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A mixed-integer linear program for optimizing sensor locations along freeway corridors

TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2011年第1期45卷 208-217页

作者： Danczyk, Adam Liu, Henry X. Univ Minnesota Dept Civil Engn Minneapolis MN 55455 USA

How to optimally allocate limited freeway sensor resources is of great interest to transportation engineers. In this paper, we focus on the optimal allocation of point sensors, such as loop detectors, to minimize performance measurement errors. Although it has been shown that the minimization problem can be intuitively formulated as a nonlinear program, the formulation is so complex that only heuristic approaches can be used to solve the problem. In this paper, we transform the nonlinear program into an equivalent mixed-integer linear model. The linearized model is shown to have a graphical interpretation and can be solved using resource constrained shortest path algorithms. A customized Branch-and-Bound technique is then proposed to solve the resource constrained shortest path problem. Numerical experiments along an urban freeway corridor demonstrate that this sensor location model is successful in allocating loop detectors to improve the accuracy of travel time estimation. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Sensor location problem mixed-integer linear program Branch-and-Bound techniques Loop detectors

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Optimal Assignment and Scheduling of Cranes in Slab Yard for Iron and Steel Production Enterprises

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 7349-7360页

作者： Wang, Xu Zhou, Mengchu Zhao, Qiuhong Liu, Shixin Guo, Xiwang Qi, Liang Albeshri, Aiiad Shenyang Univ Chem Technol Sch Comp Sci & Technol Shenyang 110142 Peoples R China Macau Univ Sci & Technol Macao Inst Syst Engn Macau 999078 Peoples R China New Jersey Inst Technol Dept Elect & Comp Engn Newark NJ 07102 USA Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China Liaoning Shihua Univ Coll Comp & Commun Engn Fushun 113001 Peoples R China Shandong Univ Sci & Technol Coll Comp Sci & Engn Qingdao 266590 Peoples R China King Abdulaziz Univ Dept Comp Sci Jeddah 21481 Saudi Arabia

Slab yards serve as temporary slab storage between a continuous casting stage and a rolling stage. Considering non-crossing and safe clearance constraints of slab yard cranes, this work studies a multi-crane assignment and scheduling problem in the slab yard. An mixed-integer linear programming (MILP) is formulated to minimize the slab completion time. Due to its NP-hardness, the problem for large-sized instances is computationally intractable. Thus, we develop a logic-based benders decomposition algorithm (LBBD) to solve it. First, we exploit a generalized decomposition of this problem into a relaxed main problem (RMP) and a sub-problem (SP). Solving the former allocates slabs to each crane. Then, the sequence of the assigned slabs can be found by solving its corresponding sub-problem. Finally, to verify the effectiveness of LBBD, we identify a lower bound (LB) of the optimal objective function. The problem instances on real data from an iron and steel plant are created. The result of LBBD is close to such lower bound and can be found efficiently. Note to Practitioners-This work deals with a crane assignment problem with multiple cranes for handling input slabs in a slab yard. This problem is formulated as an MILP model to minimize the completion time. Its time complexity grows exponentially with the problem size. Thus, we develop a LBBD to solve it. The numerical results reveal that LBBD can find the optimal or near-optimal solution for all realistic instances in affordable computational time. Its use can ensure the high utilization of cranes and efficient service in iron and steel plants.

关键词： Cranes Slabs Containers Processor scheduling Steel Production Iron Indexes Casting Logistics Slab yard multi-crane scheduling logic-based benders decomposition logistics mixed-integer linear program

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New and tractable formulations for the eco-driving and the eco-routing-and-driving problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2025年第2期321卷 445-461页

作者： Wu, Fuliang Ye, Hongbo Bektas, Tolga Dong, Ming Shanghai Jiao Tong Univ Antai Coll Econ & Management 1954 Huashan Rd Shanghai 200030 Peoples R China Hong Kong Polytech Univ Dept Elect & Elect Engn Hung Hom Hong Kong 999077 Peoples R China Univ Liverpool Sch Management Chatham St Liverpool L69 7ZH England

