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A polyhedral study of event-based models for the resource-constrained project scheduling problem

JOURNAL OF SCHEDULING 2020年第2期23卷 233-251页

作者： Tesch, Alexander ZIB Takustr 7 D-14195 Berlin Germany

In this paper, we study event-based mixed-integer programming (MIP) formulations for the resource-constrained project scheduling problem (RCPSP) that represent an alternative to the more common time-indexed model (DDT) (Pritsker et al. in Manag Sci 16(1):93-108, 1969;Christofides et al. in Eur J Oper Res 29(3):262-273, 1987) for the case when the scheduling horizon is large. In contrast to time-indexed models, the size of event-based models does not depend on the time horizon. For two event-based models OOE and SEE introduced by Kone et al. (Comput Oper Res 38(1):3-13, 2011), we first present new valid inequalities that strengthen the original formulation. Furthermore, we state a new event-based model, the Interval Event-Based Model (IEE), and deduce natural linear transformations between all three models. Those transformations yield the strict domination order IEE > SEE > OOE for their respective linear programming relaxations, meaning that the new IEE model has the strongest linear relaxation among all known event-based models. In addition, we show that DDT can be retrieved from IEE by subsequent expansion and projection of the underlying solution space. This yields a unified polyhedral view on a complete branch of MIP models for the RCPSP. Finally, we also compare the computational performance between all models on common test instances of the PSPLIB (Kolisch and Sprecher in Eur J Oper Res 96(1):205-216, 1997).

关键词： Scheduling Resource-constrained project scheduling mixed-integer programming Polyhedral study Event-based models Affine transformations

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Optimal vendor selection in a multiproduct supply chain with truckload discounts

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TRANSPORTATION RESEARCH PART E-LOGISTICS AND TRANSPORTATION REVIEW 2008年第5期44卷 684-695页

作者： Glickman, Theodore S. White, Susan C. George Washington Univ Sch Business Dept Decis Sci Washington DC 20052 USA

When products are sold by multiple vendors in various locations, the purchaser must decide what to order from each vendor and where to send it. To solve this decision problem, a novel optimization model is developed and applied to a situation involving the nationwide wholesale distribution of grocery products. Comparing the model's solution with the actual record of shipments reveals instances in which the model selected higher-priced vendors in order to capitalize on truckload cost savings, which are seen to be an important factor in vendor selection. Additional models are developed to reduce computation time and assign shipments to vehicles. (c) 2007 Elsevier Ltd. All rights reserved.

关键词： vendor selection supply chain truckload discount mixed-integer programming distribution

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A Configuration-Component-Based Hybrid Model for Combined-Cycle Units in MISO Day-Ahead Market

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IEEE TRANSACTIONS ON POWER SYSTEMS 2019年第2期34卷 883-896页

作者： Dai, Chenxi Chen, Yonghong Wang, Fengyu Wan, Jie Wu, Lei Clarkson Univ Elect & Comp Engn Dept Potsdam NY 13699 USA Midcontinent Independent Syst Operator Inc Carmel IN 46032 USA GE Grid Software Solut Redmond WA 98052 USA

This paper proposes a hybrid combined-cycle gas turbine (CCGT) model for day-ahead market clearing, in order to enhance the operation flexibility of CCGTs in practice. The proposed hybrid model, by taking benefits of combined offers from market participants on both configurations and individual physical turbines, can more accurately reflect physical operation features of CCGTs than existing CCGT models. A comprehensive review on existing CCGT models in academia and industry practice with their advantages and shortcomings is conducted. By taking benefits of the two most investigated models, i.e., configuration-based model and component-based model, the mapping relationship between these two models is revealed for deriving the proposed hybrid model. Tight formulations are further discussed for achieving the better computational performance. The proposed hybrid model is tested and compared with other CCGT models via the modified IEEE 118-bus system and the midcontinent independent system operator system. Results show notable benefits in maintaining operation flexibility and enhancing social welfare.

