Near-optimal staff scheduling using a mixed integer model

Abstract

Making a feasible staff schedule is both a time consuming and a difficult task for companies that have employees working on irregular schedules. We introduce a mathematical model, using mixed integer programming, which makes a feasible schedule that fulfills as many of employees requests as possible while satisfying all hard constraints and as many soft constraints as possible. Our goal with this model is to develop a mathematical model that creates feasible staff schedules of high quality. The results from the model are in worst case 10% worse than the optimal solution.We present the mixed integer programming model and show results from four Icelandic companies and institutions as well as comparing it to a local-search based algorithm. The results show that it is possible to use mathematical programming techniques to make staff schedules, even though it is a problem with multiple and often changing objectives and goals.