Solution methods for the tray optimization problem

Twan Dollevoet, J. Theresia van Essen, Kristiaan M. Glorie

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Abstract

In order to perform medical surgeries, hospitals keep large inventories of surgical instruments. These instruments need to be sterilized before each surgery. Typically the instruments are kept in trays. Multiple trays may be required for a single surgery, while a single tray may contain instruments that are required for multiple surgical procedures. The tray optimization problem (TOP) consists of three main decisions: (i) the assignment of instruments to trays, (ii) the assignment of trays to surgeries, and (iii) the number of trays to keep in inventory. The TOP decisions have to be made such that total operating costs are minimized and such that for every surgery sufficient instruments are available. This paper presents and evaluates several exact and heuristic solution methods for the TOP. We compare solution methods on computation time and solution quality. Moreover, we conduct simulations to evaluate the performance of the solutions in the long run. The novel methods that are provided are the first methods that are capable of solving instances of realistic size. The most promising method consists of a highly scalable advanced greedy algorithm. Our results indicate that the outcomes of this method are, on average, very close to the outcomes of the other methods investigated, while it may be easily applied by (large) hospitals. The findings are robust with respect to fluctuations in long term OR schedules.

Original languageEnglish
Pages (from-to)1070-1084
Number of pages15
JournalEuropean Journal of Operational Research
Volume271
Issue number3
DOIs
Publication statusPublished - 2018

Keywords

  • Heuristics
  • Integer Linear Programming
  • OR in health services
  • Row & column generation
  • Sterile inventory

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