Eco-driving and eco-routing problems are both concerned with minimizing the fuel consumption of a single vehicle;the former does so by optimizing the vehicle's speed profile on a given road segment, and the latter selects the best path for a vehicle from a given origin to a given destination. This paper studies a problem that combines the two, namely an eco-routing-and-driving problem, in which the path and the speed profile on each link of the chosen path are optimized simultaneously. Using the comprehensive modal emissions model as the fuel consumption model, this paper describes new and tractable formulations for both the ecodriving and the eco-routing-and-driving problems through discretization, convexification and approximation, leading to a linear program for the former and a mixed-integer linear program for the latter. Computational results indicate that the new formulation of the eco-driving problem yields significant reductions in the solution time as compared to alternative formulations and algorithms, and that the new formulation of the eco-routing-and-driving problem affords further reductions in fuel consumption when compared with other methods.

关键词： Eco-driving Eco-routing-and-driving problem Fuel consumption mixed-integer linear program

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An adaptive large neighborhood search method for the AGV scheduling problem with a limited number of chargers

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2025年

作者： Li, Yantong Ren, Bo Wen, Xin Chung, Sai-Ho Dalian Maritime Univ Sch Maritime Econ & Management Dalian Peoples R China Hong Kong Polytech Univ Dept Ind & Syst Engn Kowloon Hong Kong Peoples R China

Automated guided vehicles (AGVs) are widely used in various fields to fulfill the transportation demands of factories or workshops due to their intelligence, flexibility, and efficiency. Scheduling multiple AGVs in the operational practice under these scenarios is challenging, where charging operations must be jointly optimised with the task processing process. Most studies on the AGV scheduling problem assume that the charging station can simultaneously charge an unlimited number of AGVs, where each AGV must be fully charged upon each charging operation. We investigate a new AGV scheduling problem with a limited number of chargers and a flexible charging strategy, denoted as ASP-LC-FCS. We first formulate the problem as a mixed-integer linear program (MILP) and show that it is strongly NP-hard. We then derive a valid lower bound. Considering the NP-hardness of the problem, we then develop a tailored adaptive large neighbourhood search (ALNS) algorithm based on the problem structure. The ALNS employs a matheuristic to generate initial feasible solutions, designs problem-specific destroy and repair operators, and innovatively uses a local search mechanism to improve the solution during each iteration. Computational experiments on 729 randomly generated instances demonstrate the good performance of the proposed ALNS, which significantly outperforms the state-of-the-art commercial solver CPLEX and an adapted artificial bee colony algorithm. Besides, we apply the proposed ALNS method to solve a real industrial case to provide practical solutions and managerial insights.

关键词： AGV scheduling limited number of chargers flexible charging mixed-integer linear program adaptive large neighbourhood search

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Robust doctor-patient assignment with endogenous service duration uncertainty and no-show behavior

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2025年 133卷

作者： Ji, Menglei Wang, Shanshan Peng, Chun Li, Jinlin China Acad Safety Sci & Technol Dept Rural Safety Beijing 100012 Peoples R China Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China Beijing Jiaotong Univ Sch Econ & Management Beijing 100044 Peoples R China Beijing Inst Technol Sch Management & Econ Beijing 100081 Peoples R China

In practice, patient's service duration might be influenced by the workload of doctors who need to provide healthcare service. However, most existing studies have overlooked this correlation when scheduling patients and doctors. Motivated by this context, we incorporate the endogenous (decision-dependent) uncertain service duration, the presence of uncertainty dependent on assignment decisions, into the doctor-patient assignment problem with patient no-show behavior and propose a novel modeling framework. Specifically, we employ the distributionally robust optimization (DRO) approach that uses decision-dependent moment information to construct the ambiguity set of the service duration distribution. A novel decision-dependent DRO (DDRO) model is proposed for the doctor-patient assignment problem. The goal is to minimize the sum of the doctor's assignment cost and penalty cost and the worst-case expected cost of overtime and cancellation cost. To solve this model, we propose an effective nested column-and-constraint generation (C&CG) solution scheme. This approach involves decomposing the model into an outer-level problem and an inner-level problem, both of which can be solved using the C&CG algorithm. This nested scheme enables us to efficiently solve the model and obtain optimal solutions. Numerical results show that the algorithm can solve most realistic-sized problem instances optimally within the two-hour time limit. In addition, to show the effectiveness of our new modeling framework, we also propose the classical DRO and stochastic programming (SP) models as the benchmark models in our out-of-sample test. The extensive numerical results show that when there exists variability in service duration and robustness in the ambiguity set, our DDRO model outperforms the DRO and SP approaches. In addition, when there are relatively enough doctors, the DDRO method is the best option for decision-makers to make assignment plans. We also show that the no-show behavior fact

