• Title, Summary, Keyword: Transportation problem

### Fixed Charge Transportation Problem and Its Uncertain Programming Model

• Sheng, Yuhong;Yao, Kai
• Industrial Engineering and Management Systems
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• v.11 no.2
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• pp.183-187
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• 2012
• In this paper, we study the fixed charge transportation problem with uncertain variables. The fixed charge transportation problem has two kinds of costs: direct cost and fixed charge. The direct cost is the cost associated with each source-destination pair, and the fixed charge occurs when the transportation activity takes place in the corresponding source-destination pair. The uncertain fixed charge transportation problem is modeled on the basis of uncertainty theory. According to inverse uncertainty distribution, the model can be transformed into a deterministic form. Finally, in order to solve the uncertain fixed charge transportation problem, a numerical example is given to show the application of the model and algorithm.

### Simple Solution for Multi-commodity Transportation Problem (복합상품 운송 문제의 간단한 해법)

• Lee, Sang-Un;Choi, Myeong-Bok
• The Journal of The Institute of Internet, Broadcasting and Communication
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• v.13 no.5
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• pp.173-181
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• 2013
• This paper proposes a heuristic optimal solution of multicommodity transportation problem. The proposed algorithm has 3 steps. First the proposed algorithm transforms multicommodity transshipment problem to a general transportation problem, but if the problem is a multicommodity transportation problem, it is not transformed. And the multicommodity is disassembled to a single commodity. Second if it is a multicommodity transportation problem, the algorithm selects the minimum cost according to commodity, on the other hand if it is a multicommodity transshipment problem, the algorithm directly selects the minimum cost based on demand area. And the algorithm assigns carloadings to be satisfied the supply and demand quantity. The algorithm repeats these processes until a given demand quantity is satisfied. Last if it has a condition that is able to reduce the transportation expense, the proposed algorithm controls the assignment quantity of the initial value that got from the step 2. The proposed algorithm was applied to two multicommodity transportation problem and three multicommodity transshipment problem and it got more good result than an existing linear programming method.

### Solving Nonlinear Fixed Charge Transportation Problem by Spanning Tree-based Genetic Algorithm (신장트리 기반 유전자 알고리즘에 의한 비선형 fcTP 해법)

• Jo, Jung-Bok;Ko, Suc-Bum;Gen, Mitsuo
• Journal of KIISE:Software and Applications
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• v.32 no.8
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• pp.752-758
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• 2005
• The transportation problem (TP) is known as one of the important problems in Industrial Engineering and Operational Research (IE/OR) and computer science. When the problem is associated with additional fixed cost for establishing the facilities or fulfilling the demand of customers, then it is called fixed charge transportation problem (fcTP). This problem is one of NP-hard problems which is difficult to solve it by traditional methods. This paper aims to show the application of spanning-tree based Genetic Algorithm (GA)approach for solving nonlinear fixed charge transportation problem. Our new idea lies on the GA representation that includes the feasibility criteria and repairing procedure for the chromosome. Several numerical experimental results are presented to show the effectiveness of the proposed method.

• Arora, S.R.;Khurana, Archana
• Management Science and Financial Engineering
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• v.7 no.2
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• pp.13-30
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• 2001
• This paper discusses a paradox in an Indefinite Quadratic transportation Problem. Here, the objective function is the product of two linear functions. A paradox arises when the transportation problem admits of a total cost which is lower than the optimum cost, by transporting larger quantities of goods over the same route. A sufficient condition for the existence of a paradox is established. Paradoxical Range of flow is obtained for any given flow in which the corresponding objective function value is less than the optimum value of the given transportation problem. It is illustrated with the help of a numerical example.

