Models of manufacturing systems
The class of convex production planning models is an important paradigm in the operations management/operations research literature. The earliest formulation of a convex production planning problem in a discrete-time framework dates back to Modigliani and Hohn  in 1955. They were interested in obtaining a production plan over a finite horizon in order to satisfy a deterministic demand and minimize the total discounted convex costs of production and inventory holding. Since then the model has been further studied and extended in both continuous-time and discrete-time frameworks by a number of researchers, including Johnson , Arrow, Karlin, and Scarf , Veinott , Adiri and Ben-Israel , Sprzeuzkouski , Lieber , and Hartl and Sethi . A rigorous formulation of the problem along with a comprehensive discussion of the relevant literature appears in Bensoussan, Crouhy, and Proth .
KeywordsManufacturing System Setup Cost Admissible Control Part Type Wafer Fabrication
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