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mixed-integer linear programming method for coordination of overcurrent and distance relays incorporating overcurrent relays characteristic selection

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2019年第Sep.期110卷 246-257页

作者： Maleki, Mandi Ghotbi Chabanloo, Reza Mohammadi Taheri, Mohammad Reza Shahid Beheshti Univ Elect Engn Dept AC Tehran Iran

Coordination of overcurrent-overcurrent (OC) and overcurrent-distance (Dis) relays is one of the important issues in sub-transmission and distribution networks. In this paper, three approaches based on mixed-integer linear programming (MILP) is proposed for OC-OC and OC-Dis relays' coordination. Two of these proposed approaches are based on previously presented MILP-based approaches that were introduced for determining time and pickup-current settings in OC-OC relays' coordination problem. These predefined approaches are developed for obtaining optimal types of OC relays in addition to time and pickup-current settings in OC-OC and OC-Dis relays' coordination problem. A new MILP-based approach with less variables than the developed approaches is also proposed. This new approach has the ability to reach the best result in the short simulation time. In the new proposed approach, a cubic term which has two binary variables and one continuous variable must be replaced with a linear term. Therefore, a new linearization method is presented for this purpose. Three proposed approaches are implemented on the IEEE 8-buses and the IEEE 30-buses network. It is illustrated that new proposed approach from the point of view of objective function and simulation time is better than other methods especially for large networks. Therefore, new proposed approach is suitable for employing in the computing software as an efficient algorithm for relays' coordination.

关键词： Distance relay mixed-integer linear programming Overcurrent relay Relays coordination

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mixed-integer linear programming for project scheduling under various resource constraints

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第1期319卷 79-88页

作者： Klein, Nicklas Gnagi, Mario Trautmann, Norbert Univ Bern Dept Business Adm Engehaldenstr 4 CH-3012 Bern Switzerland

Project scheduling is an important management task in many companies across different industries. Generally, projects require resources, such as personnel or funds, whose availabilities are limited, giving rise to the challenging problem of resource-constrained project scheduling. In this paper, we consider the scheduling of a project consisting of precedence-related activities that require time and two types of resources for execution: storage resources representing, e.g., the project budget;and renewable resources representing, e.g., personnel or equipment. Storage resources are consumed by activities at their start or produced upon their completion, while renewable resources are allocated to activities at their start and released upon their completion. The resource-constrained project scheduling problem with consumption and production of resources (RCPSP-CPR) consists of determining a minimum-makespan schedule such that all precedence relations are respected, the demand for each renewable resource never exceeds its capacity, and the stock level of each storage resource never falls below a prescribed minimum. Due to the consideration of storage resources, the feasibility variant of this problem is NP-complete. We propose a novel compact mixed-integer linear programming (MILP) model based on a novel type of sequencing variables. These variables enable us to identify which activities are processed in parallel and whether a sequencing of activities is necessary to respect the resource capacities. Our computational results indicate that our novel model significantly outperforms state-of-the-art MILP models for all considered scarcity settings of the storage resources. Additionally, our results indicate a superior performance for instances of the well-known resource-constrained project scheduling problem (RCPSP).

关键词： Project scheduling mixed-integer linear programming Resource-constrained project scheduling Consumption and production of resources

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mixed-integer linear programming, constraint programming and column generation approaches for operating room planning under block strategy

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APPLIED MATHEMATICAL MODELLING 2022年 105卷 438-453页

作者： Ghandehari, Najmeh Kianfar, Kamran Univ Isfahan Fac Adm Sci & Econ Dept Management Esfahan *** Iran Univ Isfahan Fac Engn Esfahan *** Iran

The planning of operating rooms under block strategy is addressed in this study. The decisions are about opening the operating rooms and assigning specialties and surgeons to blocks at the tactical level, and sequencing the surgeries at the operational level. This problem aims to minimize the costs of opening the operating rooms and their overtime, the waiting costs of patients, and the surgeons' idle costs. We propose two mixed integer linear programming models, a constraint programming (CP) model and a constraint programming-based column generation (CPCG) method for handling the problem. The performance of the models is evaluated by random test instances. The results indicate that CP and CPCG models are more efficient than the linear programming models in terms of computational time, and the number of variables and constraints. The proposed method CPCG generates optimal solutions for problem instances of up to 30 surgeries in less than 4 min. The CP model finds the optimal solutions in about one minute but proving the optimality of the found solutions is time-consuming in some instances. The maximum optimality gap for the proposed two-step linear programming model is 2%, while its run time is less than 20 s. A sensitivity analysis is done on the main parameters of the problem like objectives' weights, opening cost of ORs, unit waiting cost of patients, and the maximum available time in surgery blocks. Among the three objectives, the unit waiting cost of patients has the most sensitivity to variations of the objective function weights.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Operating room planning Block strategy Master surgery schedule mixed-integer linear programming Constraint programming Column generation

