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A sequencing problem with family setup times

DISCRETE APPLIED MATHEMATICS 1996年第2期66卷 161-183页

作者： Zdrzalka, S Institute of Engineering Cybernetics Technical University of Wroc&z.xl law ul. Janiszewskiego 11/17 50-372 Wrocław Poland

We study the single-machine scheduling problem with release and delivery times in which the set of jobs to be scheduled consists of job families requiring a machine setup between two consecutively scheduled jobs from two different families. The setup time depends only on the family to be sequenced next, and the objective is to minimize the makespan. For the case where all the jobs of each family have to be scheduled contiguously, called the family sequencing problem, a generalization of the extended Jackson's rule is introduced and its properties are analyzed. As a result, a branch and bound algorithm is developed which is capable of solving problem instances with hundreds of jobs in very short time. Results of computational experiments are reported. For the problem with families divisible into batches, several heuristics are proposed and analyzed. The general approach consists in successively applying one of the family sequencing algorithms, heuristic or exact, to the set of batches,each lime modifying the current partition of families. Results of the worst-case analysis and computational experiments are shown.

关键词： single-machine scheduling setup times batching branch and bound algorithm worst-case analysis

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Production and transport logistics scheduling with two transport mode choices

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NAVAL RESEARCH LOGISTICS 2005年第8期52卷 796-809页

作者： Wang, HY Lee, CY Hong Kong Univ Sci & Technol Dept Ind Engn & Engn Management Hong Kong Hong Kong Peoples R China

This paper considers a new class of scheduling problems arising in logistics systems in which two different transportation modes are available at the stage of product delivery. The mode with the shorter transportation time charges a higher cost. Each job ordered by the customer is first processed in the manufacturing facility and then transported to the customer. There is a due date for each job to arrive to the customer. Our approach integrates the machine scheduling problem in the manufacturing stage with the transportation mode selection problem in the delivery stage to achieve the global maximum benefit. In addition to studying the NP-hard special case in which no tardy job is allowed, we consider in detail the problem when minimizing the sum of the total transportation cost and the total weighted tardiness cost is the objective. We provide a branch and bound algorithm with two different lower bounds. The effectiveness of the two lower bounds is discussed and compared. We also provide a mathematical model that is solvable by CPLEX. Computational results show that our branch and bound algorithm is more efficient than CPLEX. (C) 2005 Wiley Periodicals, Inc.

关键词： scheduling logistics transportation modes branch and bound algorithm

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Integrated problem of soaking pit heating and hot rolling scheduling in steel plants

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COMPUTERS & OPERATIONS RESEARCH 2019年 108卷 238-246页

作者： Li, Feng Zhang, Yanyan Wei, Han Lai, Xiaofan Huazhong Univ Sci & Technol Sch Management Wuhan 430074 Hubei Peoples R China Northeastern Univ Inst Ind & Syst Engn Shenyang 110819 Liaoning Peoples R China Sun Yat Sen Univ Business Sch Guangzhou 510275 Guangdong Peoples R China

This paper considers an integrated problem of soaking pit heating and hot rolling scheduling that arises in steel plants. Both soaking pit and hot rolling mill are batching machines with capacity considerations. The processing time of a batch in the soaking pit is equal to the longest processing time of the jobs in the batch, whereas the processing time of a batch on the hot rolling mill is equal to the sum of the processing times of the jobs in the batch. Setup time is required whenever a batch is formed on the hot rolling mill. For this problem, we must determine the formation of batches and the sequences of these batches in the soaking pit and on the hot rolling mill such that makespan is minimized. First, we formulate the problem as a mixed integer linear programming model (MILPM) and analyze its computational complexity. Second, we provide a fast heuristic algorithm with worst-case bound to generate near-optimal solutions, and a branch and bound algorithm to solve the problem to optimality. Finally, computational experiments using randomly generated data demonstrate that our heuristic algorithm is very efficient and effective, and the branch and bound algorithm significantly outperforms CPLEX on MILPM in terms of computational time and the number of instances solved to optimality within the given time limit. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Flow shop Batch scheduling NP-hard Dynamic programming Heuristics Worst-case analysis branch and bound algorithm

