An Extended Programming Experience

1981 ◽  
Vol 13 (1) ◽  
pp. 19-27 ◽  
Author(s):  
B Harris
Keyword(s):  
Linear Programming ◽  
Transportation Problem ◽  
Dual Methods ◽  
Solution Methods ◽  
Research Problems ◽  
Computational Aspects ◽  
Standard Solution ◽  
Order Bounds

The paper summarizes a twenty-year experience with the computational aspects of the transportation problem of linear programming. The problem is completely described and standard solution methods are summarized. The order bounds for these computations are examined. Attention then turns to some sample research problems, including shortening the search for a move, solving a condensed problem, choosing a starting basis, and several recently developed dual methods. Brief reference is made to the difficulties which arise in publishing unorthodox approaches such as those discussed in the paper.

scholarly journals Statistical Methods for Solving Transportation Problems

2019 ◽  
Vol 25 (2) ◽  
pp. 10-13
Author(s):  
Alina Baboş
Keyword(s):  
Linear Programming ◽  
Statistical Methods ◽  
Approximation Method ◽  
Transportation Problem ◽  
Feasible Solution ◽  
Basic Feasible Solution ◽  
Statistical Tools ◽  
Numerical Examples ◽  
North West ◽  
Shipping Cost

Abstract Transportation problem is one of the models of Linear Programming problem. It deals with the situation in which a commodity from several sources is shipped to different destinations with the main objective to minimize the total shipping cost. There are three well-known methods namely, North West Corner Method Least Cost Method, Vogel’s Approximation Method to find the initial basic feasible solution of a transportation problem. In this paper, we present some statistical methods for finding the initial basic feasible solution. We use three statistical tools: arithmetic and harmonic mean and median. We present numerical examples, and we compare these results with other classical methods.

Computational aspects of linear programming Simplex method

2000 ◽  
Vol 31 (8-9) ◽  
pp. 539-545 ◽  
Author(s):  
D.T. Nguyen ◽  
Y. Bai ◽  
J. Qin ◽  
B. Han ◽  
Y. Hu
Keyword(s):  
Linear Programming ◽  
Simplex Method ◽  
Computational Aspects

scholarly journals Lexicographic Methods for Fuzzy Linear Programming

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1540
Author(s):  
Boris Pérez-Cañedo ◽  
José Luis Verdegay ◽  
Eduardo René Concepción-Morales ◽  
Alejandro Rosete
Keyword(s):  
Linear Programming ◽  
Fuzzy Linear Programming ◽  
Theoretical Research ◽  
Practical Applications ◽  
Decision Variables ◽  
Solution Methods ◽  
Computer Codes ◽  
Model Components ◽  
Sets Theory ◽  
Lp Theory

Fuzzy Linear Programming (FLP) has addressed the increasing complexity of real-world decision-making problems that arise in uncertain and ever-changing environments since its introduction in the 1970s. Built upon the Fuzzy Sets theory and classical Linear Programming (LP) theory, FLP encompasses an extensive area of theoretical research and algorithmic development. Unlike classical LP, there is not a unique model for the FLP problem, since fuzziness can appear in the model components in different ways. Hence, despite fifty years of research, new formulations of FLP problems and solution methods are still being proposed. Among the existing formulations, those using fuzzy numbers (FNs) as parameters and/or decision variables for handling inexactness and vagueness in data have experienced a remarkable development in recent years. Here, a long-standing issue has been how to deal with FN-valued objective functions and with constraints whose left- and right-hand sides are FNs. The main objective of this paper is to present an updated review of advances in this particular area. Consequently, the paper briefly examines well-known models and methods for FLP, and expands on methods for fuzzy single- and multi-objective LP that use lexicographic criteria for ranking FNs. A lexicographic approach to the fuzzy linear assignment (FLA) problem is discussed in detail due to the theoretical and practical relevance. For this case, computer codes are provided that can be used to reproduce results presented in the paper and for practical applications. The paper demonstrates that FLP that is focused on lexicographic methods is an active area with promising research lines and practical implications.

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