Scheduling of elective patients considering upstream and downstream units and emergency demand using robust optimization

Surgery is a vital process in Healthcare Centers (HCs). The importance of a surgery department is not only due to its direct impact on the health but also due to its high impact on the income and costs of HCs. Considering the upward trend of population aging in societies, increasing demand for surgery, and limited resources of HCs, providing an efficient schedule for Operating Room (OR) is essential. In this paper, a multi-objective mathematical model is proposed considering upstream and downstream units. The proposed model consists of three objectives in which the first one minimizes the number of deferred patients to the next planning horizon. The second one minimizes the waiting cost of scheduled patients and the cost of extra beds acquired in the ward, and the last one minimizes the idleness and overtime of ORs, lateness in operating children and earliness in operating patients far from HC. Then, the robust counterpart is proposed to evaluate some uncertain parameters, such as surgery t, Length of Stay (LoS) in upstream and downstream units and emergency demand. Since this problem is NP-hard, a new Mixed Integer Programming based Local Search Neighborhood (MIP-based LNS) algorithm is applied. Afterward, the effect of increasing number of slots on the CPU time is studied using a sensitivity analysis. Finally, a real case study entitled 'Alborz Hospital' is investigated. The obtained results show that applying the proposed model and increasing two beds in the Intensive Care Unit (ICU) could potentially decrease the number of deferred patients by 58.33% as compared to the traditional schedule (i.e., a schedule based on trial and error). Furthermore, the average idleness of ORs could be reduced by 36.58% as compared to the traditional schedule.