Basic feasible solutions and decomposition principle for linear fractional functionals programming problem

1971 ◽  
Vol 22 (1-2) ◽  
pp. 185-193
Author(s):  
R. K. Gupta
Keyword(s):  
Programming Problem ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Decomposition Principle

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

2020 ◽  
Vol 5 (1) ◽  
pp. 456
Author(s):  
Tolulope Latunde ◽  
Joseph Oluwaseun Richard ◽  
Opeyemi Odunayo Esan ◽  
Damilola Deborah Dare
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Transportation Cost ◽  
North West ◽  
Life Problems ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Road Freight Transportation ◽  
The Cost ◽  
Cost Of Transportation

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

A numerical approach for time-optimal path-planning of kinematically redundant manipulators

Robotica ◽  
1994 ◽  
Vol 12 (5) ◽  
pp. 401-410 ◽  
Author(s):  
Chia-Ju Wu
Keyword(s):  
Nonlinear Programming ◽  
Path Planning ◽  
Programming Problem ◽  
Optimal Path ◽  
Numerical Approach ◽  
Redundant Manipulators ◽  
Nonlinear Programming Problem ◽  
Optimal Path Planning ◽  
Time Optimal ◽  
Feasible Solutions

SUMMARYIn this paper, a numerical approach is proposed to solve the time-optimal path-planning (TOPP) problem of kinematically redundant manipulators between two end-points. The first step is to transform the TOPP problem into a nonlinear programming problem by an iterative procedure. Then an approach to find the initial feasible solutions of the problem is proposed. Since initial feasible solutions can be found easily, the optimization process of the nonlinear programming problem can be started from different points to find the global minimum. A planar three-link robotic manipulator is used to illustrate the validity of the proposed approach.

A METHOD FOR GENERATING ALL THE EFFICIENT SOLUTIONS OF A 0-1 MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEM

2004 ◽  
Vol 21 (01) ◽  
pp. 127-139 ◽  
Author(s):  
G. R. JAHANSHAHLOO ◽  
F. HOSSEINZADEH LOTFI ◽  
N. SHOJA ◽  
G. TOHIDI
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Feasible Solution ◽  
Efficient Solutions ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Multi Objective ◽  
Feasible Solutions ◽  
Single Objective

In this paper, a method using the concept of l1-norm is proposed to find all the efficient solutions of a 0-1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0-1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0-1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0-1 single objective linear programming problem are efficient solutions of the 0-1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0-1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0-1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.

A tutorial proof that extreme points are basic feasible solutions

1977 ◽  
Vol 1 (5) ◽  
pp. 337-338
Author(s):  
Donald C. Aucamp ◽  
Haluk Bekiroglu
Keyword(s):  
Extreme Points ◽  
Basic Feasible Solutions ◽  
Feasible Solutions

Converging upon basic feasible solutions through Dantzig–Wolfe decomposition

2012 ◽  
Vol 8 (1) ◽  
pp. 171-180 ◽  
Author(s):  
Joseph L. Rios ◽  
Kevin Ross
Keyword(s):  
Basic Feasible Solutions ◽  
Feasible Solutions
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