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A weapon-target assignment approach to media allocation

APPLIED MATHEMATICS AND COMPUTATION 2006年第2期175卷 1266-1275页

作者： Cetin, Eyup Esen, Seda Tolun Istanbul Univ Fac Business Adm Quantitat Methods Dept TR-34320 Istanbul Turkey

An important problem which media planners face with is media allocation including budget allocation for an advertising campaign in an optimal frame. This study developed a near optimization model, originated from the weapon-target assignment problem of military operations research, that allocates both media and budget. The proposed model, which is independent of the duration of an advertising campaign, also schedules advertisements during the day. The presented model is an integer nonlinear programming problem. A hypothetical example is given and solved by MS Excel as a powerful spreadsheet tool. MS Excel's Solver is also proposed to solve NP-complete type problems. This study is a good example of military operations research models that can be adapted to contemporary business world applications. (c) 2005 Elsevier Inc. All rights reserved.

关键词： media modeling advertising campaign budget allocation integer nonlinear programming spreadsheet modeling military operations research

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integer programming SUBJECT TO MONOMIAL CONSTRAINTS

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SIAM JOURNAL ON OPTIMIZATION 2010年第6期20卷 3297-3311页

作者： Buchheim, Christoph Michaels, Dennis Weismantel, Robert Tech Univ Dortmund Fac Math D-44227 Dortmund Germany ETH Inst Operat Res CH-8092 Zurich Switzerland

We investigate integer programs containing constraints of the type Pi i is an element of I(x)i(alpha i) - b. Due to the number-theoretic nature of these constraints, standard methods based on linear algebra cannot be applied directly. Instead, we present a reformulation resulting in integer programs with linear constraints and polynomial objective functions, using prime decompositions of the right-hand sides b. Moreover, we show that minimizing a linear objective function with nonnegative coefficients over bivariate constraints is possible in polynomial time.

关键词： integer nonlinear programming monomial constraints

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Optimal schemes for resubmitted lot acceptance using previous defect count data

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COMPUTERS & INDUSTRIAL ENGINEERING 2015年 87卷 66-73页

作者： Fernandez, Arturo J. Univ La Laguna Dept Matemat Estadist & Invest Operat San Cristobal la Laguna 38071 Camay Islands Spain

Optimal defects-per-unit inspection schemes for screening batches of manufactured material are obtained by minimizing the expected sampling effort. Nonaccepted lots may be resubmitted for resampiing inspection, whereas the Poisson model is used to describe the random behavior of the number of nonconformities per sampled unit. A coefficient is presented to assess the similarity degree between the available previous information and the current inspection, and truncated gamma distributions are adopted to quantify the natural prior uncertainty about the defect rate using past count data and expert opinions. A step-by-step computational procedure is proposed to solve the underlying integer nonlinear programming problem in order to find the best resubmitted lot sampling plan with controlled expected producer and consumer risks based on previous objective and subjective knowledge. In many practical cases, the inclusion of lot resubmissions and past information into the inspection process provides substantial savings in sample size, as well as more reliable evaluations of the existing producer and consumer risks. The proposed approach allows the practitioners to consider a restricted interval for the defect rate, which is reasonable in practice and unfeasible under the frequentist perspective. Moreover, a mechanism is suggested to update the prior distribution based on past performance of the inspection plan. For illustrative purposes, the methodology developed is applied to the manufacturing of glass. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Expected producer and consumer risks Industrial quality control integer nonlinear programming Poisson distribution Truncated gamma prior model

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Crew pairing at Air France

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1997年第2期97卷 245-259页

作者： Desaulniers, G Desrosiers, J Dumas, Y Marc, S Rioux, B Solomon, MM Soumis, F ECOLE POLYTECH DEPT MATH & GENIE IND MONTREAL PQ H3C 3A7 CANADA ECOLE HAUTES ETUD COMMERCIALES MONTREAL PQ CANADA AD OPT TECHNOL INC MONTREAL PQ CANADA AIR FRANCE PARIS FRANCE NORTHEASTERN UNIV COLL BUSINESS ADM MANAGEMENT SCI GRP BOSTON MA 02115 USA

