Mixed integer linear programming problem for personnel multi-day shift scheduling: A case study in an Iran hospital

Abstract

The application of mathematical and systematic models and approaches to health is on the rise. In this study, a mixed-integer linear programming problem with cost (staff payroll) objective function is proposed to determine homogeneous personnel shift scheduling so that the constraints of the number of personnel per shift are met. The purpose of this study is to optimize the scheduling of personnel with the same skills to minimize variable hospital costs. In a hospital, homogeneous personnel might be skilled nurses who can work in the same departments or service staff of the departments. First, a mathematical model is proposed for scheduling as a linear problem and solved using Lingo software. By analyzing the results for a personnel working time period in Pasargad Hospital in Tehran (Iran), it is found that while optimizing the utilization of the skilled staff within departments, the variable costs (payroll) related to the department for that specified period (month), which includes overtime, overnight and holidays, are reduced by around 10 percent.