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Optimal capacitor placement using deterministic and genetic algorithms

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IEEE TRANSACTIONS ON POWER SYSTEMS 2000年第3期15卷 1041-1046页

作者： Delfanti, M Granelli, GP Marannino, P Montagna, M Univ Pavia Dipartimento Ingn Elettr I-27100 Pavia Italy

A procedure for solving the capacitor placement problem is presented. The objective is to determine the minimum investment required to satisfy suitable reactive constraints. Due to the discrete nature of reactive compensation devices, optimal capacitor placement leads to a nonlinear programming problem with mixed (discrete and continuous) variables, It is solved with an iterative algorithm based on successive linearizations of the original nonlinear model. The mixed integer linear programming problem to be solved at each iteration of the procedure is tackled by applying both a deterministic method (branch and bound) and genetic algorithm techniques, A hybrid procedure, aiming to exploit the best features of both algorithms is also considered. The proposed procedures are tested and compared with reference to a small CIGRE system and two actual networks derived from the Italian transmission and distribution system.

关键词： branch and bound algorithm genetic algorithms mixed integer programming VAR planning

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Optimization-Based Scheduling Method for Agile Earth-Observing Satellite Constellation

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JOURNAL OF AEROSPACE INFORMATION SYSTEMS 2018年第11期15卷 611-626页

作者： Cho, Doo-Hyun Kim, Jun-Hong Choi, Han-Lim Ahn, Jaemyung Korea Adv Inst Sci & Technol Dept Aerosp Engn Daejeon 34141 South Korea

This Paper proposes a two-step binary linear programming formulation for task scheduling of a constellation of low-Earth-orbit satellites and demonstrates its applicability and scalability to obtain high-quality solutions using a standard mixed-integer linear programming solver. In this instance, the goal of satellite constellation task scheduling is to allocate each task for the satellites and to determine the task starting times in order to maximize the overall mission performance metric. The scheduling problem is formulated to find the solution by first finding a set of candidate communication time intervals for each satellite/ground-station pair as one of the key constraints and time tabling the observation task to acquire the user-requested data, with the incorporation of key constraints for satellite constellation operation. Numerical experiments are designed for investigating the trends, sensitivity, and characteristics of scheduling outputs based on multiple representative instances. The performance of the scheduling solutions by the proposed two-step binary linear programming method exhibits significant improvement of up to 35% in the number of assignments and the sum of profits over the general greedy algorithm.

关键词： Low Earth Orbit Satellites Earth branch and bound algorithm Constellations Ant Colony Optimization algorithms Mixed Integer Linear Programming Satellite Ground Station Ground Station EOS Data Store

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A two-stage stochastic optimization model for the transfer activity choice in metro networks

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2016年 83卷 271-297页

作者： Yang, Lixing Zhang, Yan Li, Shukai Gao, Yuan Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

This research focuses on finding the best transfer schemes in metro networks. Using sample-based time-invariant link travel times to capture the uncertainty of a realistic network, a two-stage stochastic integer programming model with the minimized expected travel time and penalty value incurred by transfer activities is formulated. The first stage aims to find a sequence of potential transfer nodes (stations) that can compose a feasible path from origins to destinations in the transfer activity network, and the second stage provides the least time paths passing by the generated transfer stations in the first stage for evaluating the given transfer schemes and then outputs the best routing information. To solve our proposed model, an efficient hybrid algorithm, in which the label correcting algorithm is embedded into a branch and bound searching framework, is presented to find the optimal solutions of the considered problem. Finally, the numerical experiments are implemented in different scales of metro networks. The computational results demonstrate the effectiveness and performance of the proposed approaches even for the large-scale Beijing metro network. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Transfer activity scheme Two-stage stochastic programming model branch and bound algorithm Label correcting algorithm

