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A branch-and-price algorithm for the capacitated facility location problem

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期179卷 1109-1125页

作者： Klose, Andreas Goertz, Simon Univ Zurich Inst Operat Res CH-8044 Zurich Switzerland Univ Gesamthsch Wuppertal Fac Econ & Social Sci D-42119 Wuppertal Germany

The capacitated facility location problem (CFLP)is a well-known combinatorial optimization problem with applications in distribution and production planning. It consists in selecting plant sites from a finite set of potential sites and in allocating customer demands in such a way as to minimize operating and transportation costs. A number of solution approaches based on Lagrangean relaxation and subgradient optimization has been proposed for this problem. Subgradient optimization does not provide a primal (fractional) optimal solution to the corresponding master problem. However, in order to compute optimal solutions to large or difficult problem instances by means of a branch-and-bound procedure information about such a primal fractional solution can be advantageous. In this paper, a (stabilized) column generation method is, therefore, employed in order to solve a corresponding master problem exactly. The column generation procedure is then employed within a branch-and-price algorithm for computing optimal solutions to the CFLP. Computational results are reported for a set of larger and difficult problem instances. (c) 2006 Elsevier B.V. All rights reserved.

关键词： capacitated facility location mixed-integer programming Lagrangean relaxation column generation branch-and-price

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A knowledge-based approach for multi-factory production systems

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COMPUTERS & OPERATIONS RESEARCH 2017年第0期77卷 72-85页

作者： Karimi, N. Davoudpour, H. Amirkabir Univ Technol Dept Ind Engn & Management Syst 424 Hafez Ave Tehran *** Iran

This paper investigates scheduling of jobs with deadlines across a serial multi-factory supply chain which involves minimizing sum of total tardiness and total transportation costs. Jobs can be transported among factories and can be delivered to the customer in batches which have limited capacity. The aim of this optimization problem is threefold: (1) determining the number of batches, (2) assigning jobs to batches,and (3) scheduling the batches production and delivery in each factory. The proposed problem formulated as a mixed-integer linear program. Then the model's performance is analyzed and evaluated through two examples. Moreover, a knowledge-based imperialistic competitive algorithm (KBICA) is also presented to find an approximate optimum solution for the problem. Computational experiments of the proposed problem investigate the efficiency of the method through different sizes of the test problems. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Multi-factory production systems Batch delivery mixed-integer programming Knowledge-based approach Imperialist competitive algorithm

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Operational optimization of a grid-connected factory with onsite photovoltaic and battery storage systems

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APPLIED ENERGY 2017年 205卷 1538-1547页

作者： Zhang, Hao Cai, Jie Fang, Kan Zhao, Fu Sutherland, John W. Purdue Univ Sch Mech Engn Ray W Herrick Lab W Lafayette IN 47907 USA Tianjin Univ Coll Management & Econ Tianjin Peoples R China Purdue Univ Sch Mech Engn W Lafayette IN 47907 USA Purdue Univ Div Environm & Ecol Engn W Lafayette IN 47907 USA

Driven by fast advancements in wind and photovoltaic (PV) technologies, onsite renewable electricity generation is becoming attractive to manufacturers since they are able to reduce electricity purchases from the grid and may lower their electricity costs. This paper proposes a methodology to minimize the electricity cost of a grid-connected factory that also has onsite solar power generation and battery storage. Purchases from the grid are subject to time-of-use electricity rate schedules. The problem is formulated as a mixed-integer programming problem and GAMS is used to find the optimal manufacturing and onsite energy flow schedules that have the minimal electricity cost. A case study with one hybrid flow shop, onsite PV power generation, and a battery was used to test the proposed method. Testing results showed that the factory's electricity cost can be reduced by 54.0% under summer TOU rate on a typical day while a 0.7% electricity cost reduction can be achieved for a representative day under a winter TOU rate. An annual electricity cost savings of 28.1% can be obtained with the optimal schedules. In addition, a parametric study incorporating the optimal schedules was performed to understand the economic performances associated with different PV capacity and battery bank size for the factory.

关键词： Manufacturing scheduling Energy optimization mixed-integer programming Onsite renewable generation

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An efficient formulation of the flow refueling location model for alternative-fuel stations

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IIE TRANSACTIONS 2012年第8期44卷 622-636页

作者： Capar, Ismail Kuby, Michael Texas A&M Univ Ind Distribut Program College Stn TX 77843 USA Arizona State Univ Sch Geog Sci & Urban Planning Tempe AZ 85287 USA

The Flow-Refueling Location Model (FRLM) locates a given number of refueling stations on a network to maximize the traffic flow among origin-destination pairs that can be refueled given the driving range of alternative-fuel vehicles. Traditionally, the FRLM has been formulated using a two-stage approach: the first stage generates combinations of locations capable of serving the round trip on each route, and then a mixed-integer programming approach is used to locate p facilities to maximize the flow refueled given the feasible combinations created in the first stage. Unfortunately, generating these combinations can be computationally burdensome and heuristics may be necessary to solve large-scale networks. This article presents a radically different mixed-binary-integer programming formulation that does not require pre-generation of feasible station combinations. Using several networks of different sizes, it is shown that the proposed model solves the FRLM to optimality as fast as or faster than currently utilized greedy and genetic heuristic algorithms. The ability to solve real-world problems in reasonable time using commercial math programming software offers flexibility for infrastructure providers to customize the FRLM to their particular fuel type and business model, which is demonstrated in the formulation of several FRLM extensions.

