• Title, Summary, Keyword: Linear programming (LP)

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Optimization of water intake scheduling based on linear programming (선형계획법을 이용한 정수장 취수계획 최적화)

  • Jeong, Gimoon;Lee, Indoe;Kang, Doosun
    • Journal of Korea Water Resources Association
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    • v.52 no.8
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    • pp.565-573
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    • 2019
  • An optimization model of water intake planning is developed based on a linear programming (LP) for the intelligent water purification plant operation system. The proposed optimization model minimizes the water treatment costs of raw water purification by considering a time-delay of treatment process and hourly electricity tariff, which is subject to various operation constraints, such as water intake limit, storage tank capacity, and water demand forecasts. For demonstration, the developed model is applied to H water purification center. Here, we have tested three optimization strategies and the results are compared and analyzed in economic and safety aspects. The optimization model is expected to be used as a decision support tool for optimal water intake scheduling of domestic water purification centers.

A Study on ESS Optimal Operation Strategy Using Two Stage Hybrid Optimization (Two Stage Hybrid Optimization을 사용한 ESS 최적 운전 전략에 대한 연구)

  • Gong, Eun-Kyoung;Sohn, Jin-Man
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.67 no.7
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    • pp.833-839
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    • 2018
  • This paper presents an analysis and the methodology of optimal operation strategy of the ESS(Energy Storage System) for reduce electricity charges. Electricity charges consist of a basic charge based on the contract capacity and energy charge according to the power usage. In order to use electrical energy at minimal charge, these two factors are required to be reduced at the same time. QP(Quadratic Programming) is appropriate for minimization of the basic charge and LP(Linear Programmin) is adequate to minimize the energy charge. However, the integer variable have to be introduced for modelling of different charge and discharge efficiency of ESS PCS(Power Conversion System), where MILP(Mixed Integer Linear Programming) can be used. In this case, the extent to which the peak load savings is accomplished should be assumed before the energy charge is minimized. So, to minimize the electricity charge exactly, optimization is sequentially performed in this paper, so-called the Two Stage Hybird optimization, where the extent to which the peak load savings is firstly accomplished through optimization of basic charge and then the optimization of energy charge is performed with different charge and discharge efficiency of ESS PCS. Finally, the proposed method is analyzed quantitatively with other optimization methods.

Software Development of Generalized Linear/Goal Programming for Microcomputer (일반화된 선형/목표계획법의 마이크로컴퓨터용 소프트웨어 개발)

  • 차동완;고재문;이원택
    • Journal of the Korean Operations Research and Management Science Society
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    • v.11 no.1
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    • pp.51-58
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    • 1986
  • The propose of this study is to presnet a generalized linear/goal programming software, which has been developed to run on mickrocomputers with at least 512 K bytes of memory. The main characteristics of our algorithm for solving LP/GP problems are outlined as follows ; First, it uses the revised simplex algorithm, which is the most efficient computational procedure for computers. Second, it employs the sparse matrix technique to overcome the limited memory of microcomputers. Last, it uses the modified product form of invers (MPFI) to reduce round-off errors. The test runs with our code written in FORTRAN show that it can be used as an effective tool for solving linear/goal programming problems of considerable size.

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On visualization of solutions of the linear Programming (선형계획법의 해의 이동에 관한 시각화)

  • 이상욱;임성묵;박순달
    • Korean Management Science Review
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    • v.19 no.1
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    • pp.67-75
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    • 2002
  • This paper deals with the visualization method of solutions of the linear programming Problem. We used the revised simplex method for the LP algorithm. To represent the solutions at each iteration, we need the informations of feasible legion and animated effect of solutions. For the visualization in high dimension space, we used the method of Projection to the three dimensions if the decision variable vector is over three dimensions, and we studied the technique of preserving original Polyhedral information such as the number of vertices. In addtion, we studied the method of visualizing unbounded feasible region and the adjacency relationship of the vortices welch is Indispensable to cisualize feasible legion.

ABS ALGORITHM FOR SOLVING A CLASS OF LINEAR DIOPHANTINE INEQUALITIES AND INTEGER LP PROBLEMS

  • Gao, Cheng-Zhi;Dong, Yu-Lin
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.349-353
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    • 2008
  • Using the recently developed ABS algorithm for solving linear Diophantine equations we introduce an algorithm for solving a system of m linear integer inequalities in n variables, m $\leq$ n, with full rank coefficient matrix. We apply this result to solve linear integer programming problems with m $\leq$ n inequalities.

