Thus, uneven lot sizes are produced at various stages without the requirement of integer multiple lot sizes. The model determines the start-up and shut-down schedule of each production stage which minimizes the sum of the recurring set-up costs and inventory costs of the system.
Taha and Skeith [9] assume non-instantaneous production, varying lot sizes at different stages and backlogging of unfulfilled demand of finished products. In their model they calculate the optimum lot size of the finished product and allow overproduction of integer multiple lot sizes at those preceding stages where the large set-up cost warrants a holdover of process inventory to subsequent manufacturing cycles.