Solving the generalized apportionment problem through the optimization of discrepancy functions

Bautista, Joaquı́n; Companys, Ramón; Corominas, Albert

doi:10.1016/s0377-2217(00)00110-7

Cited by 4 publications

(1 citation statement)

References 9 publications

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“…Among the various methods, we have considered divisor methods to link up with sum deviation JIT sequencing problem. The generalized apportionment problem is studied in [13] via the optimization of discrepancy functions, where a more general formalization of the problem and an optimization procedure are presented together with some properties and examples to optimize some specific functions. Moreover, this procedure can be regarded as a generalization of the divisor methods.…”

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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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: 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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A branch and bound algorithm for the response time variability problem

García‐Villoria

Corominas

Delorme

et al. 2012

J Sched

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The response time variability problem (RTVP) is an NP-hard scheduling problem that has been studied intensively recently and has a wide range of real-world applications in mixed-model assembly lines, multithreaded computer systems, network environments and others. The RTVP arises whenever products, clients or jobs need to be sequenced in order to minimise the variability in the time between two successive points at which they receive the necessary resources. To date, the best exact method for solving this problem is a mixed integer linear programming (MILP) model, which solves to optimality most of instances with up to 40 units to be scheduled in a reasonable amount of time. The goal of this paper is to increase the size of the instances that can be solved to optimality. We have designed an algorithm based on the branch and bound (B&B) technique to take advantage of the particular features of the problem. Our computational experiments show that the B&B algorithm is able to solve larger instances with up to 55 units to optimality in a reasonable timePeer ReviewedPostprint (published version

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Beyond the Cambridge Compromise algorithm towards degressively proportional allocations

2017

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Although proportional allocation methods are well-known and widely used in the parliamentary tradition, they cannot be applied in a wide variety of cases. Such problems occur in the European Parliament, where a constitutional principle is to assure that less populous countries will not be dominated by the others, which implies that allocations have to be degressively proportional. However, under this assumption an exhaustive search of the solution space is intractable. To solve the problem, the Cambridge Compromise algorithm was proposed, which is durable, transparent, impartial to politics and unambiguous, but the allocations obtained are not degressively proportional. Therefore, we propose an allocation algorithm derived from operations research that inherits the transparency of the Cambridge Compromise and produces an unambiguous degressively proportional allocation. Hence, the paper aims at testing our alternative allocation method and comparing its outcomes during computational analysis.

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Solving the generalized apportionment problem through the optimization of discrepancy functions

Cited by 4 publications

References 9 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

A branch and bound algorithm for the response time variability problem

Beyond the Cambridge Compromise algorithm towards degressively proportional allocations

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