An optimal bin-packing algorithm to minimize the number of washing cycles in a hostipal sterilization service.
Résumé
The problem we study arises from the washing step of hospital sterilization services. A hospital sterilization service is a reproduction system for medical devices (MDs). Sterilization services are composed of following steps: pre-disinfection, rinsing, washing, verification, packing, sterilization and storage before reuse. In the problem we treat, all MDs are available at the same time. This is typically the case of an external sterilization service, or, if a sterilization service starts the pre-disinfection of MDs after all surgeries have been finished According to a questionnaire carried out among some hospitals of Rhône-Alpes region in France, it is reported that the washing step is generally the bottleneck of the system. In this study, we aim at optimizing the utilization of washing resources by minimizing the number of launched washing cycles. After modeling the washing step as a bin-packing problem, we are inspired by the linear programming model of Gilmore and Gomory (1961). This model consists of a column generation method where each created column in the solution represents the combination of different MD sets to be washed together in our problem. The small number of different item sizes in our problem makes possible to create all columns of the linear model. We developed an algorithm to create all the columns and then we use linear programming to solve the problem optimally. Finally we test the impact of this optimization on the whole sterilization service using a simulation model and compare it to a case where first fit decreasing algorithm is applied to the washing resources. Computational results show that the optimal method helps smoothening the production by decreasing the waiting of MDs between different steps.