Robust surgery planning and scheduling with downstream bed capacity constraint in ICU

As a critical part of the allocation of healthcare resources, planning and scheduling surgeries is a complicated combinatorial optimization problem because of the coupled effect of multiple sources of uncertainty, such as surgery duration, length-of-stay in ICU and so on. In this paper, we incorporate the downstream bed capacity in ICU, employ ellipsoid and box uncertainty set to capture the uncertainties of surgery duration and length-of-stay in ICU. Then, we formulate a two-stage robust model to address these uncertainties, derive the tractable robust counterpart and propose a column generation algorithm. Numerical results show that, compared with uncertainty of length-of-stay, surgery duration uncertainty has a significant effect on the total cost and the overtime of blocks, whereas uncertainty of length-of-stay has a dramatic impact on the amount of short beds in ICU. Hospital managers should choose the proper combination of uncertain level parameters, and make a balanced trade-off between overtime of block and the shortage of beds in ICU, so as to maximize the utilization of healthcare resources.