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Abstract

This study is to find the analytic solution for determining the optimal capacity (lot size) of a multiproduct, sequential, multistage production and inventory system to meet the finished product demand. It overcame the limitation of the classical lot sizing method developed based on the single product and single-stage assumption. The superstructure of the plant consisted of a network of serially and/or parallel interlinked batch processes and storage units. The processes involve chemical reactions with multiple feedstock materials and multiple products, as well as mixing, splitting, or transportation of materials. The objective function for optimization is minimizing the total cost composed of setup and inventory holding costs, as well as the capital costs of constructing processes and storage units. The resulting simple analytic solution can greatly enhance the proper and quick investment decision for the preliminary plant design problem confronted with diverse economic situations.