Optimal control of parallel machine systems
Thompson and Sethi  consider a deterministic single machine, single product production planning model whose purpose is to obtain the production rate over time to minimize an integral representing a discounted quadratic loss function. The model is solved both with and without nonnegative production constraints. It is shown that there exists a turnpike level of inventory, to which the optimal inventory level approaches monotonically over time. The model was generalized by Sethi and Thompson [155, 156] and Bensoussan, Sethi, Vickson, and Derzko  by incorporating an additive white noise term in the dynamics of the inventory process. Moreover, the concept of turnpike inventory level for the stochastic production planning problem was introduced.
KeywordsInventory Level Strict Convexity Optimal Feedback Control Constant Demand Production Planning Problem
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