Abstract:
Minimization of transportation time is a great concern of the transportation problems like the cost minimizing transportation problems. In this writing, a transportation algorithm is developed and applied to obtain an Initial Basic Feasible Solution (IBFS) of transportation problems in minimizing transportation time. The developed method has also been illustrated numerically to test the efficiency of the method where it is observed that the proposed method yields a better result.

Abstract:
In this paper we study the stability of the feasible set of a balanced transportation problem. A transportation problem is balanced when the total supply is equal to the total demand. One can easily see that when we make minor adjustments to the data (supply and demand), the resulting problem may lose the property of balance. Therefore, although the transportation problem is a particular case of linear programming, you cannot apply the familiar results of stability. For a fixed number of origins and destinations we have obtained a vector representation for any feasible solution of the transportation problem. We have used this representation to prove that the feasible set mapping is continuous. We have also proved that the extreme point set mapping is lower semi continuous.

Abstract:
Transportation Problem is an important problem which has been widely studied in Operations Research domain. It has been often used to simulate different real life problems. In particular, application of this Problem in NP Hard Problems has a remarkable significance. In this Paper, we present the closed, bounded and non empty feasible region of the transportation problem using fuzzy trapezoidal numbers which ensures the existence of an optimal solution to the balanced transportation problem. The multivalued nature of Fuzzy Sets allows handling of uncertainty and vagueness involved in the cost values of each cells in the transportation table. For finding the initial solution of the transportation problem we use the Fuzzy Vogel Approximation Method and for determining the optimality of the obtained solution Fuzzy Modified Distribution Method is used. The fuzzification of the cost of the transportation problem is discussed with the help of a numerical example. Finally, we discuss the computational complexity involved in the problem. To the best of our knowledge, this is the first work on obtaining the solution of the transportation problem using fuzzy trapezoidal numbers.

Abstract:
In this paper we propose a new algorithm for the initial fuzzy feasible solution to a fully fuzzy transportation problem. Then by using fuzzy version of modified distribution method, we obtain the fuzzy optimal solution for the fully fuzzy transportation problem without converting to a classical transportation problem. A numerical example is provided to illustrate the proposed algorithm. It can be seen that the proposed algorithm gives a better fuzzy optimal solution to the given fuzzy transportation problem.

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.

Transportation issue is one of the significant zones of utilization of Linear
Programming Model. In this paper, transportation model is utilized to decide
an ideal answer for the transportation issue in a run of the mill world class
university utilizing Covenant University as a contextual analysis. Covenant
University is a potential world class University. The quick development of
Covenant University Campus over the most recent fourteen years affects its
transportation framework. This paper particularly takes a gander at streamlining
the time spent by the students moving from their lodgings to lecture
rooms. Google guide was utilized to figure the separation and time between
every cause and every goal. North-west corner technique, Least Cost strategy
and Vogel’s estimation technique were utilized to decide the underlying fundamental
plausible arrangement (initial feasible solution) and MODI strategy
was utilized to locate the ideal arrangement (optimal solution). The last outcome
demonstrates that the development of understudies from hostel to lecture
rooms can be streamlined if the total time spent is decreased.

Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. In this paper, two methods are proposed to find an initial basic feasible solution for the transportation problems. The South-East Corner Method (SECM) and the North-East Corner Method (NECM) are adopted to compute the Initial Basic Feasible Solution (IBFS) of the transportation problem. A comparative study is carried out with existing methods like Vogel’s approximation method (VAM) which is to find an initial basic feasible solution and Modified Distribution (MODI) Method which is to find the optimal solution and the methods are also illustrated with numerical examples.

Abstract:
Finding
an initial basic feasible solution is the prime requirement to obtain an optimal
solution for the transportation problems. In this article, a new approach is
proposed to find an initial basic feasible solution for the transportation
problems. The method is also illustrated with numerical examples.

Abstract:
In this paper the existing simplex splitting algorithm for finding a feasible solution of systems of linear inequalities is modified by evolving a vertex-determination technique. The existing algorithm cannot determine when the system of linear inequalities is infeasible hence the need for a modification. The modified algorithm is able to determine the feasible solution whenever it exists and to detect infeasibility whenever it occurs. The modified algorithm is tested on a problem that has a feasible solution and also on a problem that has no feasible solution and is found to work perfectly well.

Abstract:
The facility layout approaches can generally be classified into two groups, constructive approaches and improvement approaches. All improvement procedures require an initial solution which has a significant impact on final solution. In this paper, we introduce a new technique for accruing an initial placement of facilities on extended plane. It is obtained by graph theoretic facility layout approaches and graph drawing algorithms. To evaluate the performance, this initial solution is applied to rectangular facility layout problem. The solution is improved using an analytical method. The approach is then tested on five instances from the literature. Test problems include three large size problems of 50, 100, and 125 facilities. The results demonstrate effectiveness of the technique especially for large size problems. 1. Introduction The facility layout problem seeks the best positions of facilities to optimize some objective. The common objective is to reduce material handling costs between the facilities. The problem has been modeled by a variety of approaches. A detailed review of the different problem formulations can be found in Singh and Sharma [1]. The facility layout problem is an optimization problem which arises in a variety of problems such as placing machines on a factory floor, VLSI design, and layout design of hospitals, schools. The facility layout approaches can generally be classified into two groups, constructive methods and improvement methods. In this paper, we consider the placement of facilities on an extended plane. Many improvement approaches have been proposed for this problem. All improvement procedures require an initial solution. Some approaches start from a good but infeasible solution [2–4]. These models contain a penalty component in their objective function. Hence, these approaches minimize objective function value for feasible solutions. But some approaches require a feasible initial solution. These approaches use a randomly generated initial solution [5, 6]. Mir and Imam [7] have proposed simulated annealing for a better initial solution. They have shown that a good initial solution has a significant impact on final solution. In this paper, we introduce a new technique for accruing an initial placement of facilities on an extended plane. The technique consists of two stages. In the first stage, a maximal planar graph (MPG) is obtained. In the second stage, the vertices of MPG are drawn on the plane by graph drawing algorithms. Then, vertices are replaced by facilities. Hence, an initial solution is obtained. In an MPG,