• Journal of the Korea Society of Computer and Information
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• v.20 no.6
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• pp.51-58
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• 2015

This paper suggests assignment-swap algorithm with time complexity O(mn) to obtain the optimal solution for large-scale of transportation problem (TP) with incomplete cost lists. Generally, the TP with complete cost lists can be solved with TSM (Transportation Simplex Method). But, we can't be solved for large-scale of TP with TSM. Especially. It is hard to solve for large-scale TP with incomplete cost lists using TSM. Therefore, experts simply using commercial linear programming package. Firstly, the proposed algorithm applies assignment strategy of transportation quantity to ascending order of transportation cost. Then, we reassign from surplus of supply to shortage of demand. Secondly, we perform the 2-opt and 1-opt swap optimization to obtain the optimal solution. Upon application to $31{\times}15$ incomplete cost matrix problem, the proposed assignment-swap algorithm more improves the solution than LINGO of commercial linear programming.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.1
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• pp.153-162
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• 2013

This paper proposes the most simple method for optimal solution of the transshipment problem. Usually the transshipment problem is solved by direct linear programming or TSM (Transportation Simplex Method). The method using TSM has two steps. First it is to get a initial solution using NCM, LCM, or VAM, second to refine the initial solution using MOD or SSM. However the steps is complex and difficult. The proposed method applies the method that transforms transshipment problem to transportation problem. In the proposed method it simply selects the minimum cost of rows about transportation problem, and then it applies the method that assigns a transported volume as an ascending sort of the costs of rows about the selected costs. Our method makes to be very fast got the initial value. Also we uses the method that controls assignment volume, if a heavy item of cost is assigned to a transported volume and it has a condition to be able to transform to more lower cost. The proposed algorithm simply got the optimal solution with applying to 11 transshipment problem.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.5
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• pp.181-188
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• 2021

In preparing a aggregate production plan(APP), the transportation method generally uses a linear planning(LP) software package for TSM(transportation simplex method), which seeks initial solutions with either NCM, LCM, or VAM specialized in transportation issues and optimizes them with either SSM or MODI. On the other hand, this paper proposes a transportation method that easily, quickly, and accurately prepares a APP without software package assistance. This algorithm proposed simply assigned to least cost-first, and minimized the inventory periods. Applying the proposed algorithm to 6-benchmarking data, this algorithm can be obtained better optimal solution than VAM or LP for 4 data, and we obtain the same results for the remained 2 data.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.2
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• pp.93-102
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• 2013

This paper proposes an algorithm designed to obtain the optimal solution for transportation problem. The transportation problem could be classified into balanced transportation where supply meets demand, and unbalanced transportation where supply and demand do not converge. The archetypal TSM (Transportation Simplex Method) for this optimal solution firstly converts the unbalanced problem into the balanced problem by adding dummy columns or rows. Then it obtains an initial solution through employment of various methods, including NCM, LCM, VAM, etc. Lastly, it verifies whether or not the initial solution is optimal by employing MODI. The abovementioned algorithm therefore carries out a handful of complicated steps to acquire the optimal solution. The proposed algorithm, on the other hand, skips the conversion stage for unbalanced transportation problem. It does not verify initial solution, either. The suggested algorithm firstly allocates resources so that supply meets demand, in the descending order of its loss cost. Secondly, it optimizes any surplus quantity (the amount by which the initially allocated quantity exceeds demand) in such a way that the loss cost could be minimized Once the above reallocation is terminated, an additional arrangement is carried out by transferring the allocated quantity in columns with the maximum cost to the rows with the minimum transportation cost. Upon application to 2 unbalanced transportation data and 13 balanced transportation data, the proposed algorithm has successfully obtained the optimal solution. Additionally, it generated the optimal solution for 4 data, whose solution the existing methods have failed to obtain. Consequently, the suggested algorithm could be universally applied to the transportation problem.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.4
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• pp.223-230
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• 2015

As the Transportation Simplex Method of the general transportation problem are inapplicable to the large-scale unbalanced transportation problem, a commercialized linear programming package remains as the only viable means. There is, however, no method made available to verify the optimality of solutions attained by the package. This paper therefore proposes a simple heuristic algorithm to the large-scale unbalanced transportation problem. From a given problem of $31{\times}15$supply and demand areas, the proposed algorithm determines the number of demands areas for each supply area and executes on the latter in the ascending order of each of their corresponding demand areas. Next, given a single corresponding demand area, it supplies the full demand volume and else, it supplies first to an area of minimum associated costs and subsequently to the rest so as to meet the demand to the fullest extent. This initial optimal value is then optimized through an adjustment process whereby costs are minimized as much as possible. When tested on the $31{\times}15$cost matrix, the proposed algorithm has obtained an optimal result improved from the commercial linear programming package by 8.9%.