Constraint Programming Based Column Generation for Employee Timetabling

The Employee Timetabling Problem (ETP) is a general class of problems widely encountered in service organizations (such as call centers for instance). Given a set of activities, a set of demand curves (specifying the demand in terms of employees for each activity for each time period) the problem consists of constructing a set of work shifts such that each activity is at all time covered by a sufficient number of employees. Work shifts can cover many activities and must meet work regulations such as breaks, meals and maximum working time constraints. Furthermore, it is often desired to optimize a global objective function such as minimizing labor costs or maximizing a quality of service measure. This paper presents variants of this problem which are modeled with the Dantzig formulation. This approach consists of first generating all feasible work shifts and then selecting the optimal set. We propose to address the shift generation problem with constraint satisfaction techniques based on expressive and efficient global constraints such as gcc and regular. The selection problem, which is modeled with an integer linear program, is solved by a standard MIP solver for smaller instances and addressed by column generation for larger ones. Since a column generation procedure needs to generate only shifts of negative reduced cost, the optimization constraint cost-regular is introduced and described. Preliminary experimental results are given on a typical ETP.