Parametric methods of apportionment, rounding and production

Balinski, Michel; Ramírez, Victoriano

doi:10.1016/s0165-4896(98)00027-4

Cited by 48 publications

(16 citation statements)

References 13 publications

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“…Moreover, they are cyclic generating cyclic JIT sequences: for two instances of the JIT sequencing D1 = d1, d2, · · · , dn, and D2 = kD1 = kd1, kd2, · · · , kdn, the sequence for D2 is obtained by k repetitions of the sequence for problem D1. As δ increases from 0 to 1, seats are given up by the smaller states in favor of the larger states [25] . That is, a parametric method φ α gives up to another parametric method φ β if and only if α < β.…”

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

confidence: 99%

“…However, the impossibility theorem of Balinski and Young in [12] puts a limitation that there is no perfect apportionment method satisfying all properties at a time. The JIT sequencing problem in terms of parametric divisor methods is studied in [25]. Jozefowska et al [27] characterized some of the algorithms of JIT sequencing via apportionment theory with suitable transformation of the problems.…”

Section: From Apportionment Theory To Jit Sequencingmentioning

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: From Apportionment Theory To Jit Sequencingmentioning

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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“…(Even if the electors opted to retain MMP in 2011 the referendum ballot included a second question asking which of four other systems they would prefer if MMP was to be replaced.) Balinski and Ramirez Gonzales 1999;Pukelsheim 2006Pukelsheim , 2009 but as yet not for elections to national legislatures. 19 Much was done to educate the electorate regarding the various electoral systems on the referendum menu, but little on the possible consequences in terms of the allocation of power.…”

Section: Postscript 2011mentioning

confidence: 99%

Power, Voting, and Voting Power: 30 Years After

Holler¹,

Nurmi²

2013

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“…To ensure a representative randomized sampling, we employed a stratified sampling design (Wildi 1986) and developed a ranking method based on the d'Hondt divisor rules procedure (Balinski and Ramirez 1999;Palomares and Ramirez 2003;Taagepera and Shugart 1989). For this purpose, Fig.…”

Section: Spatial Layoutmentioning

confidence: 99%

The BIOTA Biodiversity Observatories in Africa—a standardized framework for large-scale environmental monitoring

Jürgens

Schmiedel

Haarmeyer

et al. 2011

Environ Monit Assess

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The international, interdisciplinary biodiversity research project BIOTA AFRICA initiated a standardized biodiversity monitoring network along climatic gradients across the African continent. Due to an identified lack of adequate monitoring designs, BIOTA AFRICA developed and implemented the standardized BIOTA Biodiversity Observatories, that meet the following criteria (a) enable long-term monitoring of biodiversity, potential driving factors, and relevant indicators with adequate spatial and temporal resolution, (b) facilitate comparability of data generated within different ecosystems, (c) allow integration of many disciplines, (d) allow spatial up-scaling, and (e) be applicable within a network approach. A BIOTA Observatory encompasses an area of 1 km(2) and is subdivided into 100 1-ha plots. For meeting the needs of sampling of different organism groups, the hectare plot is again subdivided into standardized subplots, whose sizes follow a geometric series. To allow for different sampling intensities but at the same time to characterize the whole square kilometer, the number of hectare plots to be sampled depends on the requirements of the respective discipline. A hierarchical ranking of the hectare plots ensures that all disciplines monitor as many hectare plots jointly as possible. The BIOTA Observatory design assures repeated, multidisciplinary standardized inventories of biodiversity and its environmental drivers, including options for spatial up- and downscaling and different sampling intensities. BIOTA Observatories have been installed along climatic and landscape gradients in Morocco, West Africa, and southern Africa. In regions with varying land use, several BIOTA Observatories are situated close to each other to analyze management effects.

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Parametric methods of apportionment, rounding and production

Abstract: The class of ''parametric'' methods of apportionment, of rounding, or for minimizing the variation of production rates in just-in-time production systems is characterized in several different ways that depend on the underlying qualitative behavior of its solutions.

Cited by 48 publications

References 13 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

Power, Voting, and Voting Power: 30 Years After

The BIOTA Biodiversity Observatories in Africa—a standardized framework for large-scale environmental monitoring

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