Silver and Moon [E.A. Silver and I. Moon, JORS 50(8)(1999) 789-796] address the problem of minimising total average cycle stock subject to two practical constraints. They provide a dynamic programming formulation for obtaining an optimal solution and propose a simple and efficient heuristic algorithm. Hsieh [Y.-C. Hsieh, JORS 52(4)(2001) 463-470] proposes a 0-1 linear programming approach to the problem and a simple heuristic based upon the relaxed 0-1 programming formulation. We show in this paper that the formulation of Hsieh can be improved for solving very large size instances of this inventory problem. So the mathematical approach is interesting for several reasons: the definition of the model is simple, its implementation is immediate by using a mathematical programming language together with a mixed integer programming software and the performance of the approach is excellent. Computational experiments carried out on the set of realistic examples considered in the above references are reported. We also show that the general framework for modelling given by mixed integer programming allows the initial model to be extended in several interesting directions. Keywords: inventory; cycle stock; mixed integer programming; computational experiments