• Management Science and Financial Engineering
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• v.14 no.2
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• pp.25-44
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• 2008

This paper concentrates on reduction of a Quadratic Fractional Integer Programming Problem (QFIP) to a 0-1 Mixed Linear Programming Problem (0-1 MLP). The solution technique is based on converting the integer variables to binary variables and then the resulting Quadratic Fractional 0-1 Programming Problem is linearized to a 0-1 Mixed Linear Programming problem. It is illustrated with the help of a numerical example and is solved using the LINDO software.

• IE interfaces
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• v.21 no.2
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• pp.170-176
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• 2008

Consider a multi-floor facility with multiple rooms of unequal size on each floor. Students come from many organizations to attend the conference to be held at this facility. In assigning the rooms to the students, several constraints must be met; such as boys and girls must not be assigned to the rooms on the same floor. Given the capacity of each room and the number of students from each organization, the problem is assigning students to rooms under a set of constraints and various objectives. We present six models with different objective functions; and formulate them as binary integer programming problems. A numerical example and a case study follow to illustrate the proposed models.

• Industrial Engineering and Management Systems
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• v.16 no.1
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• pp.141-153
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• 2017

A binary integer programming model is proposed for a complex timetabling problem in a university faculty which conducts various degree programs. The decision variables are defined with fewer dimensions to economize the model size of large scale problems and to improve modeling efficiency. Binary matrices are used to incorporate the relationships between the courses and students, and the courses and teachers. The model includes generally applicable constraints such as completeness, uniqueness, and consecutiveness; and case specific constraints. The model was coded and solved using Open Solver which is an open-source optimizer available as an Excel add-in. The results indicate that complicated timetabling problems with large numbers of courses and student groups can be formulated more efficiently with fewer numbers of variables and constraints using the proposed modeling framework. The model could effectively generate timetables with a significantly lower number of work hours per week compared to currently used timetables. The model results indicate that the particular timetabling problem is bounded by the student overlaps, and both human and physical resource constraints are insignificant.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.5
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• pp.1069-1084
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• 2011

This paper considers an optimal base station clustering problem for designing a mobile (wireless) communication network. For a given network with a set of nodes (base stations), the problem is to optimally partition the set of nodes into subsets (each called a cluster) such that the associated inter-cluster traffic is minimized under certain topological constraints and cluster capacity constraints. In the problem analysis, the problem is formulated as an integer programming problem. The integer programming problem is then transformed into a binary integer programming problem, for which the associated linear programming relaxation is solved in a column generation approach assisted by a branch-and-bound procedure. For the column generation, both a heuristic algorithm and a valid inequality approach are exploited. Various numerical examples are solved to evaluate the effectiveness of the LP (Linear Programming) based branch-and-bound algorithm.

• Journal of the Korea Society of Computer and Information
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• v.24 no.9
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• pp.9-20
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• 2019

In this paper, we study the university timetabling problem, which consists of two subproblems, the university course timetabling problem and the examination timetabling problem. Given a set of classrooms, students, teachers, and lectures, the problem is to assign a number of courses (and examinations) to suitable timeslots and classrooms while satisfying the given set of constraints. We discuss the modeling and solution approaches to construct course and examination timetables for one of the largest Korean university. By using binary integer programming formulations, we describe these two complex real-world problems. Then, we propose a solution method, called NOGOOD, to solve the examination timetabling model. The computation results show that NOGOOD finds the optimal examination schedule for the given instance. Although we consider a specific instance of the university timetabling problem, the methods we use can be applicable to modeling and solving other timetabling problems.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.293-303
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• 2006

This paper describes a numerical scheme for optimal control of a time-dependent linear system to a moving final state. Discretization of the corresponding differential equations gives rise to a linear algebraic system. Defining some binary variables, we approximate the original problem by a mixed integer linear programming (MILP) problem. Numerical examples show that the resulting method is highly efficient.

• Journal of the Korea Society of Computer and Information
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• v.15 no.10
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• pp.1-9
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• 2010

In this paper, we propose a methodology in which a power-delay product of a binary adder is optimized based on the heterogeneous adder architecture. We formulate the power-delay product of the heterogeneous adder by using integer linear programming(ILP). For the use of ILP optimization, we adopt a transformation technique in which the initial non-linear expression for the power-delay product is converted into linear expression. The experimental result shows the superiority of the suggested method compared to the cases in which only conventional adder is used.

• Proceedings of the Korean Information Science Society Conference
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• 2010.11a
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• pp.32-33
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• 2010

• Honam Mathematical Journal
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• v.28 no.4
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• pp.521-531
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• 2006

In this paper, we construct a procedure of Maple programming for (0, 1)-matrix with a prescribed permanent, $1,2,...,2^{n-1}$. An application of such construction is given, and we obtain the some results of (0, 1)-matrices with the permanent less than or equal to n! by replacing elements 0's by 1's.

• Journal of the Korean Society of Marine Environment & Safety
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• v.6 no.1
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• pp.23-33
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• 2000

This paper is concerned with finding the global optimal solutions for the redundancy optimization problems in series-parallel systems related with system safety. This study transforms the difficult problem, which is classified as a nonlinear integer problem, into a 0/1 IP(Integer Programming) by using binary integer variables. And the global optimal solution to this problem can be easily obtained by applying GAMS (General Algebraic Modeling System) to the transformed 0/1 IP. From computational results, we notice that GA(Genetic Algorithm) to this problem, which is, to our knowledge, known as a best algorithm, is poor in many cases.