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COMPARISON OF ROUTING algorithmS FOR STORAGE AND RETRIEVAL MECHANISM IN CYLINDRICAL AS/RS

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TRANSPORT 2016年第1期31卷 11-21页

作者： Janilionis, Vytautas V. Bazaras, Zilvinas Janilionis, Vytautas [a] Dept of Transport Engineering Kaunas University of Technology Kaunas Lithuania[b] Dept of Applied Mathematics Kaunas University of Technology Lithuania

The objective of this research is to propose new routing algorithms for the Storage and Retrieval Mechanism (SRM) in the Cylindrical Automated Storage and Retrieval System (C-AS/RS) and contribute to the system conceptualization by investigating the maximum achievable retrieval request rates for different routing algorithms and system parameters. For this purpose, flexible and detailed simulation model was developed and investigated for 2 SRM types, 3 routing algorithms and a feasible set of system movement and load transfer time parameters. Based on the simulation output, the regression models for different SRM types and routing algorithms were developed for predicting the maximum retrieval request rate. The differences of the average maximum retrieval request rate were evaluated for various system configurations and routing algorithms. The alternative to optimal routing algorithm was proposed, reducing the system performance only by 1.4?÷?2.4% on average, but requiring significantly less calculations when planning the SRM tour. In addition, the system analysis indicated that SRM vertical velocity and load transfer time have the highest impact on the system performance and for different SRM types the average maximum retrieval request rates differ by 22.2?÷?31.8%.

关键词： cylindrical automated storage and retrieval system routing algorithm branch and bound algorithm automated warehouse simulation regression analysis

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Rotation cycle schedulings for multi-item production systems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第2期135卷 361-372页

作者： Chan, GH Song, YY Natl Univ Singapore Dept Math Kent Ridge Digital Labs Singapore 119613 Singapore Natl Univ Singapore Dept Math Singapore 119260 Singapore

Consider the production planning and scheduling on a single machine with finite constant production rate over a planning horizon N. For single-item production problem, we have characterised the structure of the optimal solution when N approaches to infinity. This result suggests a near optimal solution when the planning horizon N is large. For multi-item production problem, we restrict our analysis on the Rotation Cycle policies. Under the assumptions of the policy, we convert the problem into a generalised travelling salesman problem and hence a branch and bound algorithm is proposed to solve the problem. For a given error bound of the solution, the algorithm can be further simplified to determine a near-optimal rotation cycle. (C) 2001 Published by Elsevier Science B.V.

关键词： branch and bound algorithm travelling salesman rotation cycle

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Minimizing total tardiness on a single machine with unequal release dates

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第2期186卷 496-503页

作者： Su, Ling-Huey Chen, Chung-Jung Chung Yuan Christian Univ Dept Ind Engn Chungli Taiwan

This study addresses the problem of minimizing total tardiness on a single machine with unequal release dates. Dominance properties established in previous literatures and herein are adopted to develop branch and bound and heuristic procedures. Computational experiments were conducted to evaluate the approaches. The results revealed that the branch and bound algorithm is efficient in solving hard problems and easy problems that involve up to 50 and 500 jobs, respectively. The computational effectiveness of the heuristic is also reported. (C) 2007 Elsevier B.V. All rights reserved.

关键词： single machine total tardiness unequal release dates branch and bound algorithm Heuristic algorithm

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STACKING-SEQUENCE OPTIMIZATION FOR BUCKLING OF LAMINATED PLATES BY INTEGER PROGRAMMING

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AIAA JOURNAL 1992年第3期30卷 814-819页

作者： HAFTKA, RT WALSH, JL NASA LANGLEY RES CTRINTERDISCIPLINARY RES OFFHAMPTONVA 23665

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

关键词： Buckling branch and bound algorithm Aspect Ratio Composite Laminates Structural Optimization Bending Stiffness Elastic Properties Trusses

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