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Modeling and Optimization of Time-of-Use Electricity Pricing Systems

IEEE TRANSACTIONS ON SMART GRID 2019年第4期10卷 4116-4127页

作者： Hung, Ying-Chao Michailidis, George Natl Chengchi Univ Dept Stat Taipei 11605 Taiwan Univ Florida Informat Inst Gainesville FL 32611 USA Univ Florida Dept Stat & Comp Sci Gainesville FL 32611 USA

Time-of-use (TOU) pricing is an important strategy for electricity providers to manage supply and make the grid more efficient;as well as for consumers seeking to manage their costs. In this paper, we discuss a general stochastic modeling framework for consumer's power demand based on which TOU contract characteristics can be selected to minimize the mean electricity price paid by the customer. We exploit the characteristics of power demand observed in real grids to model it during homogeneous peak periods as a constant level with fluctuations described by a scaled fractional Brownian motion. We analyze the exceedance process over pre-specified thresholds and use this information to formulate an optimization problem to determine the key features of the TOU contract. Due to the analytical intractability of certain expressions with the exception of short-range dependence fluctuations, the solution of the posited optimization problem requires using techniques such as Monte Carlo simulation and numerical search. The methodology for two pricing schemes is illustrated using real data.

关键词： Time-of-use pricing contract capacity self-similarity fractional Brownian motion Monte Carlo simulation mixed-integer programming

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Facets of a mixed-integer bilinear covering set with bounds on variables

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JOURNAL OF GLOBAL OPTIMIZATION 2019年第3期74卷 417-442页

作者： Rahman, Hamidur Mahajan, Ashutosh Indian Inst Technol Ind Engn & Operat Res Mumbai 400076 Maharashtra India

We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a certain way. This description does not introduce any new variables, but consists of exponentially many inequalities. An extended formulation with a few extra variables and much smaller number of constraints is presented. We also derive a linear time separation algorithm for finding the facet defining inequalities of this convex hull. We study the effectiveness of the new inequalities and the extended formulation using some examples.

关键词： Bilinear constraints mixed-integer programming Separation Global optimization Cutting-stock problem

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Characterizations of mixed binary convex quadratic representable sets

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MATHEMATICAL programming 2019年第1-2期177卷 371-394页

作者： Del Pia, Alberto Poskin, Jeffrey Univ Wisconsin Dept Ind & Syst Engn Madison WI 53706 USA Univ Wisconsin Wisconsin Inst Discovery Madison WI 53706 USA Univ Wisconsin Dept Math Madison WI 53706 USA

Representability results play a fundamental role in optimization since they provide characterizations of the feasible sets that arise from optimization problems. In this paper we study the sets that appear in the feasibility version of mixed binary convex quadratic optimization problems. We provide a complete characterization of the sets that can be obtained as the projection of such feasible regions. In order to obtain this result, we first provide a complete characterization of these sets in the special cases where (1) the feasible region is bounded, (2) only binary extended variables are present, and (3) only continuous variables are present.

关键词： mixed-integer programming Quadratic programming Representability Convex functions

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A constraint programming approach to type-2 assembly line balancing problem with assignment restrictions

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ASSEMBLY AUTOMATION 2019年第5期39卷 813-826页

作者： Pinarbasi, Mehmet Alakas, Haci Mehmet Yuzukirmizi, Mustafa Kirikkale Univ Dept Ind Engn Kirikkale Turkey

Purpose Main constraints for an assembly line balancing problem (ALBP) are cycle time/number of stations and task precedence relations. However, due to the technological and organizational limitations, several other restrictions can be encountered in real production systems. These restrictions are called as assignment restrictions and can be task assignment, station, resource and distance limitations. The purpose of the study is to evaluate the effects of these restrictions on ALBP using constraint programming (CP) model. Design/methodology/approach A novel CP model is proposed and compared to mixed-integer programming (MIP) as a benchmark. The objective is to minimize the cycle time for a given number of stations. The authors also provide explicit anthology of the assignment restriction effects on line efficiency, the solution quality and the computation time. Findings The proposed approach is verified with the literature test instances and a real-life problem from a furniture manufacturing company. Computational experiments show that, despite the fact that additional assignment restrictions are problematic in mathematical solutions, CP is a versatile exact solution alternative in modelling and the solution quality. Practical implications - Assembly line is a popular manufacturing system in the making of standardized high volume products. The problem of assembly line balancing is a crucial challenge in these settings and consists of assigning tasks to the stations by optimizing one or more objectives. Type-2 AR-ALBP is a specific case with the objective function of minimizing the cycle time for a given number of stations. It further assumes assignment restrictions that can be confronted due to the technological limitations or the strategic decisions of the company management. This is especially encountered in rebalancing lines. Originality/value Several solution approaches such as mathematical modelling, heuristic and meta-heuristic are proposed to solve the ALBP i