关键词： Combined-cycle gas turbine hybrid model mixed-integer programming security-constrained unit commitment tight formulation

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A superstructure optimization approach for process synthesis under complex reaction networks

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2018年 137卷 589-608页

作者： Ramapriya, Gautham Madenoor Won, Wangyun Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn Madison WI 53706 USA Univ Wisconsin DOE Great Lakes Bioenergy Res Ctr Madison WI 53726 USA

In this work, we present mixed integer linear programming methods for the synthesis of processes that involve complex reaction networks. Specifically, we consider the modeling of reactors and interconnecting streams in systems where the composition of the reactor inlet streams can vary substantially, thereby making the determination of the limiting component as well as the calculation of the stream heating/cooling and power requirements challenging. First, towards the modeling of reactors, we develop an extent-based method which detects the limiting reactant of each reaction occurring in parallel with others, based on the inlet flows of the reactants. Second, we develop a computationally tractable method for the calculation of the work and heating/cooling duty needed to condition any stream of a process based on simple calculations that can be performed offline. Finally, we present how the two aforementioned components can be integrated in an optimization model generated based on a process superstructure. We demonstrate the application of the developed methods for the synthesis of a biorefinery. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Process systems engineering Reactor network synthesis mixed-integer programming Biofuels

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An Integrated Approach to Tactical Transportation Planning in Logistics Networks

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TRANSPORTATION SCIENCE 2016年第2期50卷 439-460页

作者： Harks, Tobias Koenig, Felix G. Matuschke, Jannik Richter, Alexander T. Schulz, Jens Maastricht Univ Sch Business & Econ NL-6211 LM Maastricht Netherlands TomTom Int BV D-12435 Berlin Germany Tech Univ Berlin Inst Math D-10623 Berlin Germany

We propose a new mathematical model for transport optimization in logistics networks on the tactical level. The main features include accurately modeled tariff structures and the integration of spatial and temporal consolidation effects via a cyclic pattern expansion. Using several graph-based gadgets, we are able to formulate our problem as a capacitated network design problem. To solve the model, we propose a local search procedure that reroutes flow of multiple commodities at once. Initial solutions are generated by various heuristics, relying on shortest path augmentations and LP techniques. As an important subproblem we identify the optimization of tariff selection on individual links, which we prove to be NP-hard and for which we derive exact as well as fast greedy approaches. We complement our heuristics by lower bounds from an aggregated mixed-integer programming formulation with strengthened inequalities. In a case study from the automotive, chemical, and retail industries, we prove that most of our solutions are within a single-digit percentage of the optimum.

关键词： logistics freight transportation modeling capacitated network design local search mixed-integer programming

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Anticipation versus reactive reoptimization for dynamic vehicle routing with stochastic requests

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NETWORKS 2019年第3期73卷 277-291页

作者： Ulmer, Marlin W. Tech Univ Carolo Wilhelmina Braunschweig Carl Friedrich Gauss Fak Braunschweig Germany

Due to new business models and technological advances, dynamic vehicle routing is gaining increasing interest. Especially solving dynamic vehicle routing problems with stochastic customer requests becomes increasingly important, for example, in e-commerce and same-day delivery. Solving these problems is challenging, because it requires optimization along two dimensions. First, as a reaction to new customer requests, current routing plans need to be reoptimized. Second, potential future requests need to be anticipated in current decision making. Decisions need to be derived in real-time. The limited time often prohibits extensive optimization in both dimensions and the question arises how to utilize the limited calculation time effectively. In this paper, we analyze the merits of reactive route reoptimization and anticipation for a dynamic vehicle routing problem with stochastic requests. To this end, we compare an existing method from each dimension as well a policy allowing for a tunable combination of the two approaches. We show how the appropriate optimization combination is strongly connected to the degree of dynamism, the percentage of unknown requests. We also show that our combination does not provide significant benefit compared to the respectively best optimization dimension.

关键词： anticipation approximate dynamic programming degree of dynamism dynamic vehicle routing mixed-integer programming reoptimization stochastic requests

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Packaged gas supply chain planning with network-wide SKU rationalization

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INTERNATIONAL JOURNAL OF PRODUCTION ECONOMICS 2018年 204卷 346-357页

作者： Malinowski, Ethan Karwan, Mark H. Sun, Lei Pinto, Jose M. Univ Buffalo Dept Ind & Syst Engn Buffalo NY 14260 USA Praxair Inc 175 E Pk Dr Tonawanda NY 14150 USA Praxair Inc 10 Riverview Dr Danbury CT 06810 USA

Effective SKU rationalization is advantageous when applied to businesses with a high variety of product offerings. Advantages may include lower production costs, inventory simplifications, and system-wide reductions in transportation costs. We apply SKU rationalization in the form of a variant of product substitution, towards an industrial packaged gas supply chain problem which includes production, allocation, and distribution decisions. An effective mixed-integer programming formulation is developed, capable of handling additional line investment, varying degrees of substitution, economies-of-scale in production, as well as network-wide planning decisions in the supply chain. A case study based on historical data is used for testing, followed by computational results and policy implications in the form of customer incentivization.

