Titlebook: Hierarchical Decision Making in Stochastic Manufacturing Systems; Suresh P. Sethi,Qing Zhang Book 1994 Springer Science+Business Media New

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Models of manufacturing systems of researchers, including Johnson [100], Arrow, Karlin, and Scarf [8], Veinott [199], Adiri and Ben-Israel [1], Sprzeuzkouski [184], Lieber [124], and Hartl and Sethi [83]. A rigorous formulation of the problem along with a comprehensive discussion of the relevant literature appears in Bensoussan, Crouhy, and Proth [17].

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Optimal control of dynamic flowshopsachines needs to be nonnegative, the problem is inherently a state-constrained problem. Our objective is to choose admissible input rates to various machines in order to minimize a sum of expected discounted inventory/backlog costs and production costs over the infinite horizon.

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Hierarchical production and setup scheduling in a single machine systemand Srivat-san and Gershwin [187]. They have examined various possible heuristic policies and have carried out numerical computations and simulations. However, they have not studied the policies from the viewpoint of asymptotic optimality.