Annualized hours

Abstract

In this thesis, we propose two mixed integer linear program formulations for an optimization problem that incorporates annualized hours: an exact one and an approximation. The objective of our model consists of three weighted parts: a part which minimizes the difference between working hours and contract hours for each employee per week, a part which minimizes over and under staffing, and a part which minimizes the difference between contract hours and working hours for each employee over the total planning period. Additionally, the working hours need to be distributed over shifts of a fixed shift duration. We also consider an extension where skills are introduced. In this case, employees can only work on a task for which they are qualified. To test the proposed formulations, a random data generator is provided by ORTEC. The model should be solvable for a data set up to 100 employees and 52 weeks (and 5 skills). We have tested it on several data sets of that size with varying weights in our objective function. We have compared the run time of our exact model with the run time of the approximate model for different weights. The approximate model gave a relatively quick approximation of the optimal solution when we do not consider skills, and when we do consider skills and vary the weight for the first part of the objective function. For varying the weight on the second part, we used a time limited version of our exact model to approximate the optimal solution. To be able to approximate the optimal solution when varying weight on the third part of the objective function, the approximate model is used with extra weight on the first part, instead of the third.