关键词： Robust doctor-patient assignment Two-stage distributionally robust optimization mixed-integer linear program Endogenous uncertainty Uncertain service duration No-show behavior Column-and-constraint generation

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Two-indexed formulation of the traveling salesman problem with multiple drones performing sidekicks and loops

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OR SPECTRUM 2025年第1期47卷 67-104页

作者： Rave, Alexander Catholic Univ Eichstatt Ingolstadt Ingolstadt Sch Management Dept Operat Schanz 49 D-85049 Ingolstadt Germany

Aerial drone delivery has great potential to improve package delivery time, as drones can fly autonomously over obstacles at a possibly higher speed than trucks. The benefits of drones in delivery can even be increased in a truck-and-drone tandem where a truck carries multiple drones and releases them at advantageous places, i.e., the traveling salesman problem with multiple drones (TSPmD). We focus on a general version of this problem with makespan minimization, where the drones have two options after serving the customer: they can return to any node the truck visits at a later stage (sidekick) or return to the same node they were launched from (loop) - even at the depot. We introduce an efficient two-indexed mixed-integer linear program (MILP) for this TSPmD and show how to adapt the MILP to cover two problem variants, namely the multiple flying sidekick traveling salesman problem and the traveling salesman problem with drone. Our MILP formulation is an efficient formulation, as it outperforms eight state-of-the-art MILP formulations for these problem variants in nearly all larger instances. In a numerical study, we provide new optimal solutions with up to 28 nodes for benchmark purposes. Moreover, we analyze the impact of allowing drone loops on makespan minimization in general and at the depot. We find that loops mainly become relevant when drones travel faster than trucks, resulting in average makespan savings of up to 2.7%.

关键词： Unmanned aerial vehicles Routing Last-mile delivery mixed-integer linear program Benchmark instances

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Stochastic arbitrage with market index options

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JOURNAL OF BANKING & FINANCE 2025年 173卷

作者： Beare, Brendan K. Seo, Juwon Zheng, Zhongxi Univ Sydney Sch Econ Sydney NSW 2006 Australia Natl Univ Singapore Dept Econ Singapore 119077 Singapore

Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset, generates a payoff which stochastically dominates the payoff from the direct investment in the underlying asset. We provide linear and mixed-integer linear programs for computing the stochastic arbitrage opportunity providing the maximum option premium to an investor. We apply our programs to 18 years of data on monthly put and call options on the Standard & Poors 500 index, finding no evidence that stochastic arbitrage opportunities are systematically present. A skewed specification of the underlying market return distribution with a constant market risk premium and constant multiplicative variance risk premium is broadly consistent with the pricing of market index options at moderate strikes.

关键词： linear program mixed-integer linear program Option mispricing Portfolio choice Pricing kernel puzzle Stochastic arbitrage Stochastic dominance

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Finding the Nondominated Set and Efficient integer Vectors for a Class of Three-Objective mixed-integer linear programs

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MANAGEMENT SCIENCE 2023年第10期69卷 6001-6020页

作者： Ceyhan, Gokhan Koksalan, Murat Lokman, Banu Middle East Tech Univ Ind Engn TR-06800 Ankara Turkiye Univ Michigan Ross Sch Business Ann Arbor MI 48109 USA Univ Portsmouth Ctr Operat Res & Logist Sch Org Syst & People Portsmouth PO1 3DE Hants England

We consider a class of three-objective mixed-integer linear programs (MILPs) where at least one of the objective functions takes only discrete values. These problems commonly occur in MILPs where one or more of the three objective functions contain only integer decision variables. In such problems, the nondominated set consists of the union of nondominated edges and individual nondominated points. The nondominated edges can provide valuable insights on the trade-offs between the two continuous objectives at different levels of the discrete-valued objective. We develop an objective-space search algorithm that keeps partitioning the search space by progressively creating cones in the two-dimensional feasible space of the two continuous objectives for relevant values of the discrete-valued objective. The algorithm generates the nondominated points or edges in the nonincreasing order of the feasible values of the selected discrete-valued objective. Additionally, the algorithm uncovers all efficient integer variable vectors, including different vectors that lead to the same nondominated points or edges. We apply the algorithm to the day-ahead electricity market clearing problem.

