Average-cost control of stochastic manufacturing systems.
This book is a study on the optimal control of manufacturing systems subject to breakdowns and repairs. The first and the third author published another monograph on a similar subject [Hierarchical decision making in stochastic manufacturing systems. Basel: Birkhäuser (1994; Zbl 0923.90002)]. They considered a discounted cost criterion; now the cost is a long-run average cost with emphasis on stationary behaviour described by stationary distributions. Other related studies of other authors involve singular perturbations in Markov decision problems, diffusion approximations (Kushner,\dots), and time-scale separation for hierarchical decision making (Gershwin,\dots), where asymptotic results associated to slow processes lead to certain decisions, and other decisions are then devised to handle short-term fluctuations. The book could be brought into the context of the first type of studies, but within the perspective of stochastic optimal control and not Markov decision processes. The second approach raises issues regarding approximation capability for near-optimal policies. Here, great care is given to near to optimal approximating configurations; it is desired that slight changes in performance are associated to slight changes in policy, so that computation of performing policies can be handled realistically. The third approach is related to the book cited above. First, the authors describe the types of manufacturing systems that they consider: parallel machines (producing multiple products or a single product), a single product dynamic flowshop (series connection of producing units), a dynamic flowshop (parallel machines with a feedback-type structure). Second, the authors consider the existence and characterization of optimal control using the Hamilton-Jacobi-Bellman equation and a verification theorem. A chapter deals with risk sensitive control in the context of parallel machines. Third, since optimal solutions, as a rule, cannot be computed, the authors consider near-optimal policies for approximating configurations. Convergence rates of the long-run average cost for the original problem to that of the limiting problem are established; and error estimates for the controls are provided, too. A pendant to the previous chapter on risk-sensitive control is available in this part. Another part considers related open problems. Six appendices provide mathematical technical support (finite-state Markov chains, convergence and error estimates of Markov chains, convex sets and functions, viscosity solutions of HJB equations, discounted costs problems, miscellanea). 153 references are given. There is an author index as well as a subject index. This book is a useful reference on the stochastic optimal control of manufacturing systems and is recommended.
optimal control of manufacturing systems
scientific article; zbMATH DE number 2173790