关键词： mixed-integer programming Assembly line balancing Assignment restrictions Constraint programming Type-2 problem

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Solving Stochastic and Bilevel mixed-integer Programs via a Generalized Value Function

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OPERATIONS RESEARCH 2019年第6期67卷 1659-1677页

作者： Tavaslioglu, Onur Prokopyev, Oleg A. Schaefer, Andrew J. Univ Pittsburgh Dept Ind Engn Pittsburgh PA 15260 USA Rice Univ Dept Computat & Appl Math Houston TX 77005 USA

We introduce a generalized value function of a mixed-integer program, which is simultaneously parameterized by its objective and right-hand side. We describe its fundamental properties, which we exploit through three algorithms to calculate it. We then show how this generalized value function can be used to reformulate two classes of mixed-integer optimization problems: two-stage stochastic mixed-integer programming and multifollower bilevel mixed-integer programming. For both of these problem classes, the generalized value function approach allows the solution of instances that are significantly larger than those solved in the literature in terms of the total number of variables and number of scenarios.

关键词： stochastic programming mixed-integer programming global branch and bound two-stage mixed-integer programming bilevel programming multifollower bilevel programming

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Routing and Scheduling for a Last-Mile Transportation System

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TRANSPORTATION SCIENCE 2019年第1期53卷 131-147页

作者： Wang, Hai Singapore Management Univ Sch Informat Syst Singapore 178902 Singapore

The last-mile problem concerns the provision of travel services from the nearest public transportation node to a passenger's home or other destination. We study the operation of an emerging last-mile transportation system (LMTS) with batch demands that result from the arrival of groups of passengers who desire last-mile service at urban metro stations or bus stops. Routes and schedules are determined for a multivehicle fleet of delivery vehicles, with the objective of minimizing passenger waiting time and riding time. An exact mixed-integer programming (MIP) model for LMTS operations is presented first, which is difficult to solve optimally within acceptable computational times. Computationally feasible heuristic approaches are then developed: a myopic operating strategy that uses only demand information from trains that have already arrived, a metaheuristic approach based on a tabu search that employs demand information over the entire service horizon, and a two-stage method that solves the MIP model approximately over the entire service horizon. These approaches are implemented in a number of computational experiments to evaluate the system's performance, and demonstrate that LMTS is notably preferable to a conventional service system under certain conditions.

关键词： last mile batch demand routing and scheduling mixed-integer programming myopic strategy tabu search

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The robust multiple-choice multidimensional knapsack problem

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2019年 86卷 16-27页

作者： Caserta, Marco Voss, Stefan IE Univ Maria de Molina 31B Madrid 28006 Spain Univ Hamburg Inst Informat Syst Von Melle Pk 5 D-20146 Hamburg Germany Pontificia Univ Catolica Valparaiso Escuela Ingn Ind Valparaiso Chile

The multiple-choice multidimensional knapsack problem (MMKP) assumes n sets composed of mutually exclusive items. The goal is to select exactly one item per set, maximizing the overall utility, without violating a family of knapsack constraints. Motivated by recent applications of the MMKP to complex system reliability and quality of service management problems, we propose a robust version. More specifically, we relinquish the assumption that the problem parameters are deterministically known by limiting their values to a pre-specified uncertainty set. Depending on the structure of the variance-covariance matrix used to model the uncertainty, we identify four different cases, leading to robust formulations characterized by second order cone programs. We show how each of these programs is transformed into an equivalent linear program, implying that the use of a robust formulation for the MMKP comes with no extra computational complexity. Finally, using a novel matheuristic designed for the MMKP, we shed lights on the trade-off between the "price of robustness," i.e., how much worse the objective function value of a robust solution is, compared with the deterministic one, and the "reliability," i.e., the probability that a robust solution will lead to a feasible scenario for an arbitrary realization of the uncertain parameters. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Robust optimization Knapsack problems mixed-integer programming

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POD-Based mixed-integer Optimal Control of the Heat Equation

