A fuzzy multi-objective polynomial time algorithm to solve the stochastic transportation formulation of a hospital bed rearrangement problem

This article considers the problem of bed rearrangement in a hospital. The problem is formulated as multi-objective mathematical program. The objectives driving the reallocation of beds could be conflicting in nature. The number of needed beds in each department is found to be highly related to length of stay (LOS) of a patient. Some described it as a random variable following a power law distribution. Hence, determining the number of the reallocated beds in each department could be treated stochastically because it depends on the fluctuation of the LOS. The complexity of the problem is taking care of by formulating the problem as multi-objective stochastic transportation problem and finding a compromise solution using a linear fuzzy function on the deterministic equivalent. The program is polynomial time solvable. The approach is illustrated through a bi-objective bed rearrangement problem, treating the possibility of increasing the admissions and the bed occupation, with real data from a hospital.