A computationally stable solution algorithm for linear programs

Arsham, Hossein

doi:10.1016/j.amc.2006.11.031

Cited by 10 publications

(4 citation statements)

References 36 publications

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“…Another version adds the penalty terms, which are the sum of artificial variables with very large, positive coefficients. The latter approach is known as the Big-M method (Arsham, 2006(Arsham, , 2007. Understanding the intuitive notion of Standard-form, artificial variables, and Big-M, may require a greater mathematical sophistica-tion from most students/managers.…”

Section: Standard Simplex Methodsmentioning

confidence: 99%

Foundation of Linear Programming

Arsham

2012

International Journal of Strategic Decision Sciences

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The aim and scope of this paper are the infusion of purposeful action by decision makers with an explicit understanding of analytical linear programming (LP) tools in order that the managers will implement strategic results correctly. The advances in computing software have brought LP tools to the desktop for a variety of applications to support managerial decision-making. However, it is already recognized that current LP tools do not answer the managerial questions satisfactorily. For instance, there is a costly difference between the mathematical and managerial interpretations of sensitivity analysis. The LP software packages provide sensitivity results about the optimality of a basis and not about the optimality of the values of the decision variables, and the shadow prices that are of interest to the manager. Society has developed the largest sensitivity region based on “optimal solution,” not that which “preserves the basis” that allows for simultaneous dependent/independent changes. The aim and results of this article are found further in the work.

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Section: Standard Simplex Methodsmentioning

confidence: 99%

Foundation of Linear Programming

Arsham

2012

International Journal of Strategic Decision Sciences

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“…If the origin point is infeasible, it needs to add artificial variables into the model, and uses the Two-Phase simplex method or the Big-M method to solve the model, which expands the size of the linear program. As a result, many researchers have attempted to improve the simplex method without using artificial variables [10][11][12][13][14][15][16][17][18][19][20][21][22]. Moreover, other methods require finding an initial point closer to the optimal point, expecting to reduce the computational time.…”

Section: Introductionmentioning

confidence: 99%

“…Arsham's method [15,16] in 2006 provides a better initial basis without using artificial variables, which consist of three phases. Note that the right-hand-side vector of the model must be nonnegative.…”

Section: Introductionmentioning

confidence: 99%

Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method

2020

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An enthusiastic artificial-free linear programming method based on a sequence of jumps and the simplex method is proposed in this paper. It performs in three phases. Starting with phase 1, it guarantees the existence of a feasible point by relaxing all non-acute constraints. With this initial starting feasible point, in phase 2, it sequentially jumps to the improved objective feasible points. The last phase reinstates the rest of the non-acute constraints and uses the dual simplex method to find the optimal point. The computation results show that this method is more efficient than the standard simplex method and the artificial-free simplex algorithm based on the non-acute constraint relaxation for 41 netlib problems and 280 simulated linear programs.

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“…Various general algorithms have been developed for solving a range of linear problems (Myers, 1992, Arsham, 2007. The idea of adding constraints based on partial results obtained follows the classical work of Dantzig et al (1954).…”

Section: Solution Procedures Algorithmmentioning

confidence: 99%

Calibrating cross-training to meet demand mix variation and employee absence

Olivella

Nembhard

2016

European Journal of Operational Research

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Abstract:We address the problem of determining the cross-training that a work team needs in order to cope with demand mix variation and absences. We consider the case in which all workers can be trained on all tasks, the workforce is a resource that determines the capacity and a complete forecasting of demand is not available. The demand mix variation that the organization wants to be able to cope with is fixed by establishing a maximum time to devote to each product. We contend that this approach is straightforward, has managerial practicality and can be applied to a broad range of practical scenarios. It is required that the demand mix variation be met, even if there are a certain level of absences. To numerically solve the mathematical problem, a constraint-based selection procedure is developed, which we term CODEMI. We provide illustrated examples demonstrating solution quality for the approximation, and we report on an illustrative set of computational cases.

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A computationally stable solution algorithm for linear programs

Cited by 10 publications

References 36 publications

Foundation of Linear Programming

Foundation of Linear Programming

Self-Regulating Artificial-Free Linear Programming Solver Using a Jump and Simplex Method

Calibrating cross-training to meet demand mix variation and employee absence

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