• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.144-152
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• 2011

Most of the models for the vehicle routing problems studied in the literature assumed constant travel times. However, those approaches may give infeasible solutions when traffic congestion causes delays in travel time. To overcome such difficulty, there have been some researches considering the change of the travel time which is called the time dependent vehicle routing problem (TDVRP). TDVRP assumes that the travel time between two locations is not only affected by the distance traveled, but by many other factors including the time of the day. In this paper, we propose a branch-and-price algorithm to solve the TDVRP. The time dependent property of the travel time is dealt with an enumeration scheme with bounding procedures in the column generation procedure identifying a profitable route. The proposed algorithm guarantees the "Non-passing" property to be held in the solutions. The algorithm was tested on problems composed of the Solomon's benchmark instances for 25 and 50 nodes. Computational results are reported.

• Industrial Engineering and Management Systems
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• v.3 no.2
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• pp.92-99
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• 2004

We consider the ATM switching node location problem (ANLP). In this problem, there are two kinds of facilities, hub facilities and remote facilities, with different capacities and installation costs. We are given a set of customers with each demand requirements, a set of candidate installation sites of facilities, and connection costs between facilities. We need to determine the locations to place facilities, the number of facilities for each selected location, the set of customers who are connected to each installed hub via installed remote facilities with minimum cost, while satisfying demand requirements of each customer. We formulate this problem as a general integer programming problem and solve it to optimality. In this paper, we present a preprocessing procedure to tighten the formulation and develop a branch-and-price algorithm. In the algorithm, we consider the integer knapsack problem as the column generation problem. Computational experiments show that the algorithm gives optimal solutions in a reasonable time.

• Management Science and Financial Engineering
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• v.12 no.2
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• pp.37-62
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• 2006

This paper considers the problem of designing logical tunnels in virtual private networks considering QoS guarantee which restricts the number of tunnel hops for each traffic routing. The previous researches focused on the design of logical tunnel itself and Steiner-tree based solution algorithms were proposed. However, we show that for some objective settings it is not sufficient and is necessary to consider both physical and logical connectivity at the same time. Thereupon, the concept of the layered network is applied to the logical tunnel design problem in virtual private networks. The layered network approach considers the design of logical tunnel as well as its physical routing and we propose a modified branch-and-price algorithm which is known to solve layered network design problems effectively. To show the performance of the proposed algorithm, computational experiments have been done and the results show that the proposed algorithm solves the given problem efficiently and effectively.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.1
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• pp.33-43
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• 2007

The pickup and delivery problem with time windows generally involves the construction of optimal routeswhich satisfy a set of transportation requests under pairing, precedence, time window, vehicle capacity, andavailability constraints. In this paper, we added some constraints to the problem and adopted an objectivefunction based on number of used vehicles, total travel distance and total schedule duration to consider morerealistic problems. A branch and price algohthm for the problem is proposed and an enumeration method is usedfor the subproblems. The algorithm was tested on randomly generated instances and computational results werereported.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.381-385
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• 2003

We consider the bandwidth parking problem arising from telecommunication networks The problem is to determine the set of calls to be routed and an assignment or them to the paths in arc capacitated network. The objective is to maximize profit. We formulate the problem as an integer programming and propose an algorithm to solve it. Column generation technique to solve the linear programming relxation is proposed with two types of columns in addition, to obtain an optimum integer solution, we consider a new branching strategy. Computational experiments show that the algorithm gives option at solutions within reasonably small time limits.

• Journal of Digital Contents Society
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• v.3 no.2
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• pp.221-233
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• 2002

In this paper, we present integer programming models and algorithms for the Capacitated Facility Location-Allocation Problem (CFLP). The models and algorithms can be used for the design of logistics networks and for the location of telecommunication facilities. We are given a set of candidate facility installation sites, one type of facility for each candidate site with its capacity and installation cost, a set of customers with their demand requirement, and flow cost for one unit of demand flow from each customer to each candidate site. (CFLP) is to determine the number of facilities for each candidate site and the set of customers which are connected to each site with minimum cost, while satisfying the demand requirement of each customer and constraints imposed on the allocation of customers to facilities. We present two integer programming models for (CFLP), and devise a branch-and-cut algorithm and a branch-and-price algorithm for the problem.

• IE interfaces
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• v.21 no.1
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• pp.1-7
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• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.4
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• pp.51-60
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• 2007

In this study, we consider the minimum ADM problem which is the fundamental problem for the cost-effective design of SONET ADM embedded in WDM ring networks. To minimize the number of SONET ADMs, efficient algorithms for the routing and wavelength assignment are needed. We propose a mathematical model based on the graph theory for the problem and propose a branch-and-price approach to solve the suggested model effectively within reasonable time. By exploiting the mathematical structure of ring networks, we developed polynomial time algorithms for column generation subroutine at branch-and-bound tree. In a computer simulation study, the suggested approach can find the optimal solution for sufficient size networks and shows better performance than the greedy heuristic method.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.4
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• pp.171-176
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• 2021

This paper deals with bid evaluation problem that chooses the vendors and quantity with minimum purchasing cost for bid information of setup cost and unit price. For this problem, the branch-and-bound(BB) and branch-and-cut(BC) methods are well-known. But these methods can be fail to obtain the optimal solution. This paper gets the initial feasible solution with procuring quantity assignment principle in accordance with the unit price or setup cost rank-first. Then procuring quantity moving optimization(vendor change) is execute take account of unit price or setup cost rank. As a result of experimentation, the propose algorithm is significantly lower compared to BB and BC.

• Journal of Korean Institute of Industrial Engineers
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• v.30 no.3
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• pp.213-223
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• 2004

We consider the traffic grooming problem for the design of SONET/WDM(Synchronous Optical NETwork/Wavelength Division Multiplexing) ring networks. Given a physical network with ring topology and a set of traffic demands between pairs of nodes, we are to obtain a stack of rings with the objective of minimizing the number of ADMs installed at the nodes. This problem arises when a single ring capacity is not large enough to accommodate all the demands. As a solution method, an efficient algorithm based on the branch-and-price approach has been reported in the literature for the problem in which only unidirecional path switched ring (UPSR) was considered. In this study, we suggest integer programming models and the algorithms based on the same approach as the above one, considering two-fiber bidirectional line switched ring(BLSR/2), and BLSR/4 additionally. Using the results, we compare the number of required ADMs for all types of the ring architecture.