This paper deals with the problem of finding the order quantities, or cycle times, for the case of a multi-item inventory system with joint replenishment costs. The ordering cost is composed of a fixed cost independent of the number of items ordered and additional ordering costs dependent on the specific items ordered. Different solution procedures suggested for solving this problem are presented. A simulation program is developed comparing the effectiveness of these algorithms. One hundred and thirty two different settings, each consisting of one thousand examples, are analysed. Based on the simulation, two approaches are recommended for solving this problem.