• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.613-616
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• 2000

This paper considers the problem of subway crew scheduling. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper, we propose two basic techniques that solve the problem in a reasonable time, though the optimality of the solution is not guaranteed. To reduce the number of variables, we adopt column-generation technique. We could develop an algorithm that solves column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational results show column-generation makes the problem of treatable size, and variable fixing enables us to solve LP relaxation in shorter time without a considerable increase in the optimal value. Finally, we were able to obtain an integer optimal solution of a real instance within a reasonable time.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.4
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• pp.67-86
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• 2002

This paper considers subway crew scheduling problem. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper. we propose two basic techniques that solve the subway crew scheduling problem in a reasonable time, though the optimality of the solution is not guaranteed. We develop an algorithm that solves the column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational result for a real instance is reported.

• Journal of the Korean Institute of Navigation
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• v.14 no.1
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• pp.21-38
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• 1990

This paper discusses the various modes of operations of cargo ships which are liner operations, tramp shipping and industrial operations, and mathematical programming, simulation , and heuristic method that can be used to solve ships routing and scheduling problems for each of these operations. In particular, this paper put emphasis on a crude oil tanker scheduling problem. The problem is to achieve an optimal sequence of cargoes or an optimal schedule for each ship in a given fleet during a given period. Each cargo is characterized by its type, size, loading and discharging ports, loading and discharging dates, cost, and revenue. Our approach is to enumerate all feasible candidate schedate schedules for each ship, where a candidate schedule specifies a set of cargoes that can be feasibly carried by a ship within the planning horizon , together with loading and discharging dates for each cargo in the set. Provided that candidate schedules have been generated for each ship, the problem of choosing from these an optimal schedule for each ship is formulated as a set partitioning problem, a set packing problem, and a integer generalized network problem respectively. We write the PASCAL programs for schedule generator and apply our approach to the crude oil tanker scheduling problem similar to a realistic system.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.279-282
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• 2001

This paper is concerned with Vehicle Routing Problem to minimize the total delivery waiting time of customers. The delivery waiting time is the time taken to travel from the depot to the customer, which is important for the delivery of the perishing products or foods requiring freshness. We construct a mixed integer linear programming formulation of this problem, and CR(Clustering first Routing second) heuristic and SPH(set partitioning heuristic) are suggested. the results of computational experiments showed that these heuristics find successfully favorable solutions, in much shorter time than optimal.

• Journal of the Korean Society for Railway
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• v.8 no.5
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• pp.391-397
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• 2005

In this paper we present a model for the maintenance routing construction and the trainset allocation (maintenance routing problem). The model solves the maintenance routing problem using column generation algorithm which was used to combine constraint programming and linear programming. Ilog-cplex was used to solve the linear programming model and Ilog-solver was used to solve the constraint programming model. The computational experience is also provided.

• Journal of Korean Institute of Industrial Engineers
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• v.27 no.3
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• pp.250-259
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• 2001

Given a tree structured network in which each node has its own demand and also stands for a candidate location of a potential facility, such as plant or warehouse, a capacitated facility location problem on the network (CFLPOT) is to decide capacitated facility locations so that the total demand occurred on the network can be satisfied from those facilities with the minimum cost. In this paper, we first introduce a mixed integer programming formulation for CFLPOT with two additional assumptions, the indivisible demand assumption and the contiguity assumption and then show that it can be reformulated as a tree partitioning problem with an exponential number of variables. We then show that it can be solved in O($n^2b$) time by utilizing the limited column generation method developed by Shaw (1993), where n is the total number of nodes in the network and b is the maximum facility capacity. We also develop a depth-first dynamic programming algorithm with a running time of O(nb) for finding the locally maximal reduced cost which plays an important role in the limited column generation method. Finally, we implement our algorithms on a set of randomly generated problems and report the computational results.

