What is an optimal solution of transportation problem?

What is an optimal solution of transportation problem?

A feasible solution (not necessary basic) is said to be optimal if it minimizes the total transportation cost. Non-degenerate Basic Feasible Solution: A basic feasible solution to a (m×n) transportation problem that contains exactly m+n-1 allocations in independent positions.

What is a transportation model and how is it solved?

Transportation model is a special type of networks problems that for shipping a commodity from source (e.g., factories) to destinations (e.g., warehouse). Transportation model deal with get the minimum- cost plan to transport a commodity from a number of sources (m) to number of destination (n).

What means optimal solution?

(definition) Definition: A solution to an optimization problem which minimizes (or maximizes) the objective function.

What is optimality test in transportation problem?

Optimally test in a transmission problem is carried out on a non-degenerate initial feasible solution to ascertain if the IFS obtained is optimal. Optimally test in a TP is carried out by determining the opportunity costs of all empty cells in a transportation matrix.

What is a transportation model?

The transportation model addresses the concept of moving a thing from one place to another without change. It assumes that any damage en route has negative consequences, and so it’s used to analyze transportation systems and find the most efficient route for resource allocation.

What is optimal and feasible solution?

A feasible solution satisfies all the problem’s constraints. An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). A graphical solution method can be used to solve a linear program with two variables.

What is optimal and non optimal solution?

At an optimal feasible solution, the primal objective is equal to the dual objective. At a non-optimal feasible solution, the primal objective is less than the dual objective.

What do you mean by optimality test?

U-V Method Optimality Test is used to check the optimality of a basic feasible solution consisting of (m+n-1) independent positive allocations and a set of arbitrary number ui and vj (i=1,2,…m; j=1,2,… n) such that cii= ui+vj for all occupied cells (i,j) .

What are the different optimality tests?

There are two approaches to test whether the primary feasible solution in the first table needs improvement towards optimality. They are: (a) stepping-stone method and (b) modified distribution (MODI) method.

What is the aim of transportation Model?

The transportation model is a special case of linear programming problems in which the objective is to minimize the total cost of transporting goods from the various supply origins to the different demand destinations.

What is the importance of transportation model?

Models are important because transportation plans and investments are based on what the models say about future travel. Models are used to estimate the number of trips that will be made on a transportation systems alternative at some future date.

What is an optimal solution?

An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value, that means the maximum profit or the least cost.

What is an optimal solution to transportation costs?

An optimal solution is one where there is no other se of transportation routes that will further reduce the total transportation cost. Thus, we have to evaluate each unoccupied cell in the transportation table in terms of an opportunity of reducing total transportation cost.

What are the two methods for solving transportation models?

The two methods for solving a transportation model are the stepping-stone method and the modified distribution method (also known as MODI). In applying the simplex method, an initial solution had to be established in the initial simplex tableau. This same condition must be met in solving a transportation model.

What is the basic solution principle in transportation problems?

The basic solution principle in a transportation problem is to determine whether a transportation route not at present being used (i. e., an empty cell) would result in a lower total cost if it were used. For example, Table B-11 shows four empty cells (1A, 2A, 2B, 3C) representing unused routes.

What is the study of optimal transportation?

The study of optimal transportation and allocation of resources is; transportation theory or transport theory. The French mathematician Gaspard Monge formalized this problem in 1781.