Expected time in system analysis of a single-machine multi-item processing center

Traditionally, cost models are studied to support decision making for production planning. However, criticism of cost accounting methods led to a growing interest in physical measures of manufacturing performance. Time based competition is one of the concepts that supports the use of these physical measures such as manufacturing lead time. Next to factors as finite capacity and priority rules the batching decision is one of the determinants of lead time. Time in system analysis to find analytical expressions for the optimal batching decision is a complex task. For that reason one has to rely on approximating approaches. In this paper two approaches will be compared. At high utilization levels, queueing delays build up the larger part of total lead time and for that reason, a lot of authors study the relationship between queueing delays and lot sizes. However, especially for low levels of utilization queueing delay analysis won't suffice. For that reason a second effective analytical approximation of the minimal time in system and the accompanying batch sizes is derived. This approximation is based on the insensitivity of the optimal solution to the total fraction of time spent on executing setups (setup utilization).