Optimal Production Planning in a Stochastic N-machine Flowshop with Long-Run Average Cost


Book Description

This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines that are subject to breakdown and repair. The machine capacities are modeled as Markov chains. Since the number of parts in the internal buffers between any two the problem is inherently a state constrained problem. The objective is choose the input rates at the various machines over time in order to meet formulated as a stochastic dynamic programming problem. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the potential function.




On Optimality of Stochastic N-Machine Flowshop with Long-Run Average Cost


Book Description

This paper is concerned with the problem of production planning in a stochastic manufacturing system with serial machines that are subject to breakdown and repair. The machine capacities are modeled by a Markov chain. The objective is to choose the input rates at the various machines over time in order to meet the demand for the system's production at the minimum long-run average cost of production and surplus, while ensuring that the inventories in internal buffers between adjacent machines remain nonnegative. The problem is formulated as a stochastic dynamic program. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the potential function.




Average Cost Optimal Policy for a Stochastic Two-Machine Flowshop with Limited Work-in-Process


Book Description

We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.




Average-Cost Control of Stochastic Manufacturing Systems


Book Description

This book articulates a new theory that shows that hierarchical decision making can in fact lead to a near optimization of system goals. The material in the book cuts across disciplines. It will appeal to graduate students and researchers in applied mathematics, operations management, operations research, and system and control theory.




Optimal Production Planning in Stochastic Jobshops with Long-Run Average Cost


Book Description

We consider a production planning problem for a general jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are modeled as Markov chains. The objective is to choose the rates of production of the final products and intermediate parts on the various machines over time in order to meet the demand for the system's production at the minimum long-run average cost of production and surplus. The problem is formulated as a stochastic dynamic program. We prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the so-called potential function. Finally, we construct a potential function in the special case of a jobshop producing only one final product.




Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost


Book Description

This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton-Jacobi-Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.




Hierarchical Production Control in a Stochastic N-Machine Flowshop with Long-Run Average Cost


Book Description

This paper presents an asymptotic analysis of stochastic manufacturing systems consisting of machines in tandem subject to breakdown and repair and facing a constant demand, as the rates of change of the machine states approach infinity. This situation gives rise to a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem converges to the long-run average cost of the limiting problem.A method of shrinking and entire lifting is introduced in order to construct the near optimal controls for the original problem by using near optimal controls of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem is established. This helps in providing an error estimate for the constructed open-loop asymptotic optimal control.




Optimization, Dynamics, and Economic Analysis


Book Description

This book includes a collection of articles that present recent developments in the fields of optimization and dynamic game theory, economic dynamics, dynamic theory of the firm, and population dynamics and non standard applications of optimal control theory. The authors of the articles are well respected authorities in their fields and are known for their high quality research in the fields of optimization and economic dynamics.




Stochastic Theory and Control


Book Description

This volume contains almost all of the papers that were presented at the Workshop on Stochastic Theory and Control that was held at the Univ- sity of Kansas, 18–20 October 2001. This three-day event gathered a group of leading scholars in the ?eld of stochastic theory and control to discuss leading-edge topics of stochastic control, which include risk sensitive control, adaptive control, mathematics of ?nance, estimation, identi?cation, optimal control, nonlinear ?ltering, stochastic di?erential equations, stochastic p- tial di?erential equations, and stochastic theory and its applications. The workshop provided an opportunity for many stochastic control researchers to network and discuss cutting-edge technologies and applications, teaching and future directions of stochastic control. Furthermore, the workshop focused on promoting control theory, in particular stochastic control, and it promoted collaborative initiatives in stochastic theory and control and stochastic c- trol education. The lecture on “Adaptation of Real-Time Seizure Detection Algorithm” was videotaped by the PBS. Participants of the workshop have been involved in contributing to the documentary being ?lmed by PBS which highlights the extraordinary work on “Math, Medicine and the Mind: Discovering Tre- ments for Epilepsy” that examines the e?orts of the multidisciplinary team on which several of the participants of the workshop have been working for many years to solve one of the world’s most dramatic neurological conditions. Invited high school teachers of Math and Science were among the part- ipants of this professional meeting.




Hierarchical Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost


Book Description

This paper deals with an asymptotic analysis of hierarchical production planning in stochastic manufacturing systems consisting of a single or parallel failure-prone machines producing a number of different products without attrition. The objective is to choose production rates over time in order to minimize the long-run average expected cost of production and surplus. As the rate of machine break-down and repair approaches infinity, the analysis results in a limiting problem in which the stochatic machine capacity is replaced by the equilibrium mean capacity. The optimal value for the original problem is proved to converge to the optimal value of the limiting problem. This suggests a heuristic to construct an open-loop control for the original stochastic problem from the open-loop control of the limiting deterministic problem. We as well as obtain error bound estimates for constructed open-loop controls.