Lot-Sizing Models Using Multi-dimensional Clearing Functions

The order release models described in this volume rely heavily on the functional relationship between the expected output of a production resource and its expected workload which, as discussed in Chap. 2 for the case of steady-state queues, is related to the expected cycle time by Little’s Law. This relationship is significantly affected by various decision rules used within the PPC system, such as scheduling policies on the shop floor. Lot sizing, the decision as to how much of a product to produce each time a machine is set up for the product, is of particular importance in this respect. For a given production quantity, determined by the master production schedule, the lot sizes influence capacity utilization (via the amount of setup time required on the resource in a planning period), the mean and variance of the interarrival times (via the number and size of production lots), and the mean and variance of the service times (via the lot sizes). Following the discussion in Chap. 2 , we begin this section with insights from simple queueing models, and then show how these can be used to develop a system of multivariate clearing functions to address a dynamic lot-sizing problem.