Finding Near-Optimal Rosters Using Column Generation

We consider the following basic rostering problem. The days are divided in three fixed shifts (Early, Late, Night) and for each day (seven days a week) a number of personnel required is given. To man these shifts, a given number of employees are available, who all have their individual preferences. We have to find a year-roster for each person with minimum total cost. This cost consists of two components: penalties due to deviations from the desired number of personnel and ‘dissatisfaction cost’ due to a deviation from the preferences. Each roster must obey the legal regulations and some other specific constraints. Furthermore, we require a certain minimum satisfaction level for each employee. We have applied column generation to solve the above problem. Here a column corresponds to a year-roster for each employee. To reduce the computational burden, we solve the problem by a step-by-step procedure, in which we plan per four-week period, where we optimize the link between the two consecutive four-week periods. When applied in practice, we find near-optimal solutions.