In the airline industry, crew schedules consist of a number of pairings, These are round trips originating and terminating at the same crew home base composed of legal work days, called duties, separated by rest periods, The purpose of the airline crew pairing problem is to generate a set of minimal cost crew pairings covering all flight legs, The set of pairings must satisfy all the rules in the work convention and all the appropriate air traffic regulations, The resulting constraints can affect duty construction, may restrict each pairing, or be imposed on the overall crew schedule. The pairing problem is formulated as an integer, nonlinear multi-commodity network flow problem with additional resource variables. nonlinearities occur in the objective function as well as in a large subset of constraints. A branch-and-bound algorithm based on an extension of the Dantzig-Wolfe decomposition principle is used to solve this model. The master problem becomes a Set Partitioning type model, as in the classical formulation, while pairings are generated using resource constrained shortest path subproblems, This primal approach implicitly considers all feasible pairings and also provides the optimality gap value on a feasible solution. A nice feature of this decomposition process is that it isolates all nonlinear aspects of the proposed multi-commodity model in the subproblems which are solved by means of a specialized dynamic programming algorithm. We present the application and implementation of this approach at Air France. It is one of the first implementations of an optimal approach for a large airline carrier We have chosen a subproblem network representation where the duties rather than the legs are on the arcs, This ensures feasibility relative to duty restrictions by definition, As opposed to Lavoie, Minoux and Odier (1988), the nonlinear cost function is modeled without approximations. The computational experiments were conducted using actual Air France medium haul d

关键词： crew pairing integer nonlinear programming multi-commodity flow model Dantzig-Wolfe decomposition set partitioning

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A maritime scheduling transportation-inventory problem with normally distributed demands and fully loaded/unloaded vessels

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APPLIED MATHEMATICAL MODELLING 2018年 53卷 540-566页

作者： Soroush, H. M. Al-Yakoob, S. M. Kuwait Univ Dept Stat & Operat Res POB 5969 Safat 13060 Kuwait Kuwait Univ Dept Math POB 5969 Safat 13060 Kuwait

Uncertainties in oil demands have significant effects on the routing and scheduling of oil tankers and inevitably influence the pertinent fleet operational expenses, shortage and excess inventory penalties, and chartering costs. In this paper, we study a stochastic maritime scheduling transportation-inventory problem to transport crude oil from a source using a set of fully loaded heterogeneous vessels to be fully unloaded at a destination over a finite time horizon. Daily demands at the destination are normally distributed random variables and different penalties are imposed on the shortages/excesses in daily storage levels at the destination. The expected total cost of such a fleet operation, consists of the total vessels' operational expenses, expected total penalties resulting from violating specified lower and upper bounds at the destination storage facility, and chartering expenses. We aim to simultaneously optimize the fleet schedules and maintain desirable daily storage levels to meet the stochastic demand requirements at the destination with acceptable reliability levels. We formulate the problem as a stochastic optimization model and then use chance constrained programming to convert it to an exact mixed integer nonlinear program with a convex objective function and linear constraints. Solutions obtained via the proposed stochastic model and its deterministic counterpart are compared and analyzed to gain insights into the impact of the variations in demands and the probabilities of meeting demands on the overall operation and cost structure. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Stochastic vessel scheduling Transportation Inventory/shortages Chance constraints integer nonlinear programming

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Residential Load Disaggregation Considering State Transitions

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2020年第2期16卷 743-753页

作者： Zeinal-Kheiri, Sevda Shotorbani, Amin Mohammadpour Mohammadi-Ivatloo, Behnam Univ Tabriz Fac Elect & Comp Engn Tabriz 5166 Iran Univ British Columbia Sch Engn Kelowna BC V1V 1V7 Canada

