Abstract
An effective methodology is reported for determining the optimal lot size of batch processing and storage networks which include uncertain demand forecasting. We assume that any given storage unit can store one material type which can be purchased from suppliers, internally produced, infernally consumed, transported to or from other sites and/or sold to customers. We further assume that a storage unit is connected to all processing and transportation stages that consume/produce or move the material to which that storage unit is dedicated. Each processing stage transforms a set of feedstock materials or intermediates into a set of products with constant conversion factors. A batch transportation process can transfer one material or multiple materials at once between sites. The objective for optimization is to minimize the probability averaged total cost composed of raw material procurement, processing setup, transportation setup and inventory holding costs as well as the capital costs of processing stages and storage units. A novel production and inventory analysis formulation, the PSW(Periodic Square Wave) model, provides useful expressions for the upper/lower bounds and average level of the storage inventory. The expressions for the Kuhn-Tucker conditions of the optimization problem can be reduced to two sub-problems. The first yields analytical solutions for determining lot sires while the second is a separable concave minimization network flow subproblem whose solution yields the average material flow rates through the networks for the given demand forecast scenario. The result of this study will contribute to the optimal design and operation of the global supply chain.