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A Linear Program Based Heuristic for the Bit and Subchannel Allocation in an OFDM System (OFDM 시스템의 비트 및 부채널 할당을 위한 선형계획법 기반 휴리스틱)

  • Moon, Woosik;Kim, Sunho;Park, Taehyung;Im, Sungbin
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.8
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    • pp.67-75
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    • 2013
  • The advantages of the orthogonal frequency division multiplexing (OFDM) are high spectral efficiency, resiliency to RF interference, and lower multi-path distortion. To further utilize vast channel capacity of the multiuser OFDM, one has to find the efficient adaptive subchannel and bit allocation among users. In this paper, we compare the performance of the linear programming dual of the 0-1 integer programming formulation with the existing convex optimization approach for the optimal subchannel and bit allocation problem of the multiuser OFDM. Utilizing tight lower bound provided by the LP dual formulation, we develop a primal heurisitc algorithm based on the LP dual solution. The performance of the primal heuristic is compared with MAO, ESA heuristic solutions, and integer programming solution on MATLAB simulation on a system employing M-ary quadrature amplitude modulation (MQAM) assuming a frequency-selective channel consisting of three independent Rayleigh multi-paths.

A Distributed Task Assignment Method and its Performance

  • Kim, Kap-Hwan
    • Management Science and Financial Engineering
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    • v.2 no.1
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    • pp.19-51
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    • 1996
  • We suggest a distributed framework for task assignment in the computer-controlled shop floor where each of the resource agents and part agents acts like an independent profit maker. The job allocation problem is formulated as a linear programming problem. The LP formulation is analyzed to provide a rationale for the distributed task assignment procedure. We suggest an auction based negotiation procedure including a price-based bid construction and a price revising mechanism. The performance of the suggested procedure is compared with those of an LP formulation and conventional dispatching procedures by simulation experiments.

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Linear Time Algorithm for Network Reliability Problem

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.21 no.5
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    • pp.73-77
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    • 2016
  • This paper deals with the network reliability problem that decides the communication line between main two districts while the k districts were destroyed in military communication network that the n communication lines are connected in m districts. For this problem, there is only in used the mathematical approach as linear programming (LP) software package and has been unknown the polynomial time algorithm. In this paper we suggest the heuristic algorithm with O(n) linear time complexity to solve the optimal solution for this problem. This paper suggests the flow path algorithm (FPA) and level path algorithm (LPA). The FPA is to search the maximum number of distinct paths between two districts. The LPA is to construct the levels and delete the unnecessary nodes and edges. The proposed algorithm can be get the same optimal solution as LP for experimental data.

Intra-Session Network Coding for Improving Throughput in Multirate Multihop Wireless Networks (다중 레이트 멀티 홉 무선 네트워크 환경의 처리율 향상을 위한 인트라세션 네트워크 코딩)

  • Park, Mu-Seong;Yoon, Won-Sik
    • Journal of the Institute of Electronics Engineers of Korea TC
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    • v.49 no.5
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    • pp.21-26
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    • 2012
  • Intra-session network coding has been proposed to improve throughput by simplifying scheduling of multi-hop wireless network and efficiency of packet transmission. Multi-rate transmission has been used in multihop wireless networks. An opportunistic routing with multirate shows throughput improvement compared with single rate. In this paper, we propose a method of throughput improvement in multi-hop wireless network by using multi-rate and intra-session network coding. We suggest a method to select an local optimal transmission rate at each node. The maximum throughput is evaluated by using linear programming (LP). To solve the LP, we use MATLAB and lp_solve IDE program. The performance evaluation results show that end-to-end throughput is improved by using multirate and intra-session network coding can achieve better throughput than opportunistic routing.

The Cardinality Constrained Multi-Period Linear Programming Knapsack Problem (선수제약 다기간 선형계획 배낭문제)

  • Won, Joong-Yeon
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.38 no.4
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    • pp.64-71
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    • 2015
  • In this paper, we present a multi-period 0-1 knapsack problem which has the cardinality constraints. Theoretically, the presented problem can be regarded as an extension of the multi-period 0-1 knapsack problem. In the multi-period 0-1 knapsack problem, there are n jobs to be performed during m periods. Each job has the execution time and its completion gives profit. All the n jobs are partitioned into m periods, and the jobs belong to i-th period may be performed not later than in the i-th period, i = 1, ${\cdots}$, m. The total production time for periods from 1 to i is given by $b_i$ for each i = 1, ${\cdots}$, m, and the objective is to maximize the total profit. In the extended problem, we can select a specified number of jobs from each of periods associated with the corresponding cardinality constraints. As the extended problem is NP-hard, the branch and bound method is preferable to solve it, and therefore it is important to have efficient procedures for solving its linear programming relaxed problem. So we intensively explore the LP relaxed problem and suggest a polynomial time algorithm. We first decompose the LP relaxed problem into m subproblems associated with each cardinality constraints. Then we identify some new properties based on the parametric analysis. Finally by exploiting the special structure of the LP relaxed problem, we develop an efficient algorithm for the LP relaxed problem. The developed algorithm has a worst case computational complexity of order max[$O(n^2logn)$, $O(mn^2)$] where m is the number of periods and n is the total number of jobs. We illustrate a numerical example.