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When demand for employees varies throughout the day, the minimum shift design (MSD) problem aims at placing a minimum number of shifts that cover the demand with minimum overstaffing and understaffing. This paper investigates different constraint models for the problem, using a direct representation, a counting representation and a network flow based model and applies both constraint programming (CP) and mixed integer programming (MIP) solvers. The results show that the model based on network flow clearly outperforms the other models. While a CP solver finds some optimal results, with MIP solvers it can for the first time provide optimal solutions to all existing benchmark instances in short computational time.