### A Genetic Algorithm for Route Guidance System in Intermodal Transportation Networks with Time - Schedule Constraints (서비스시간 제한이 있는 복합교통망에서의 경로안내 시스템을 위한 유전자 알고리듬)

• Chang, In-Seong
• Journal of Korean Institute of Industrial Engineers
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• v.27 no.2
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• pp.140-149
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• 2001
• The paper discusses the problem of finding the Origin-Destination(O-D) shortest paths in internodal transportation networks with time-schedule constraints. The shortest path problem on the internodal transportation network is concerned with finding a path with minimum distance, time, or cost from an origin to a destination using all possible transportation modalities. The time-schedule constraint requires that the departure time to travel from a transfer station to another node takes place only at one of pre-specified departure times. The scheduled departure times at the transfer station are the times when the passengers are allowed to leave the station to another node using the relative transportation modality. Therefore, the total time of a path in an internodal transportation network subject to time-schedule constraints includes traveling time and transfer waiting time. In this paper, a genetic algorithm (GA) approach is developed to deal with this problem. The effectiveness of the GA approach is evaluated using several test problems.

### Interval Valued Solution of Multiobjective Problem with Interval Cost, Source and Destination Parameters

• Hong, Dug-Hun
• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.42-46
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• 2009
• Das et al. [EJOR 117(1999) 100-112] discussed the real valued solution procedure of the multiobjective transportation problem(MOTP) where the cost coefficients of the objective functions, and the source and destination parameters have been expressed as interval values by the decision maker. In this note, we consider the interval valued solution procedure of the same problem. This problem has been transformed into a classical multiobjective transportation problem where the constraints with interval source and destination parameters have been converted into deterministic ones. Numerical examples have been provided to illustrate the solution procedure for this case.

### Optimization of the Transportation of International Container Cargoes Considering Short Sea Shipping (근해운송을 고려한 국제컨테이너 화물운송의 최적화)

• Kim, Hwa-Joong;Chang, Young-Tae;Lee, T.W.
• Proceedings of the Korea Port Economic Association Conference
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• pp.161-173
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• 2007
• This paper considers the problem of determining the cargo flow and the transportation mode in each trade route while satisfying the demand. Especially, the problem incorporates short sea shipping in Korea, which is becoming more important in order to improve efficiency of Logistics. The objective is to minimize the sum of shipping and inland transportation costs. To solve optimally the problem, this paper employs a linear programming model, which is an operations research technique for optimization. The problem is formulated by extending the well-known network design problem by considering capacity at seaport and limitation of total number of vehicles. The model is solved using CPLEX, a commercial linear program software. The test results using a real cargo flow data in Korea show that the model represents closely the real situation.

### A Transportation Problem with Uncertain Truck Times and Unit Costs

• Mou, Deyi;Zhao, Wanlin;Chang, Xiaoding
• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.30-35
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• 2013
• Motivated by the emergency scheduling in a transportation network, this paper considers a transportation problem, in which, the truck times and transportation costs are assumed as uncertain variables. To meet the demand in the practical applications, two optimization objectives are considered, one is the total costs and another is the completion times. And then, a multi-objective optimization model is developed according to the situation in applications. Because there are commensurability and conflicting between the two objectives commonly, a solution does not necessarily exist that is best with respective to the two objectives. Therefore, the problem is reduced to a single objective model, which is an uncertain programming with a chance-constrain. After some analysis, its equivalent deterministic form is obtained, which is a nonlinear programming. Based on a stepwise optimization strategy, a solution method is developed to solve the problem. Finally, the computational results are provided to demonstrate the effectiveness of our model and algorithm.

### Optimal Solution for Transportation Problems (수송문제의 최적해)

• Lee, Sang-Un
• 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.

### A Genetic Algorithm for Searching Shortest Path in Public Transportation Network (대중교통망에서의 최단경로 탐색을 위한 유전자 알고리즘)

• 장인성;박승헌
• Korean Management Science Review
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• v.18 no.1
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• pp.105-118
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• 2001
• The common shortest path problem is to find the shortest route between two specified nodes in a transportation network with only one traffic mode. The public transportation network with multiple traffic mode is a more realistic representation of the transportation system in the real world, but it is difficult for the conventional shortest path algorithms to deal with. The genetic algorithm (GA) is applied to solve this problem. The objective function is to minimize the sum of total service time and total transfer time. The individual description, the coding rule and the genetic operators are proposed for this problem.