Analytical Evaluation of Hierarchical Planning Systems

Dempster, M. A. H.; Fisher, Marshall L.; Jansen, Leo; Lageweg, B.J.; Lenstra, Jan Karel; Kan, A. H. G. Rinnooy

doi:10.1287/opre.29.4.707

Cited by 110 publications

(48 citation statements)

References 7 publications

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“…Since the large number of machines, workers, part types, and operations are involved in real production systems, hierarchical structures have been proposed for production control in order to reduce the problem size and complexity ([121, [13], [14], [15], and [16]). The goal is to replace one large problem by a set of many small ones because latter is invariably easier to solve.…”

Section: Previous Researchmentioning

confidence: 99%

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Scheduling manufacturing systems with work-in-process inventory control: single-part-type systems

Bai

Gershwin

1995

IIE Transactions

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In this paper, a real-time feedback control algorithm is developed for scheduling single-part-type production lines in which there are three important classes of activities: operations, failures, and starvation or blockage. The scheduling objectives are to keep the actual production as close to the demand as possible, and to keep the level of work-in-process inventory as low as possible. By relating the starvation and blockage to the system capacity, the buffer sizes and the target buffer levels are chosen according to the demands and machine parameters.The processing time for each operation is deterministic. Failure and repair times are random. Whenever a machine fails or is starved or blocked, the scheduling system recalculates short term production rates.To begin with, we study a very simple case, a two machine and one part type system, to get insight into the buffer effects and production control policies. Using the relationship between system capacity and starvation or blockage, we find desirable buffer levels and buffer sizes. The production control policy is determined to meet the system performance requirements concerning low WIP inventory and tardiness.The results from the simple case are extended to N-machine, one-part-type systems.

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Section: Previous Researchmentioning

confidence: 99%

“…The length of such an interval is 1/ri + -pi. 13 Define F, to be the frequency of failure of Machine i. which is given by…”

Section: Av(t))mentioning

confidence: 99%

Scheduling manufacturing systems with work-in-process inventory control: single-part-type systems

Bai

Gershwin

1995

IIE Transactions

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“…Usually the solution methods consist of solving the problems at the different levels separately and glue them together. Dempster et al [7,8] gave the first mathematically rigorous analysis of such a hierarchical planning system. They presented the result on the hierarchical scheduling problem exposed in Section 4.…”

Section: Notesmentioning

confidence: 99%

Stochastic Integer Programming

Stougie¹,

Vlerk²

1988

Springer Series in Computational Mathematics

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Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solutions. However, efficiency in the complexity theoretical sense is usually not taken into account. Quality statements mostly remain restricted to convergence to an optimal solution without accompanying implications on the running time of the algorithms for attaining more and more accurate solutions.However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared. In this direction we find both probabilistic analysis and worst-case analysis. There have been studies on performance ratios and on absolute divergence from optimality.Recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems. Polynomial time approximation algorithms and their performance guarantees for stochastic linear and integer programming problems have seen increasing research attention only very recently.Approximation in the traditional stochastic programming sense will not be discussed in this chapter. The reader interested in this issue is referred to surveys on stochastic programming, like the Handbook on Stochastic Programming [38] or the text books [3,21,35]. We concentrate on the studies of approximation algorithms which are more similar in nature to those for combinatorial optimization.

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“…· Given the formidable difficulty of stochastic integer programming, most research in the area has so far concentrated on the design and analysis of approximation algorithms. This approach is exemplified in (DEMPSTER et al (1981(DEMPSTER et al ( ), (1983; FRENK et al (1984); MARCHETII-SPACCAMELA et al (1984)), where simple heuristics are proposed for a variety of two-stage production and distribution planning problems. Probabilistic analyses of the heuristics then provide exact statements about the quality of the approximations, such as some form of asymptotic optimality.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Integer Programming by Dynamic Programming

Lageweg¹,

Lenstra²,

Kan

et al. 1988

Springer Series in Computational Mathematics

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Stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the. design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to exploit the structure of two-stage scheduling, bin packing and multi.knapsack problems. Numerical results for small instances of these problems are presented.

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Analytical Evaluation of Hierarchical Planning Systems

Cited by 110 publications

References 7 publications

Scheduling manufacturing systems with work-in-process inventory control: single-part-type systems

Scheduling manufacturing systems with work-in-process inventory control: single-part-type systems

Stochastic Integer Programming

Stochastic Integer Programming by Dynamic Programming

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