Solution methods for the tray optimization problem

• Published in: European journal of operational research Vol. 271; no. 3; pp. 1070 - 1084
• Main Authors: Dollevoet, Twan, van Essen, J. Theresia, Glorie, Kristiaan M.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 16.12.2018
• Subjects: Heuristics; Integer Linear Programming; OR in health services; Row & column generation; Sterile inventory; Sterile inventory; Row & column generation; Integer Linear Programming; Heuristics; OR in health services
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2018.05.051

•We develop several (heuristic) solution methods to optimize surgical trays.•Assigning instruments to trays and trays to surgeries is done simultaneously.•We compare the solution methods on solution quality and computation time.•The robustness of the found solutions is assessed in an extensive simulation study. 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.