关键词： Alternative-fuel vehicles facility location flow capturing mixed-integer programming

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A three-stage short-term electric power planning procedure for a generation company in a liberalized market

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2007年第5期29卷 408-421页

作者： Nabona, Narcis Pages, Adela Univ Politecn Catalunya Dept Stat & Operat Res ES-08034 Barcelona Spain

In liberalized electricity markets, generation companies bid their hourly generation in order to maximize their profit. The optimization of the generation bids over a short-term weekly period must take into account the action of the competing generation companies and the market-price formation rules and must be coordinated with long-term planning results. This paper presents a three stage optimization process with a data analysis and parameter calculation, a linearized unit commitment, and a nonlinear generation scheduling refinement. Although the procedure has been developed from the experience with the Spanish power market, with minor adaptations it is also applicable to any generation company participating in a competitive market system. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： mixed-integer programming nonlinear programming short-term power planning long-term power planning liberalized electricity markets market-price forecasting electricity generation

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Optimal Energy-Efficient Transmit Beamforming for Multi-User MISO Downlink

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第20期63卷 5574-5588页

作者： Tervo, Oskari Le-Nam Tran Juntti, Markku Univ Oulu Dept Commun Engn FI-90014 Oulu Finland Univ Oulu Ctr Wireless Commun FI-90014 Oulu Finland Maynooth Univ Dept Elect Engn Maynooth Kildare Ireland

This paper studies beamforming techniques for energy efficiency maximization (EEmax) in multiuser multiple-input single-output (MISO) downlink system. For this challenging nonconvex problem, we first derive an optimal solution using branch-and-reduce-and-bound (BRB) approach. We also propose two low-complexity approximate designs. The first one uses the well-known zero-forcing beamforming (ZFBF) to eliminate inter-user interference so that the EEmax problem reduces to a concave-convex fractional program. Particularly, the problem is then efficiently solved by closed-form expressions in combination with the Dinkelbach's approach. In the second design, we aim at finding a stationary point using the sequential convex approximation (SCA) method. By proper transformations, we arrive at a fast converging iterative algorithm where a convex program is solved in each iteration. We further show that the problem in each iteration can also be approximated as a second-order cone program (SOCP), allowing for exploiting computationally efficient state-of-the-art SOCP solvers. Numerical experiments demonstrate that the second design converges quickly and achieves a near-optimal performance. To further increase the energy efficiency, we also consider the joint beamforming and antenna selection (JBAS) problem for which two designs are proposed. In the first approach, we capitalize on the perspective reformulation in combination with continuous relaxation to solve the JBAS problem. In the second one, sparsity-inducing regularization is introduced to approximate the JBAS problem, which is then solved by the SCA method. Numerical results show that joint beamforming and antenna selection offers significant energy efficiency improvement for large numbers of transmit antennas.

关键词： Antenna selection Dinkelbach method energy efficiency fractional programming MISO broadcast channel mixed-integer programming second-order cone programming sequential convex approximation

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Integration N-1 of Contingency Analysis With Systematic Transmission Capacity Expansion Planning: ERCOT Case Study

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IEEE TRANSACTIONS ON POWER SYSTEMS 2016年第3期31卷 2234-2245页

作者： Majidi-Qadikolai, Mohammad Baldick, Ross Univ Texas Austin Dept Elect & Comp Engn Austin TX 78701 USA

In this paper, we propose a method for N - 1 contingency constrained transmission capacity expansion planning (TCEP), which is formulated as a mixed-integer programming (MIP) problem. In relatively well-designed power systems, a single outage of a majority of lines will not usually cause overload on other lines in most loading conditions. Thus they will not affect the feasible region and the optimal answer of the TCEP optimization problem, and can be safely removed from contingency analysis if we can identify them. A contingency identification index is developed to detect these lines and create variable contingency lists (VCL) for different network loading conditions. In our proposed method, we use results of a relaxed version of the original problem as a lower bound answer in the first step, and integrate contingencies into TCEP in the next steps to solve this optimization problem faster while still satisfying N - 1 criterion. For solving TCEP with contingencies, two options are offered, i. e., option A that uses an updated system as its base case (original existing network together with selected lines by the relaxed problem) and option B that uses the original existing network as its base case (without results of the relaxed problem). Option A is faster than option B because it usually should select fewer new lines compared to B, but cannot guarantee optimality. Option B provides the optimal answer while taking more computational time. An ERCOT case study is used to show capabilities of the proposed method for solving large scale problems, and the numerical result demonstrates this method is much faster than the integrated MIP method that directly incorporates all contingencies.

