Production allocation optimization by combining distribution free approach with open queueing network theory

We consider production allocation in a discrete manufacturing system formulated as an open queueing network (OQN) composed of some GI/G/1 queueing systems. The lead time performance, such as expectation and variance, in the manufacturing system has been analyzed and discussed using the OQN theory in the previous works. Through the improvement of lead time performance, we can discuss the decrease of the tardiness cost for delivery in the manufacturing system. Then, although the distribution of lead time is frequently required in order to evaluate the tardiness cost for delivery, it is difficult to understand the distribution of lead time exactly. In this article, we have a challenge of assessing the tardiness cost by using only the limited information, such as the expectation and variance of lead time. Concretely, we evaluate the upper bound of tardiness cost by combining the distribution free approach (DFA) with the OQN analysis. Then, a new optimal allocation policy for the production and tardiness costs is proposed.