With conventional models, in order to compare the properties of push-type production systems with those of pull-type systems, in previous works it was assumed that the ordering cycle period of the push-type system was equal to that of the pull-type system. The ordering cycle period of the push-type system is, however, usually different from that of the pull-type system in actual use. For example, the ordering cycles of the push and pull-type systems may be given every day and every three hours, respectively. The results of previous works with the same ordering cycle period cannot be applied to the above practical cases. In this paper we propose a new model in order to compare the properties of the push and pull-type systems under condition that the ordering cycle period may be different. The criteria in this paper are variances in inventory and order quantity. This is because we want to investigate the essence of the behaviors of the production systems. At first, we formulate optimal push and pull-type production systems. Secondly, we formulate a demand model in order to consider the differences in the ordering cycle periods, and apply this model to both systems. Finally, we evaluate the performance through numerical analysis. We analyze the rate of the ordering cycle period coinciding with the evaluated value of the push-type system with that of the pull-type system, which is denoted by τ^*. As the result, we show that the effect of τ to the variances is very strong. If autocorrelation of the demand is strong, then τ^* is large, however, if the autocorrelation is weak, then τ^* is smaller than 2.
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