Using mixed integer programming to design employee rosters

This paper describes the problem of rostering a workforce so as to optimise a weighted sum of three criteria while satisfying several constraints. The rostering entailed deciding on a pattern of working days and breaks over a period of (typically) one year. Demand had to meet 24 hours each day and 365 days each year. It was possible to formulate this problem as a mixed integer program and, with some experimentation, solve it using an ‘off the shelf’ linear programming package. The results obtained are compared with rosters the client now uses.