关键词： Line outage distribution factor mixed-integer programming N-1 criterion reliability system adequacy transmission capacity expansion planning

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Learning in Combinatorial Optimization: What and How to Explore

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OPERATIONS RESEARCH 2020年第5期68卷 1585-1604页

作者： Modaresi, Sajad Saure, Denis Vielma, Juan Pablo Univ N Carolina Kenan Flagler Business Sch Chapel Hill NC 27599 USA Univ Chile Ind Engn Dept Beauchef 851 Santiago 8370456 Chile MIT Sloan Sch Management Cambridge MA 02142 USA

We study dynamic decision making under uncertainty when, at each period, a decision maker implements a solution to a combinatorial optimization problem. The objective coefficient vectors of said problem, which are unobserved before implementation, vary from period to period. These vectors, however, are known to be random draws from an initially unknown distribution with known range. By implementing different solutions, the decision maker extracts information about the underlying distribution but at the same time experiences the cost associated with said solutions. We show that resolving the implied exploration versus exploitation tradeoff efficiently is related to solving a lower-bound problem (LBP), which simultaneously answers the questions of what to explore and how to do so. We establish a fundamental limit on the asymptotic performance of any admissible policy that is proportional to the optimal objective value of the LBP problem. We show that such a lower bound might be asymptotically attained by policies that adaptively reconstruct and solve the LBP at an exponentially decreasing frequency. Because the LBP is likely intractable in practice, we propose policies that instead reconstruct and solve a proxy for the LBP, which we call the optimality cover problem (OCP). We provide strong evidence of the practical tractability of the OCP, which implies that the proposed policies can be implemented in real time. We test the performance of the proposed policies through extensive numerical experiments, and we show that they significantly outperform relevant benchmarks in the long-term and are competitive in the short-term.

关键词： combinatorial optimization multiarmed bandit mixed-integer programming

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Periodic Event Scheduling for Automated Production Systems

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INFORMS JOURNAL ON COMPUTING 2022年第2期34卷 1291-1304页

作者： Helmberg, Christoph Hofmann, Tobias Wenzel, David Tech Univ Chemnitz D-09111 Chemnitz Germany Leadec Ind Serv D-09120 Chemnitz Germany German Aerosp Ctr DLR Neustrelitz D-17235 Neustrelitz Germany

Consider optimizing a periodic schedule for an automated production plant as a last step of a more comprehensive design process. In our scenario, each robot's cyclic sequence of operations and trajectories between potential waiting points have already been fully specified. Further given are those precedences that fix sequence requirements on operations between different robots. It remains to determine the starting time for each operation or movement of each robot within a common cyclic time period so as to avoid collisions of robots that operate in the same space simultaneously. So the task is to find a conflict-resolving schedule that minimizes this common periodic cycle time while observing all precedence relations and collision avoidance constraints. The proposed cycle time minimization problem for robot coordination has, to the best of our knowledge, not been studied before. We develop an approach for solving it by employing binary search for determining the smallest feasible period time of an iso-periodic event scheduling problem (IPESP). This is a variant of the periodic event scheduling problem in which the objects that have to be scheduled need to obey exactly the same period time. The possibility to wait arbitrarily long at waiting points turns out to be essential to justify the use of binary search for identifying the minimum cycle time, thereby avoiding bilinear mixed integer formulations. Special properties of the given scenario admit bounds on the periodic tension variables of an integer programming formulation. Although the IPESP subproblems remain NP-complete in general, these bounds allow solving real-world instances sufficiently fast for the approach to be applicable in practice. Numerical experiments on real-world and randomly generated data are supplied to illustrate the potential and limitations of this approach. Summary of Contribution: When designing automated production plants, a crucial step is to identify the smallest possible per unit perio

关键词： automated systems network optimization periodic event scheduling mixed-integer programming

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An MISOCP-Based Decomposition Approach for the Unit Commitment Problem With AC Power Flows

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IEEE TRANSACTIONS ON POWER SYSTEMS 2023年第4期38卷 3388-3400页

作者： Tuncer, Deniz Kocuk, Burak Sabanci Univ Fac Engn & Nat Sci TR-34956 Istanbul Tuzla Turkiye

Unit Commitment (UC) and Optimal Power Flow (OPF) are two fundamental problems in short-term electric power systems planning that are traditionally solved sequentially. The state-of-the-art mostly uses a direct current (DC) approximation of the power flow equations. However, utilizing the DC approach in the UC-level may lead to infeasible or suboptimal generator commitment schedules for the OPF problem. In this paper, we aim to simultaneously solve the UC Problem with alternating current (AC) power flow equations, which combines the challenging nature of both UC and OPF Problems. Due to the highly nonconvex nature of the AC flow equations, we utilize the mixed-integer second-order cone programming (MISOCP) relaxation of the UC Problem as the basis of our solution approach. The MISOCP relaxation is utilized for finding both a lower bound and a candidate generator commitment schedule. Once this schedule is obtained, we solve a multi-period OPF problem to obtain feasible solutions for the UC problem with AC power flows. For smaller instances, we develop two different algorithms that exploit the recent advances in the OPF literature and obtain high-quality feasible solutions with provably small optimality gaps. For solving larger instances, we develop a Lagrangian decomposition based approach that yields promising results.

关键词： Optimal power flow unit commitment mixed-integer programming nonlinear programming second-order cone programming

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