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mixed-integer linear programming model for solving reconfiguration problems in large-scale distribution systems

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ELECTRIC POWER SYSTEMS RESEARCH 2012年 88卷 137-145页

作者： Llorens-Iborra, Francisco Riquelme-Santos, Jesus Romero-Ramos, Esther Univ Cadiz Dept Elect Engn Cadiz Spain Univ Seville Dept Elect Engn Seville Spain

An improved mixed-integer linear program for determining the tree of minimum active power losses in balanced large medium voltage systems is presented and assessed throughout this paper. The proposed approach depends on a number of parameters, which can be tuned for each specific system, ensuring a desired level of accuracy in relation to the final obtained solution. Eight systems were tested with the new algorithm to highlight the efficiency and accuracy of the proposed model. The model is mainly designed for large systems with a high number of switches whose statuses need to be determined. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Distribution networks Loss minimisation Network reconfiguration mixed-integer linear programming

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mixed-integer linear programming approach for global discrete sizing optimization of frame structures

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2018年第2期57卷 579-593页

作者： Van Mellaert, R. Mela, K. Tiainen, T. Heinisuo, M. Lombaert, G. Schevenels, M. Katholieke Univ Leuven Dept Architecture Fac Engn Sci Kasteelpk Arenberg 1 Box 2431 B-3001 Leuven Belgium Tampere Univ Technol Dept Civil Engn Tampere Finland Katholieke Univ Leuven Dept Civil Engn Fac Engn Sci Leuven Belgium

This paper focuses on discrete sizing optimization of frame structures using commercial profile catalogs. The optimization problem is formulated as a mixed-integer linear programming (MILP) problem by including the equations of structural analysis as constraints. The internal forces of the members are taken as continuous state variables. Binary variables are used for choosing the member profiles from a catalog. Both the displacement and stress constraints are formulated such that for each member limit values can be imposed at predefined locations along the member. A valuable feature of the formulation, lacking in most contemporary approaches, is that global optimality of the solution is guaranteed by solving the MILP using branch-and-bound techniques. The method is applied to three design problems: a portal frame, a two-story frame with three load cases and a multiple-bay multiple-story frame. Performance profiles are determined to compare the MILP reformulation method with a genetic algorithm.

关键词： Global optimization Discrete optimization Sizing optimization Frame structures mixed-integer linear programming

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mixed-integer linear programming and constraint programming formulations for solving resource availability cost problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期266卷 472-486页

作者： Kreter, Stefan Schutt, Andreas Stuckey, Peter J. Zimmermann, Juergen Tech Univ Clausthal Inst Management & Econ Operat Res Grp Julius Albert Str 2 D-38678 Clausthal Zellerfeld Germany CSIRO Decis Sci Data61 Canberra ACT Australia Univ Melbourne Dept Comp & Informat Syst Melbourne Vic 3010 Australia

We consider the resource availability cost problem and two extensions through general temporal constraints and calendar constraints. With general temporal constraints minimum and maximum time lags between the activities can be ensured. Calendar constraints are used to model breaks in the availability of a resource, e.g., weekends or public holidays of resource types that equal staff. Especially if long-term and capital-intensive projects are under consideration, resource availability cost problems should be applied because in such projects it is more important to minimize the cost than, e.g., the project duration. We present mixed-integer linear programming (MILP) formulations as well as constraint programming (CP) models for the three problems. In a performance study we compare the results of the MILP formulations solved by CPLEX and the CP models solved by the lazy clause generation solver CHUFFED on benchmark instances from literature and also introduce new benchmarks. Our CP models close all open instances for resource availability cost problems from the literature. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Project scheduling Resource availability cost problem General temporal constraints and calendars Lazy clause generation mixed-integer linear programming

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mixed-integer linear programming models for the type-II resource-constrained assembly line balancing problem

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ASSEMBLY AUTOMATION 2022年第5期42卷 585-594页

作者： Michels, Adalberto Sato Costa, Alysson M. Univ Melbourne Sch Math & Stat Melbourne Vic Australia

Purpose Resource-constrained assembly lines are widely found in industries that manufacture complex products. In such lines, tasks may require specific resources to be processed. Therefore, decisions on which tasks and resources will be assigned to each station must be made. When the number of available stations is fixed, the problem's main goal becomes the minimisation of cycle time (type-II version). This paper aims to explore this variant of the problem that lacks investigation in the literature. Design/methodology/approach In this paper, the authors propose mixed-integer linear programming (MILP) models to minimise cycle time in resource-constrained assembly lines, given a limited number of stations and resources. Dedicated and alternative resource types for tasks are considered in different scenarios. Findings Besides, past modelling decisions and assumptions are questioned. The authors discuss how they were leading to suboptimal solutions and offer a rectification. Practical implications The proposed models and data set fulfil more practical concerns by taking into account characteristics found in real-world assembly lines. Originality/value The proposed MILP models are applied to an existing data set, results are compared against a constraint programming model, and new optimal solutions are obtained. Moreover, a data set extension is proposed due to the simplicity of the current one and instances up to 70 tasks are optimally solved.

