### TIGA JAWABAN PENYELESAIAN OPTIMAL DALAM PROBLEM TRANSPORTASI DENGAN VAM AND MODI METHOD

#### Abstract

The famous method to determine and solve transportation problem is the transportation model VAM and MODI method, the Northwest-Corner and Stepping-Stone method, and the Assignment method. We see how to develop an initial aolution to the transportation problem with VAM (Vogel’s Approximation Method) and MODI (Modified Distribution). VAM is not quite as simple as the Northwest Corner approach. But it facilitates a very good initial solution, as a matter of fact, one that is often the optimal solution.

VAM method trackles the problem of finding a good initial solution by taking into account the cost the costs associated with each route alternative. This is something that Northwest Corner Rules does not do. To apply VAM, we first compute for each row and column the penalty faced if we should ship over the second-best route instead of the least-cost route. After the initial of VAM solution has been found, you should evaluate it with either the Stepping-Stone method or the MODI method. The MODI (Modified Distribution) method allows us to compute improvement indices quickly for each unused square without drawing all of the closed paths. Because of this, it can often provide considerable time savings over the Stepping-Stone method for solving transportation problems. If there is a negative index indicating an imporovemet can be made, then only one Stepping-Stone path must be found. This is used as it was before to determine what changes should be made to obtain the improved solution.

In the Northwest-corner rule, the largest possible allocation is made to the cell in the upper left-hand corner of the tableau, followed by allocations to adjacent feasible celss. While the Stepping-stone method is an interactive technique for moving from an initial feasible solution to an optimal feasible solution, and continues will until the optimal solution is reached. The Stepping-stone path method is used to calculate improvement indices for the empty cells. Improved solutions are developed using a Stepping-stone path.

The assignment method, which is simple and faster to solve the transportation problem by reducing the numbers (cost) in the table/tableau until a series of zeros is found, or zero opportunity costs, which mean that we will reach the optimal cost allocations. Once we have reached the optimal cost allocations, we the allocate each sources or supply according to some point of demand (destinations). Assignment Method is a specialized form of optimization linear programming model that attempts to assign limited capacity to various demand points in a way that minimizes costs.

The special cases of transportation problem included degeneracy (a condition that occurs when the number of occupied squares in any solution is less than the number of rows plus the number of columns minus 1 in a transportation table), unbalanced problems, and multiple optimal solutions. We will see how the VAM and MODI method may be viewed as a special case of solving the multiple optimal solutions of the transportation problem.

Keywords : transportation, VAM and MODI

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