A continuous approximation procedure for determining inventory distribution schemas within supply chains: gradual and intermittent shipping patterns

The popularity of supply chain integration models is increasing. The research in this paper builds upon prior research and presents an integrated inventory supply chain optimisation model that incorporates the issues of location, production, inventory, and transportation simultaneously. The objective of the current research is to determine the optimal number as well as the optimal size of shipments under a variety of production and shipping rate scenarios. Previous research in this area assumed instantaneous shipping. Herein, this assumption is generalised to include a non-instantaneous, gradual shipping pattern as well as staggered, more intermittent shipping pattern. These two more generalised shipping scenarios (each with several sub-scenarios) are investigated and closed form expressions for the optimal number and the optimal size of shipments for each scenario are obtained. A detailed numerical example is presented to demonstrate the efficacy of the approach.