关键词： SKU rationalization Product substitution Packaged gas supply chain mixed-integer programming Incentivization

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A New General-Purpose Algorithm for mixed-integer Bilevel Linear Programs

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OPERATIONS RESEARCH 2017年第6期65卷 1615-1637页

作者： Fischetti, Matteo Ljubic, Ivana Monaci, Michele Sinnl, Markus Univ Padua Dept Informat Engn I-35131 Padua Italy ESSEC Business Sch Paris F-95021 Cergy Pontoise France Univ Bologna DEI Guglielmo Marconi I-40136 Bologna Italy Univ Vienna Dept Stat & Operat Res A-1090 Vienna Austria

Bilevel optimization problems are very challenging optimization models arising in many important practical contexts, including pricing mechanisms in the energy sector, airline and telecommunication industry, transportation networks, critical infrastructure defense, and machine learning. In this paper, we consider bilevel programs with continuous and discrete variables at both levels, with linear objectives and constraints (continuous upper level variables, if any, must not appear in the lower level problem). We propose a general-purpose branch-and-cut exact solution method based on several new classes of valid inequalities, which also exploits a very effective bilevel-specific preprocessing procedure. An extensive computational study is presented to evaluate the performance of various solution methods on a common testbed of more than 800 instances from the literature and 60 randomly generated instances. Our new algorithm consistently outperforms (often by a large margin) alternative state-of-the-art methods from the literature, including methods exploiting problem-specific information for special instance classes. In particular, it solves to optimality more than 300 previously unsolved instances from the literature. To foster research on this challenging topic, our solver is made publicly available online.

关键词： bilevel optimization mixed-integer programming cutting planes intersection cuts branch and cut computational analysis

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Hybrid soft computing algorithmic framework for smart home energy management

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SOFT COMPUTING 2013年第11期17卷 1983-2005页

作者： Severini, Marco Squartini, Stefano Piazza, Francesco Univ Politecn Marche Dept Informat Engn 3MediaLabs I-60131 Ancona Italy

Energy management in Smart Home environments is undoubtedly one of the pressing issues in the Smart Grid research field. The aim typically consists in developing a suitable engineering solution able to maximally exploit the availability of renewable resources. Due to the presence of diverse cooperating devices, a complex model, involving the characterization of nonlinear phenomena, is indeed required on purpose. In this paper an Hybrid Soft Computing algorithmic framework, where genetic, neural networks and deterministic optimization algorithms jointly operate, is proposed to perform an efficient scheduling of the electrical tasks and of the activity of energy resources, by adequately handling the inherent nonlinear aspects of the energy management model. In particular, in order to address the end-user comfort constraints, the home thermal characterization is needed: this is accomplished by a nonlinear model relating the energy demand with the required temperature profile. A genetic algorithm, based on such model, is then used to optimally allocate the energy request to match the user thermal constraints, and therefore to allow the mixed-integer deterministic optimization algorithm to determine the remaining energy management actions. From this perspective, the ability to schedule the tasks and allocate the overall energy resources over a finite time horizon is assessed by means of diverse computer simulations in realistic conditions, allowing the authors to positively conclude about the effectiveness of the proposed approach. The degree of realism of the simulated scenario is confirmed by the usage of solar energy production forecasted data, obtained by means of a neural-network based algorithm which completes the framework.

关键词： Smart home energy management Task and energy resource scheduling Thermal comfort mixed-integer programming Soft computing Genetic algorithm Neural networks Smart grid

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Least cost influence propagation in (social) networks

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MATHEMATICAL programming 2018年第1期170卷 293-325页

作者： Fischetti, Matteo Kahr, Michael Leitner, Markus Monaci, Michele Ruthmair, Mario Univ Padua DEI Padua Italy Univ Vienna Dept Stat & Operat Res Vienna Austria Univ Bologna DEI Bologna Italy

Influence maximization problems aim to identify key players in (social) networks and are typically motivated from viral marketing. In this work, we introduce and study the Generalized Least Cost Influence Problem (GLCIP) that generalizes many previously considered problem variants and allows to overcome some of their limitations. A formulation that is based on the concept of activation functions is proposed together with strengthening inequalities. Exact and heuristic solution methods are developed and compared for the new problem. Our computational results also show that our approaches outperform the state-of-the-art on relevant, special cases of the GLCIP.

关键词： Influence maximization mixed-integer programming Social network analysis

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