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JOURNAL OF SCIENTIFIC COMPUTING 2019年第1期81卷 48-75页

作者： Freya, Bachmann Dennis, Beermann Lu Jianjie Stefan, Volkwein Univ Konstanz Dept Math & Stat Univ Str 10 D-78457 Constance Germany

In the present paper an optimal control problem governed by the heat equation is considered, where continuous as well as discrete controls are involved. To deal with the discrete controls a variant of the branch-and-bound method is utilized, where in each node a relaxed control constrained optimal control problem has to be solved involving only continuous optimization variables. However, the solutions to many relaxed optimal control problems have to be computed numerically. For that reason tailored second-order methods as well as model-order reduction are efficiently combined to speed-up the branch-and-bound method while still ensuring a desired accuracy. In this work the method of proper orthogonal decomposition (POD) is used for the model-order reduction. A posteriori error estimation in each node of the branch-and-bound method guarantees that the calculated solutions are sufficiently accurate. Numerical experiments illustrate the efficiency of the proposed strategy.

关键词： mixed-integer programming Optimal control PDE-constrained optimization Proper orthogonal decomposition Error analysis

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Improving physician schedules by leveraging equalization: Cases from hospitals in US

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2019年 85卷 182-193页

作者： Damci-Kurt, Pelin Zhang, Minjiao Marentay, Brian Govind, Nirmal Lightning Bolt Solut San Francisco CA 94080 USA Kennesaw State Univ Dept Econ Finance & Quantitat Anal Kennesaw GA 30144 USA Netflix Los Gatos CA 95032 USA

In this paper, we consider physician scheduling problems originating from a medical staff scheduling service provider based in the United States. Creating a physician schedule is a complex task. It must balance several goals, including adequately staffing required assignments to ensure quality patient care;adhering to rules that vary by hospital and medical specialty, and helping physicians to maintain work/life balance. We study various types of physician and hospital requirements with different priorities, focusing on achieving an equal distribution of the workload among physicians to produce a schedule that they perceive as fair, while all other group requirements are met. We observe that as the number of such equalization constraints increases, the physician scheduling optimization problem becomes more complex and it requires a longer time to find an optimal schedule. We begin by constructing mathematical models to formulate the physician scheduling problem requirements, and then for the relaxation of the problem that includes equalization constraints we derive a new class of valid inequalities, along with a polynomial separation algorithm for them. A branch-and-cut algorithm using these valid inequalities notably improves the quality of the schedules with respect to the soft constraints. We discuss in detail an example problem from a hospitalist department and present improvements to other schedules representing different specialties and hospitals. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Physician scheduling Optimization Soft constraints Workload distribution Valid inequalities mixed-integer programming

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Ellipsoidal Methods for Adaptive Choice-Based Conjoint Analysis

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OPERATIONS RESEARCH 2019年第2期67卷 315-338页

作者： Saure, Denis Vielma, Juan Pablo Univ Chile Ind Engn Santiago 8370456 Chile MIT Sloan Sch Management Cambridge MA 02142 USA

Questionnaires for adaptive choice-based conjoint analysis aim at minimizing some measure of the uncertainty associated with estimates of preference parameters (e.g., partworths). Bayesian approaches to conjoint analysis quantify this uncertainty with a multivariate distribution that is updated after the respondent answers. Unfortunately, this update often requires multidimensional integration, which effectively reduces the adaptive selection of questions to impractical enumeration. An alternative approach is the polyhedral method for adaptive conjoint analysis, which quantifies the uncertainty through a (convex) polyhedron. The approach has a simple geometric interpretation and allows for quick credibility-region updates and effective optimization-based heuristics for adaptive question selection. However, its performance deteriorates with high response-error rates. Available adaptations to this method do not preserve all of the geometric simplicity and interpretability of the original approach. We show how, by using normal approximations to posterior distributions, one can include response error in an approximate Bayesian approach that is as intuitive as the polyhedral approach and allows the use of effective optimization-based techniques for adaptive question selection. This ellipsoidal approach extends the effectiveness of the polyhedral approach to the high response-error setting and provides a simple geometric interpretation (from which the method derives its name) of Bayesian approaches. Our results precisely quantify the relationship between the most popular efficiency criterion and heuristic guidelines promoted in extant work. We illustrate the superiority of the ellipsoidal method through extensive numerical experiments.

关键词： conjoint analysis geometric methods Bayesian models mixed-integer programming

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