• Proceedings of the KSR Conference
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• 2004.06a
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• pp.514-521
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• 2004

A routing is the path that an actual train set follows as it moves from one train to another train in a timetable. The number of routings is equivalent to the number of trainsets required to cover the timetable. The primary factors of rolling stock requirement plan include evaluating the minimum number of routings. This can be formulated as a set partitioning problem and solved using enumeration method or column generation method. In this paper we presents an enumeration algorithm which is useful to implement the enumeration method for the rolling stock requirement plan.

• KIPS Transactions on Computer and Communication Systems
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• v.10 no.4
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• pp.93-100
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• 2021

The Ethereum shard system for solving the scalability problem of the blockchain has a load balancing issue, which is modeled as a graph partitioning problem. In this paper, we propose an adaptive online weighted graph partitioning algorithm that can negotiate between two utility of the shard system using the game theory's bargaining solution. The bargaining solution is an axiomatic solution that can fairly determine the points of conflict of utility. The proposed algorithm was improved to apply the existing online graph partitioning algorithm to the weighted graph, and load balancing was performed efficiently through the design considering the situation of the sharding system using the extension of Nash bargaining solution, which is extended to apply solution to non-convex feasible set of bargaining problem. As a result of the experiment, it showed up to 37% better performance than typical load balancing algorithm of shard system.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.8
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• pp.337-347
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• 2007

An embedded system is called a multi-mode embedded system if it performs multiple applications by dynamically reconfiguring the system functionality. Further, the embedded system is called a multi-mode multi-task embedded system if it additionally supports multiple tasks to be executed in a mode. In this Paper, we address a HW/SW partitioning problem, that is, HW/SW partitioning of multi-mode multi-task embedded applications with timing constraints of tasks. The objective of the optimization problem is to find a minimal total system cost of allocation/mapping of processing resources to functional modules in tasks together with a schedule that satisfies the timing constraints. The key success of solving the problem is closely related to the degree of the amount of utilization of the potential parallelism among the executions of modules. However, due to an inherently excessively large search space of the parallelism, and to make the task of schedulabilty analysis easy, the prior HW/SW partitioning methods have not been able to fully exploit the potential parallel execution of modules. To overcome the limitation, we propose a set of comprehensive HW/SW partitioning techniques which solve the three subproblems of the partitioning problem simultaneously: (1) allocation of processing resources, (2) mapping the processing resources to the modules in tasks, and (3) determining an execution schedule of modules. Specifically, based on a precise measurement on the parallel execution and schedulability of modules, we develop a stepwise refinement partitioning technique for single-mode multi-task applications. The proposed techniques is then extended to solve the HW/SW partitioning problem of multi-mode multi-task applications. From experiments with a set of real-life applications, it is shown that the proposed techniques are able to reduce the implementation cost by 19.0% and 17.0% for single- and multi-mode multi-task applications over that by the conventional method, respectively.

• The Transactions of the Korea Information Processing Society
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• v.7 no.3
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• pp.943-952
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• 2000

The surface reconstruction problem from a set of wire-frame contours is very important in diverse fields such as medical imaging or computer animation. In this paper, surface triangulation method is proposed for solving the problem. Generally, many optimal triangulation techniques suffer from the large computation time but heuristic approaches may produce very unnatural surface when contours are widely different in shape. To compensate the disadvantages of these approaches, we propose a new heuristic triangulation method which iteratively decomposes the surface generation problem from a band (a pair of vertices chain) into tow subproblems from two sub-bands. Generally, conventional greedy heuristic contour triangulation algorithm, suffer from the drastic error propagation during surface modeling when the adjacent contours are different in shape. Our divide-and-conquer algorithm, called band partitioning algorithm, processes eccentric parts of the contours first with more global information. Consequently, the resulting facet model becomes more stable and natural even though the shapes are widely different. An interesting property of our method is hat it supports multi-resolution capability in surface modeling time. According to experiments, it is proved to be very robust and efficient in many applications.