Optimal control of parallel machine systems

Abstract

Thompson and Sethi [192] 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 [18] 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.