Hierarchical Decomposition Of Production And Capacity Investment Decisions In Stochastic Manufacturing Systems

This paper is concernced with hierarchical decisions regarding production and investment in capacity in manufacturing systems with production subject to breakdown and repair. The production capacity can be increased by investing continuously in new capacity which is available upon completion. The decision variables are the rates of production and investment in capacity. The investment rate is assumed to have an upper bound. If, as assumed, the rates of breakdown and repair of production equipment are much larger than the rate of discounting of costs, the given problem can be approximated by a simpler problem in which the stochastic production capacity is replaced by the average capacity. Asymptotically optimal controls for the given problem are constructed from nearly optimal controls of the limiting problem. In addition, we analyze the behavior of the solution as the investment rate is allowed to become arbitrarily large.

One of the most important methods in dealing with the optimization of large, complex systems is that of hierarchical decomposition. The idea is to reduce the overall complex problem into manageable approximate problems or subproblems, to solve these problems, and to construct a solution of the original problem from the solutions of these simpler prob lems. Development of such approaches for large complex systems has been identified as a particularly fruitful area by the Committee on the Next Decade in Operations Research (1988) [42] as well as by the Panel on Future Directions in Control Theory (1988) [65]. Most manufacturing firms are complex systems characterized by sev eral decision subsystems, such as finance, personnel, marketing, and op erations. They may have several plants and warehouses and a wide variety of machines and equipment devoted to producing a large number of different products. Moreover, they are subject to deterministic as well as stochastic discrete events, such as purchasing new equipment, hiring and layoff of personnel, and machine setups, failures, and repairs.

We present a new paradigm of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shop floor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and The results are obtained via an asymptotic analysis of a manufacturing system with convex costs, constant demand, and with machines subject to random breakdown and repair. The decision variables are purchase time of a new machine at a given fixed cost and production plans before and after the costs of investment, production, inventories, and backlogs. If the rate of change in machine states such as up and down is assumed to be much larger than the rate of discounting costs, one obtains a simpler limiting mean. We develop methods for constructing asymptotically optimal decisions for the original problem from the optimal decisions for the limiting problem. We obtain error estimates for these constructed decisions.

We present an approach of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shopfloor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and production decisions.The results are obtained via an asymptotic analysis of hierarchical investment and production decisions in a manufacturing system with machines subject to breakdown and repair. The demand facing the system is assumed to be a deterministic monotone increasing function. The production capacity can be increased by purchasing a finite number of new machines over time. The control variables are a sequence of purchasing times and a production plan. The rate of change in machine states is assumed to be much larger than the rate of discounting of costs. This gives rise to a limiting problem in which the stochastic machine availability is replaced by the equilibrium mean availability. The value function for the original problem converges to the value function of the limiting problem. Three different methods are developed for constructing decisions for the original problem from the optimal solution of the limiting problem in a way which guarantees the asymptotic optimality of constructed decisions. Finally, it is shown that as the number of machine that could be purchased tends to infinity, the problem approximates the corresponding problem with no limit on number of machine purchases.

Drawn from a conference honoring Gerald L. Thompson, the pioneer of operations research, this volume brings together some of the latest writings of major figures in the field. The volume is divided into four parts: the first part reviews the career and significance of Thompson, the second concentrates on linear and nonlinear optimization, the third looks at network and integer programming, and the fourth provides examples of applications-oriented research in manufacturing. This volume will be an invaluable resource for all scholars and researchers involved in theory and methodology in operations research and management science.

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of different types of events in the system results in decisions that are asymptotically optimal as the rates of some events become large compared to those of others. Manufacturing systems that are addressed include single machine systems, flowshops, and jobshops producing multiple products, incorporate random production capacity and demands, and involve such decisions as production rates, capacity expansion, and promotional campaigns. The paper concludes with a review of computational results and areas of applications.

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of different types of events in the systems results in decisions that are asymptotically optimal as the rates of some events become large compared to those of others. The paper also reviews the research on stochastic optimal control problems associated with manufacturing systems, their dynamic programming equations, existence of solutions of these equations, and verification theorems of optimality for the systems. Manufacturing systems that are addressed include single machine systems, dynamic fowshops, and dynamic jobshops producing multiple products. These systems may also incorporate random production capacity and demands, and decisions such as production rates, capacity expansion, and promotional campaigns are also presented.

We present some insights obtained from the considerable research that has accumulated in proving that a hierarchical decomposition based on the frequencies of occurence of different types of events in the system results in near-optimal decisions as the rates of some events become large compared to those of others. In the simple context of dynamic two-machine flowshops, we observe a capacity loss phenomenon which must be accounted for in any construction of a near-optimal decision. We also show that a threshold-type control known as Kanban control is nearly optimal in some cases and not in others.

Manufacturing systems rarely perform exactly as expected and predicted. Unexpected events, such as order changes, equipment failures and product defects, affect the performance of the system and complicate decision-making. This volume is devoted to the development of analytical methods aiming at responding to variability in a way that limits its corrupting effects on system performance. The book includes fifteen novel chapters that mostly focus on the development and analysis of performance evaluation models of manufacturing systems using decomposition-based methods, Markovian and queuing analysis, simulation, and inventory control approaches. They are organized into four distinct sections to reflect their shared viewpoints: factory design, unreliable production lines, queuing network models, production planning and assembly.