Abstract
In this paper a hybrid two-stage algorithm is proposed to find the optimal solution for transportation problem (TP). The proposed algorithm consists of two stages: the first stage uses genetic algorithm (GA) to find an improved nonartificial feasible solution for the problem and the second stage utilizes this solution as a starting point in the RSM algorithm to find the optimal solution for the problem. The algorithm utilizes big M method to handle ? constraints and northwest corner method, minimum cost method, and Vogel's method are also used to generate the initial population for the GA. Performance of the algorithm is tested under different simulated scenarios and compared to both GA and revised simplex method (RSM). The results showed that the new hybrid algorithm performs competitively against GA and RSM. The proposed algorithm can be easily extended to cover different kinds of linear programming (LP) problems with minor changes such as inventory control, employment scheduling, personnel assignment and transshipment problems.
Highlights
Matrix notation is widely used to express linear programming (LP) problems
This study investigated the benefit of using a hybrid two stage algorithm (GA-revised simplex method (RSM)) to solve the transportation problem (TP) problem
The improved nonartificial initial basic variables set were used in the second stage as the starting point for the RSM
Summary
Matrix notation is widely used to express linear programming (LP) problems In this notation, let X be an n-vector that represents the variables in the problem, A be an (m by n)-matrix that represents the constraints coefficients in the problem, and C be an n-vector that represents the objective function coefficients in the problem, the LP problem with m constraints and n variables can be expressed in a matrix notation as Maximize or min imize z CX s.t. AX = b. X 0 where b is an m-vector that represents the right hand side values of the constraints in the LP problem. Another widely used notation for AX b constraints is n j Pj x j. Let XB be the set of the basic variables, B is said to form a basis if the m-vectors in B are linearly independent
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