrid solution approach for the Integrated Healthcare Timetabling Competition 2024

Daniela Guericke, Rolf van der Hulst, Asal Karimpour, Ieke Schrader, Matthias Walter

TL;DR

The paper addresses integrated hospital timetabling across admissions, room allocation, nurse scheduling, and operating-theater planning. It presents a hybrid, three-phase decomposition that jointly leverages MILP, CP, and simulated annealing, executed in parallel to produce high-quality solutions within time limits and to generate useful lower bounds. Key contributions include lower bounds on optimal values for IHTC 2024 instances, a detailed decomposition with phase-wise information exchange, and an open set of future research directions to further improve exactness and scalability. The approach demonstrates competitive performance and provides insights into the practical benefits and limitations of hybrid, multi-phase strategies for complex, multi-decision healthcare scheduling problems.

Abstract

We report about the algorithm, implementation and results submitted to the Integrated Healthcare Timetabling Competition 2024 by Team Twente, which scored third in the competition. Our approach combines mixed-integer programming, constraint programming and simulated annealing in a 3-phase solution approach based on decomposition into subproblems. Next to describing our approach and describing our design decisions, we share our insights and, for the first time, lower bounds on the optimal solution values for the benchmark instances. We finally highlight open problems for which we think that addressing them could improve our approach even further.

A hybrid solution approach for the Integrated Healthcare Timetabling Competition 2024

TL;DR

The paper addresses integrated hospital timetabling across admissions, room allocation, nurse scheduling, and operating-theater planning. It presents a hybrid, three-phase decomposition that jointly leverages MILP, CP, and simulated annealing, executed in parallel to produce high-quality solutions within time limits and to generate useful lower bounds. Key contributions include lower bounds on optimal values for IHTC 2024 instances, a detailed decomposition with phase-wise information exchange, and an open set of future research directions to further improve exactness and scalability. The approach demonstrates competitive performance and provides insights into the practical benefits and limitations of hybrid, multi-phase strategies for complex, multi-decision healthcare scheduling problems.

Abstract

We report about the algorithm, implementation and results submitted to the Integrated Healthcare Timetabling Competition 2024 by Team Twente, which scored third in the competition. Our approach combines mixed-integer programming, constraint programming and simulated annealing in a 3-phase solution approach based on decomposition into subproblems. Next to describing our approach and describing our design decisions, we share our insights and, for the first time, lower bounds on the optimal solution values for the benchmark instances. We finally highlight open problems for which we think that addressing them could improve our approach even further.

Paper Structure

This paper contains 21 sections, 25 equations, 2 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem setting and nomenclature
  3. Solution approach
  4. Phase 2: Decomposition
  5. Phase 3: Finalization of the nurse-room assignment.
  6. Phase 1: Computation of care-cost bounds
  7. Preprocessing
  8. Subproblems
  9. Subproblems
  10. Patient-Admission MIP
  11. Patient-room assignment
  12. Operating-theater assignment
  13. Heuristic nurse-room assignment
  14. Care-cost estimates
  15. Exact nurse-room assignment
  16. ...and 6 more sections

Figures (2)

  • Figure 1: Interplay of decisions ( ), soft- ( ) and hard- ( ) constraints.
  • Figure 2: Overview of the phases of the solution approaches including allocation to threads and information exchange. Solid boxes indicate mixed-integer programs, the dashed box indicates a constraint-programming approach and the rounded corners indicate the simulated annealing approach. Arrows indicate the flow of (partial) solution information.