关键词： Assembly line balancing Resource constraints Type-II problem mixed-integer linear programming

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mixed-integer linear programming method for multi-degree and multi-hoist cyclic scheduling with time windows

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ENGINEERING OPTIMIZATION 2018年第11期50卷 1978-1995页

作者： Mao, Yong-nian Tang, Qiu-hua Li, Zi-xiang Zhang, Li-ping Wuhan Univ Sci & Technol Key Lab Met Equipment & Control Technol Wuhan Hubei Peoples R China Wuhan Univ Sci & Technol Hubei Key Lab Mech Transmiss & Mfg Engn Wuhan Hubei Peoples R China

Multi-degree cyclic hoist scheduling and multi-hoist cyclic scheduling are both capable of improving the throughput in an automatic electroplating line. However, previous research on integrated multi-degree and multi-hoist cyclic scheduling is rather limited. This article develops an optimal mixed-integer linear programming model for the integrated multi-degree and multi-hoist cyclic scheduling with time window constraints. This model permits overlap on hoist coverage ranges, and it proposes new formulations to avoid hoist collisions, by which time window constraints and tank capacity constraints are also formulated. A set of available benchmark instances and newly generated instances are solved using the CPLEX solver to test the performance of the proposed method. Computational results demonstrate that the proposed method outperforms the zone partition heuristic without overlapping, and the throughputs are improved by a significant margin using the proposed method, especially for large-size instances.

关键词： Multi-degree cyclic scheduling multi-hoist scheduling mixed-integer linear programming time windows

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mixed-integer linear programming heuristics for the prepack optimization problem

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DISCRETE OPTIMIZATION 2016年第PartA期22卷 195-205页

作者： Fischetti, Matteo Monaci, Michele Salvagnin, Domenico Univ Padua DEI Padua Italy

In this paper we consider a packing problem arising in inventory allocation applications, where the operational cost for packing the bins is comparable, or even higher, than the cost of the bins (and of the items) themselves. This is the case, for example, of warehouses that have to manage a large number of different customers (e.g., stores), each requiring a given set of items. For this problem, we present mixed integer linear programming heuristics based on problem substructures that lead to easy-to-solve and meaningful subproblems, and exploit them within an overall meta heuristic framework. The new heuristics are evaluated on a standard set of instances, and benchmarked against known heuristics from the literature. Computational experiments show that very good (often proven optimal) solutions can consistently be computed in short computing times. (C) 2015 Elsevier B.V. All rights reserved.

关键词： mixed-integer linear programming Matheuristics Packing problems Prepack optimization

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mixed-integer linear programming models for batch sterilization of packaged-foods plants

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JOURNAL OF SCHEDULING 2013年第1期16卷 59-68页

作者： Simpson, R. Abakarov, A. Univ Tecn Federico Santa Maria Dept Ingn Quim & Ambiental Valparaiso Chile CREAS Valparaiso Chile

Batch sterilization with individual retorts is a common mode of operation in many food-canning plants. Although high-speed processing with continuous rotary or hydrostatic retort systems is used in very large canning factories, such systems are not economically feasible in the majority of small- to medium-sized canneries. In such canneries, sterilization is carried out in a battery of retorts as a batch process. Although the unloading and reloading operations for each retort are labor intensive, a well-designed and managed plant can operate with surprising efficiency if it has the optimum number of retorts and scheduling of retort operation. The objective of this research was to present two mathematical models for sterilization scheduling in food-canning plants. The first model developed is for the case where given amount of different canned food products with specific quality requirements would be sterilized within a minimum plant operation time in an autoclave of given capacity. The second model addresses the problem of maximizing the amount of sterilized products in an autoclave of given capacity for given plant operation time. The developed models were based on mixed-integer linear programming and incorporated the possibility of simultaneous sterilization. Simultaneous sterilization applies mainly to small canneries with few retorts. In these situations, retorts often operate with only partial loads because of the small lot sizes, and they are severely under-utilized. In order to demonstrate the feasibility of the mixed-integer linear programming (MILP) models, several examples involving the sterilization of different products were included in this research. The methodology proposed in this study is of special relevance for small- and medium-sized food-canning plants that normally work with many different products at the same time.

关键词： Scheduling Food-canning plants mixed-integer linear programming Simultaneous sterilization

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