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Structural Insights and an IP-based Solution Method for Patient-to-room Assignment under Consideration of Single Room Entitlements

Tabea Brandt, Christina Büsing, Felix Engelhardt

TL;DR

This work presents combinatorial insights about the feasibility of PRA and about the assignment of patients to single rooms, and develops a fast IP-based solution approach which obtains high quality solution.

Abstract

Patient-to-room assignment (PRA) is a scheduling problem in decision support for hospitals. It consists of assigning patients to rooms according to certain objectives, e.g., avoiding transfers and respecting single-room requests. This work presents combinatorial insights about the feasibility of PRA and about the assignment of patients to single rooms. We further compare different IP-formulations for PRA as well as the influence of different objectivs on the runtime. Based on these results, we develop a fast IP-based solution approach which obtains high quality solution. The applicability is verified through a computational study with instances derived from real-world data. Results indicate that large, real world instances can be solved to a high degree of optimality within (fractions of) seconds.

Structural Insights and an IP-based Solution Method for Patient-to-room Assignment under Consideration of Single Room Entitlements

TL;DR

This work presents combinatorial insights about the feasibility of PRA and about the assignment of patients to single rooms, and develops a fast IP-based solution approach which obtains high quality solution.

Abstract

Patient-to-room assignment (PRA) is a scheduling problem in decision support for hospitals. It consists of assigning patients to rooms according to certain objectives, e.g., avoiding transfers and respecting single-room requests. This work presents combinatorial insights about the feasibility of PRA and about the assignment of patients to single rooms. We further compare different IP-formulations for PRA as well as the influence of different objectivs on the runtime. Based on these results, we develop a fast IP-based solution approach which obtains high quality solution. The applicability is verified through a computational study with instances derived from real-world data. Results indicate that large, real world instances can be solved to a high degree of optimality within (fractions of) seconds.
Paper Structure (18 sections, 4 theorems, 42 equations, 9 figures)

This paper contains 18 sections, 4 theorems, 42 equations, 9 figures.

Table of Contents

  1. Introduction and problem definition
  2. Literature review
  3. Combinatorial insights
  4. Feasibility
  5. Maximum number of private patients in single rooms
  6. Comparison of different IP-formulations
  7. Minimize transfers only
  8. Integration of single room constraints
  9. IP-formulation without transfers
  10. Dynamic PRA
  11. Future work
  12. Scaling to multiple wards
  13. Patient conflicts
  14. Patient preferences
  15. Accompanying person
  16. ...and 3 more sections

Key Result

Lemma 1

Consider a ward with room capacities $c_r\in\{1,c\}$ with $c\in\mathbb{N}$ for all rooms $r\in\mathcal{R}$. Let the number of female and male patients $F_t,M_t\in\mathbb{N}_0$, be given. If $R_1\geq c-1$, then the instance is feasible if and only if the number of patients does not exceed the ward's holds true for every time period $t \in \mathcal{T}$.

Figures (9)

  • Figure 1: Example for $\mathcal{T}=3$ with one private patient where a patient transfer is necessary for feasibility
  • Figure 2: Comparison of IPs A - D using 62 real-life instances, after 12 h 61 instances were solved to optimality by IPs C and D with objective value 0
  • Figure 3: Comparison of IPs E - H using 62 real-life instances, maximum runtime 12h
  • Figure 4: Performance of IP K using 62 real-life instances, maximum runtime 12h
  • Figure 5: Comparison of IPs \ref{['IP:M']}-\ref{['IP:P']} using 62 real-life instances
  • ...and 4 more figures

Theorems & Definitions (10)

  • Definition 1: Feasibility Problem
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Definition 2: Private Patient Problem (PPP)
  • Lemma 3
  • proof
  • Lemma 4
  • proof