Linear Programming and Network Flows

Bazaraa, Mokhtar S.; Jarvis, John J.; Sherali, Hanif D.

doi:10.1002/9780471703778

Cited by 651 publications

(956 citation statements)

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“…of Bazaraa, Jarvis, and Sherali [5] and the above expressions that if µ 11 µ 22 − µ 21 µ 12 > 0, then x is the unique optimal solution of (P). Combining this with S x = S, we have the uniqueness of the optimal policy in the class of Markovian stationary deterministic policies.…”

Section: Is Blocked or Station 2 Is Starved And Assigns Both Servers mentioning

confidence: 99%

“…In order to do this, we verify that condition (3.6) on page 94 of Bazaraa, Jarvis, and Sherali [5] is satisfied for all nonbasic variables. Using the notation in Bazaraa, Jarvis, and Sherali [5], let c B be the vector of the coefficients of the positive elements of x in the objective function of (P) and B be the matrix of the coefficients of the positive elements of x in the constraint matrix of (P). We have x((B + 2, 0), a 22 ), respectively, in the objective function of (P).…”

Section: Is Blocked or Station 2 Is Starved And Assigns Both Servers mentioning

confidence: 99%

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Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Andradóttir¹,

Ayhan²,

Down³

2008

Prob. Eng. Inf. Sci.

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Consider a tandem queueing network with an infinite supply of jobs in front of the first station, infinite room for completed jobs after the last station, finite buffers between stations, and a number of flexible servers who are subject to failures. We study the dynamic assignment of servers to stations with the goal of maximizing the long-run average throughput. Our main conclusion is that the presence of server failures does not have a major impact on the optimal assignment of servers to stations for the systems we consider. More specifically, we show that when the servers are generalists, any non-idling policy is optimal, irrespective of the reliability of the servers. We also provide theoretical and numerical results for Markovian systems with two stations and two or three servers that suggest that the structure of the optimal server assignment policy does not depend on the reliability of the servers, and that ignoring server failures when assigning servers to stations yields near-optimal throughput. Finally, we present numerical results that illustrate that simple server assignment heuristics designed for larger systems with reliable servers also yield good throughput performance in Markovian systems with three stations and three failure-prone servers.

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Section: Is Blocked or Station 2 Is Starved And Assigns Both Servers mentioning

confidence: 99%

Section: Is Blocked or Station 2 Is Starved And Assigns Both Servers mentioning

confidence: 99%

Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Andradóttir¹,

Ayhan²,

Down³

2008

Prob. Eng. Inf. Sci.

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“…The optimization model includes constraints, decision variables, and an objective function (Bazaraa et al 1990). The main purpose of this model is to find the best outcome like maximum profit or minimum cost.…”

Section: Introductionmentioning

confidence: 99%

Impact of climate change on food security in Malaysia: economic and policy adjustments for rice industry

Vaghefi

Shamsudin

Radam

et al. 2015

Journal of Integrative Environmental Sciences

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“…If the variables λ n+1 xy with (x, y) in ( R n+1 ) c are the non basic variables of the T n+1 problem, then the set of the extreme points of the T n+1 problem coincides with the set of the extreme points of the LP n+1 problem (see Bazaraa et al, 2010, Chapter 3).…”

Section: Remark 4 Let Be ( Rmentioning

confidence: 99%

“…and under this condition the T n problem has an optimal solution (see Bazaraa et al, 2010). Now, if { λ n xy } is an optimal solution to a T n problem, the measure is defined as Gabriel et al, 2010, Theorem 4.5).…”

Section: Remark 3 Note Thatmentioning

confidence: 99%

A metaheuristic for a numerical approximation to the mass transfer problem

Avendaño-Garrido

Gabriel-Arguelles

Quintana-Torres

et al. 2016

International Journal of Applied Mathematics and Computer Science

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This work presents an improvement of the approximation scheme for the Monge-Kantorovich (MK) mass transfer problem on compact spaces, which is studied by Gabriel et al. (2010), whose scheme discretizes the MK problem, reduced to solve a sequence of finite transport problems. The improvement presented in this work uses a metaheuristic algorithm inspired by scatter search in order to reduce the dimensionality of each transport problem. The new scheme solves a sequence of linear programming problems similar to the transport ones but with a lower dimension. The proposed metaheuristic is supported by a convergence theorem. Finally, examples with an exact solution are used to illustrate the performance of our proposal.

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Linear Programming and Network Flows

Cited by 651 publications

References 0 publications

Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Maximizing the Throughput of Tandem Lines With Flexible Failure-Prone Servers and Finite Buffers

Impact of climate change on food security in Malaysia: economic and policy adjustments for rice industry

A metaheuristic for a numerical approximation to the mass transfer problem

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