Optimal inventories in group technology production systems for a continuous consumption pattern

Abstract

In this paper, a mathematical model to determine the optimal lot size in group technology systems is developed, based on a continuous consumption pattern. The optimal lot size formula that minimizes total cost is then determined. This formula is found to be similar to the standard economic production quantity formula, except for the cost elements associated with items' production and the opportunity cost associated with total machines set-up time. However, it is shown that in practical situations, where machine set-up consumes a limited time, the difference between the two formulas is insignificant. A variant formula for the case where storage cost is based on a fixed charge in a random access storage is also derived. Sensitivity analysis with respect to annual demand rate, annual carrying cost rate, cost of raw material handling, total machine set-up time and cost per unit time is presented. Finally, an example is worked out to illustrate the analytical results.