Cutting Plane Technique for the Set Covering Problem with Linear Fractional Functional

Arora, Sonika; Swarup, Kanti; Puri, Munish

doi:10.1002/zamm.19770571006

Cited by 8 publications

(11 citation statements)

References 6 publications

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“…Many researchers have developed techniques for solving this type of problem, including methods such as linearization (Williams 1974), branch‐and‐bound (Agrawal 1977, Robillard 1971), cutting plane (Granot and Granot 1977, Grunspan and Thomas 1973), enumerative (Arora et al. 1977, Granot and Granot 1976), approximation (Hashizume et al. 1987), and parametric (Radzik 1998, Wang et al.…”

Section: Literature Reviewmentioning

confidence: 99%

Supply Constrained Location‐Distribution in Not‐for‐Profit Settings

Park

Berenguer

2020

Production and Operations Management

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Inspired by the World Food Programme's activity in the post‐civil war food crisis in Angola, this study proposes a systematic approach to address the location distribution problem in not‐for‐profit settings, where a limited volume of supply has to be allocated to different demand regions. The use of utility functions is key in our framework because it allows the decision‐maker to establish priorities by representing the heterogeneous effects of distributing supply to different demand locations (location effect) and to different individuals in the same demand location (diminishing returns effect). We propose the use of two fractional objectives with the utility functions embedded into them: an efficiency measure and a new inequity measure related to the Gini coefficient. The suggested problem has the form of a bi‐objective integer linear fractional program and our resolution optimization technique is designed to solve for multiple fractional objective measures. Novel analytical results for the worst‐case performance of the proposed resolution technique are provided. Our numerical experiments assess computational efficiency and provide concrete managerial prescriptions. Finally, an illustrative application of our approach in the context of the food crisis in Angola is presented based on an efficiency‐inequity trade‐off analysis.

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Section: Literature Reviewmentioning

confidence: 99%

Supply Constrained Location‐Distribution in Not‐for‐Profit Settings

Park

Berenguer

2020

Production and Operations Management

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“…The problem has been formulated using the model of set covering problem (SCP) for LFP 1 . We have used the Section II and III to solve this problem.…”

Section: Condition Of Fathoming Partial Feasible Solution For 0-1mentioning

confidence: 99%

“…Many real life oriented models can be formulated with this type of structure such as set covering problem 1 . In the next Section, we summarize the idea of additive algorithm.…”

Section: Introductionmentioning

confidence: 99%

Additive Algorithm for Solving 0-1 Integer Linear Fractional Programming Problem

Arefin

Hossain

Islam

2013

Dhaka Univ. J. Sci.

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In this paper, we present additive algorithm for solving a class of 0-1 integer linear fractional programming problems (0-1 ILFP) where all the coefficients at the numerator of the objective function are of same sign. The process is analogous to the process of solving 0-1 integer linear programming (0-1 ILP) problem but the condition of fathoming the partial feasible solution is different from that of 0-1 ILP. The procedure has been illustrated by two examples.

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“…Tawarmalani et al [49] consider a facility location problem, where a fixed number of facilities need to be located to service customers locations with the objective of maximizing a market share. Arora et al [2] study a class of set covering problems in the context of airline crew scheduling that aim at covering all flights operated by an airline company. Furthermore, many combinatorial optimization problems can be formulated in the form (1) including the minimum fractional spanning tree problem [13,50], the maximum mean-cut problem [26,42] and the maximum clique ratio problem [45].…”

Section: Introductionmentioning

confidence: 99%

Fractional 0-1 programming and submodularity

Han¹,

Gómez²,

Prokopyev³

2020

Preprint

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In this note we study multiple-ratio fractional 0-1 programs, a broad class of N P-hard combinatorial optimization problems. In particular, under some relatively mild assumptions we provide a complete characterization of the conditions, which ensure that a single-ratio function is submodular. Then we illustrate our theoretical results with the assortment optimization and facility location problems, and discuss practical situations that guarantee submodularity in the considered application settings. In such cases, near-optimal solutions for multiple-ratio fractional 0-1 programs can be found via simple greedy algorithms.

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Cutting Plane Technique for the Set Covering Problem with Linear Fractional Functional

Cited by 8 publications

References 6 publications

Supply Constrained Location‐Distribution in Not‐for‐Profit Settings

Supply Constrained Location‐Distribution in Not‐for‐Profit Settings

Additive Algorithm for Solving 0-1 Integer Linear Fractional Programming Problem

Fractional 0-1 programming and submodularity

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