关键词： multiobjective mixed-integer linear program objective-space search algorithm

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Optimizing automotive inbound logistics: A mixed-integer linear programming approach

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2022年第0期163卷

作者： Baller, Reinhard Fontaine, Pirmin Minner, Stefan Lai, Zhen Audi AG Auto union Str 1 D-85057 Ingolstadt Germany Catholic Univ Eichstatt Ingolstadt Ingolstadt Sch Management Schanz 49 D-85049 Ingolstadt Germany Tech Univ Munich TUM Sch Management Arcisstr 21 D-80333 Munich Germany Munich Data Sci Inst MDSI Walther Von Dyck Str 10 D-85748 Garching Germany Nio GmbH Montgelasstr 14 D-81679 Munich Germany

The optimization of inbound logistics from first-tier suppliers at the aggregation level of a factory is a challenging coordination problem. In practice, different transport modes and multiple constraints exist and need to be taken into account: the available number of storage places, capacity of goods-entry, delivery profile and transportation pattern constraints, truck utilization, demand satisfaction, and the reverse flow of empty load carriers. A scalable solution method that is tailored to an automotive factory is currently not available. Optimization is usually carried out manually, e.g. experience-based or by using decision trees that follow an iterative optimization approach. Most of the mathematical models in the literature only deal with parts of the requirements and do not validate results in the required complexity. We present a mixed-integer linear programming approach to solve this complex problem using Gurobi. The solution capability and quality are enhanced by the introduction of a cyclic inventory constraint and valid inequalities. The evaluation of the approach is based on a case study of a German automotive factory with 570 suppliers and 3927 stock keeping units and reduces the as-is total cost by 33.86%. Additionally, CO2 emissions are reduced by 74.66%. We further show that variable order quantities, along with a courier and express service as an additional transport mode, are of high economic relevance. As part of a sensitivity analysis, we show how the total costs change, when (a) goods-entry handling constraints, (b) truck utilization, (c) storage constraints, or (d) transportation costs vary, and (e) the effect of a cyclic inventory constraint.

关键词： Automotive logistics Total landed costs Transportation pattern Shipment coordination mixed-integer linear program

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An Efficient Decomposition Method for Bilevel Energy Storage Arbitrage Problem

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CSEE Journal of Power and Energy Systems 2022年第2期8卷 652-658页

作者： Danman Wu Tengyun Qi Wei Wei Jianping Liu Laijun Chen Shengwei Mei the State Key Laboratory of Power Systems Department of Electrical EngineeringTsinghua UniversityBeijing 100084China China Three Gorges Renewables(Group)Co. Ltd.Beijing 100053China China Three Gorges Corporation Beijing 100038China New Energy Industry Research Center Qinghai UniversityXining 810016China

With the reduction of cost,large-capacity energy storage unit is playing an increasingly important role in modern power *** a merchant energy storage unit participates in the power market,its arbitrage problem can be modeled via a bilevel *** lower-level problem simulates power market clearing and gives the nodal price,based on which the upperlevel problem maximizes the arbitrage profit of energy *** solve this bilevel problem,the conventional method replaces the lower level problem with its KKT optimality conditions and further performs ***,because the size of the market clearing problem grows with the scale of the power system and the number of periods,the resulting MILP(mixed-integer linear program)is very challenging to *** paper proposes a decomposition method to address the bilevel energy storage arbitrage ***,the locational marginal price at the storage connection node is expressed as a piecewise constant function in the storage bidding strategy,so the market clearing problem can be ***,the storage bidding problem is formulated as a mixed-integer linear program,which contains only a few binary *** experiments validate the proposed method is exact and highly efficient.

关键词： Bilevel program energy storage nodal price mixed-integer linear program strategic bidding

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