A simple approach to the product rate variation problem via axiomatics

Balinski, Michel; Shahidi, Niousha

doi:10.1016/s0167-6377(98)00008-x

Cited by 24 publications

(13 citation statements)

References 8 publications

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“…There are infinitely many parametric divisor functions lying between a and a + 1 depending upon the value of δ such that 0 δ 1. Balinski and Shahidi [8] concluded that the method W with δ = 1/2 is simply the best method since it respects priorities and it is cyclic and equilibrated. We identify the two slightly new divisors with better performance in Section 6, to which we call mean-based divisors.…”

Section: Theorem 3 An Apportionment Methods M Is House Monotone and Cmentioning

confidence: 99%

“…This heuristic shows that an earliest due date (EDD) sequence minimizes the sum of squared deviation between the ideal time and actual time in which given unit is actually produced. Balinski and Shahidi [8] proposed another type of deviation, aiming to minimize the variation of production rates from product to products. We have presented its linkage with apportionment problem in Section 8.2 in terms of local deviation measure.…”

Section: Brief Literature Reviewmentioning

confidence: 99%

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An efficient frontier for sum deviation JIT sequencing problem in mixed-model systems via apportionment

Dhamala

Thapa

2012

Int. J. Autom. Comput.

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In this paper, the sum deviation just-in-time (JIT) sequencing problem in mixed-model production systems is studied relating with the discrete apportionment problem together with their respective mathematical formulations. The assignment formulation for the first problem is briefly discussed followed by the existence of JIT cyclic sequences. Presenting the concise discussion on divisor methods for the discrete apportionment problem, we have proposed two mean-based divisor functions for this problem claiming that they are better than the existing divisors; hence, we found a better bound for the JIT sequencing problem. The linkage of both the problems is characterized in terms of similar type of objective functions. The problems are shown equivalent via suitable transformations and similar properties. The joint approaches for the two problems are discussed in terms of global and local deviations proposing equitably efficient solution.

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Section: Theorem 3 An Apportionment Methods M Is House Monotone and Cmentioning

confidence: 99%

Section: Brief Literature Reviewmentioning

confidence: 99%

An efficient frontier for sum deviation JIT sequencing problem in mixed-model systems via apportionment

Dhamala

Thapa

2012

Int. J. Autom. Comput.

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“…The constraints (5) guarantee that processing of a model copy in cycle t + 1 by station k cannot start before this station has completed the preceding unit in cycle t. Work is restricted to the stations' borders by constraints (6) and the nonnegativity constraints for s kt in (7). Equations (8) ensure that the line is in a initial state prior to and at the end of the planning horizon.…”

Section: Problem Statementmentioning

confidence: 99%

“…Additionally, the contribution MAS (multi-agent system) is considered. [ | ] M, P Aigbedo (2004) [P, euc | ] P Aigbedo and Monden (1996) [O, euc; P, euc | ] C Aigbedo and Monden (1997) [O, euc; P, euc; W, euc | k, n] M, HS Balinski and Shahidi (1998) [ Cakir and Inman (1993) [P, abs | ] M, HS Caridi and Sianesi (2000) [P | n 4,w ] M, MAS Cheng and Ding (1996) [ | ] M, HS, C Ding and Cheng (1993a+b) [ | ] M, HS Ding et al (2006) [O; P ; W | k] P, V, HS Duplaga et al (1996) [P | ] HS Duplaga and Bragg (1998) [ HS Inman and Bulfin (1991) [ HS Inman and Bulfin (1992) [P | n 4,w ] M, HS Korkmazel and Meral (2001) [ Kubiak and Sethi (1991) [ | ] M, E Kubiak and Sethi (1994) [ Kurashige et al (1999Kurashige et al ( , 2002 [W, euc | k] M, HS, HM Leu et al (1996) [P | ] HM Leu et al (1997) [ Miltenburg and Goldstein (1991) [P ; W | n w , k] M, HS, P Miltenburg and Sinnamon (1989) [P | n 4,w ] M, HS Miltenburg and Sinnamon (1992) [P | n w ] M, HS Miltenburg and Sinnamon (1995) [P | n 4,w ] P Miltenburg et al (1990) [ | ] M, E Monden (1998) [P | ] HS Morabito and Kraus (1995) [P | n 4,w ] M, P, HS Moreno and Corominas (2006) [abs, minmax | ] M, E Ng and Mak (1994) [ | ] M, B, E Steiner and Yeomans (1993) [abs, minmax | ] M, P, E Steiner and Yeomans (1996) [P, abs, minmax | n] M, P, E Sumichrast and Clayton (1996) [ Both "minimization of work overload" and "leveling part usage" turned out to be valuable but often conflicting objectives for model sequencing. Consequently, several hybrid approaches have been developed.…”

Section: Operational Characteristicsmentioning

confidence: 99%

Sequencing mixed-model assembly lines: Survey, classification and model critique

Boysen

Fliedner

Schöll

2009

European Journal of Operational Research

374

180

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Manufacturers in a wide range of industries nowadays face the challenge of providing a rich product variety at very low cost. This typically requires the implementation of cost efficient, flexible production systems. Often, so called mixed-model assembly lines are employed, where setup operations are reduced to such an extent that various models of a common base product can be manufactured in intermixed sequences. However, the observed diversity of mixed-model lines makes a thorough sequence planning essential for exploiting the benefits of assembly line production. This paper reviews and discusses the three major planning approaches presented in the literature, mixed-model sequencing, car sequencing and level scheduling, and provides a hierarchical classification scheme to systematically record the academic efforts in each field and to deduce future research issues.

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“…The roots of the general approach we employ lie in problems arising in balanced just-in-time (JIT) scheduling (see for example [ 10], [11]). In this application a factory must produce multiple products.…”

Section: Minimizing the Deviation Between The Actual And Ideal Allocamentioning

confidence: 99%

A General Approach to Equity in Traffic Flow Management and Its Application to Mitigating Exemption Bias in Ground Delay Programs

Vossen

Ball

Hoffman

et al. 2003

Air Traffic Control Quarterly

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A primary objective of the FAA's ATM functions is to provide fair and equitable access to the National Air Space. Traditionally, the FAA has interpreted fairness as prioritizing flights on a "first-come, first-served" basis. The allocation procedures introduced under Collaborative Decision Making (CDM), however, represent a departure from this paradigm: allocations are based on carriers' original flight schedules. Yet in spite of these changes, the concept of fairness under CDM is largely left implicit in the procedures. Different and even conflicting concepts are sometimes used to describe these procedures. Moreover, the achievement of equitable allocations is often complicated by practical considerations. This paper describes a general framework for equitable allocation procedures within the context of ATM, and illustrates its use in reducing certain systematic biases that exist under current procedures. We also discuss other applications of this approach, and summarize practical considerations and implementation issues.

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A simple approach to the product rate variation problem via axiomatics

Cited by 24 publications

References 8 publications

An efficient frontier for sum deviation JIT sequencing problem in mixed-model systems via apportionment

An efficient frontier for sum deviation JIT sequencing problem in mixed-model systems via apportionment

Sequencing mixed-model assembly lines: Survey, classification and model critique

A General Approach to Equity in Traffic Flow Management and Its Application to Mitigating Exemption Bias in Ground Delay Programs

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