Information about power consumption patterns of devices, helps the residential consumers manage their energy usage. Nonintrusive load monitoring is an effective tool to extract the consumption patterns from the measured aggregated data at the meter. In this paper, an optimization-based method is proposed to disaggregate the total load, using low frequency data. The proposed algorithm is enhanced by enforcing the power profiles of appliances to be piecewise constant over specific time durations. Moreover, the state transitions of the appliances are determined and then employed as the optimization constraints to improve the estimation results. The proposed method is evaluated using almanac of minutely power data set (AMPds) and reference energy disaggregation data set (REDD) datasets by several performance metrics. Results indicate that the designed algorithm is able to recognize the frequently varying appliances in spite of piecewise constancy presumption. Furthermore, breaking down the optimization problem to the smaller parts enhances the ability of the algorithm to be operated in real time.

关键词： integer nonlinear programming load disaggregation optimization piecewise constancy state transition

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Ad hoc heuristic for the cover printing problem

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DISCRETE OPTIMIZATION 2012年第1期9卷 17-28页

作者： Romero, David Alonso-Pecina, Federico Univ Nacl Autonoma Mexico Inst Matemat Cuernavaca 62210 Morelos Mexico

We address an NP-hard combinatorial optimization problem arising in a printing shop. An impression grid is composed by a set of plates. The cover printing problem consists in designing the composition of impression grids, and determining the number of times each grid is to be printed in order to fulfill the demand of different book covers at minimum total printing cost;the latter comes from three fixed costs: for printing one sheet, for producing one plate, and for composing one impression grid. For each cover an unlimited number of plates can be made. To deal with this challenging problem we present an ad hoc heuristic that outperforms all previously proposed approaches, including genetic algorithms, GRASP, and simulated annealing. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimization integer nonlinear programming Cover printing Label printing Heuristic Job splitting

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Multi-stage optimization for periodic inspection planning of geo-distributed infrastructure systems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第3期245卷 797-804页

作者： Phan, Dzung T. Zhu, Yada IBM Corp Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA

This paper develops a multi-stage optimization framework for determining periodic inspection intervals for geo-distributed infrastructure systems subject to hidden failures. We assume that the unit's failure can only be rectified at periodic inspection when a perfect repair is carried out to restore the unit to as-good-as-new condition. For large-scale systems such as fire hydrants in a city, water supply and power transformer distribution networks in urban areas, firstly, we partition the units of a system into groups based on their pre-specified features by a clustering algorithm;then compute an optimal periodic inspection interval for each group based on the expected cost per cycle;and finally, we find the inspection schedule for the whole system that not only minimizes the total inspection and maintenance cost but also satisfies the workforce and budget resource constraints. An integer nonlinear programming formulation and a heuristics are introduced to determine the inspection schedule. The proposed approach is applied to scheduling periodic inspection of large amounts of fire hydrants in a major U.S. city. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Periodic inspection Hidden failures integer nonlinear programming Clusters Maintenance cost

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AN EXTENDED CUTTING PLANE METHOD FOR SOLVING CONVEX MINLP PROBLEMS

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COMPUTERS & CHEMICAL ENGINEERING 1995年第SUPPL. 1期19卷 S131-S136页

作者： WESTERLUND, T PETTERSSON, F Process Design Laboratory at Åbo Akademi University Biskopsgatan 8 FIN-20500 Åbo Finland

An extended version of Kelley's cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while Kelley's cutting plane method was originally introduced for the solution of convex NLP (non-linear programming) problems only. The method is suitable for solving large convex MINLP problems with a moderate degree of nonlinearity. The convergence properties of the method are given in the present paper and an example is provided to illustrate the numerical procedure.

关键词： OPTIMIZATION MIXED-integer nonlinear programming integer nonlinear programming EXTENDED CUTTING PLANE

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Balancing producer and consumer risks in optimal attribute testing: A unified Bayesian/Frequentist design

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期286卷 576-587页

作者： Fernandez, Arturo J. Correa-Alvarez, Cristian D. Pericchi, Luis R. Univ La Laguna Dept Matemat Estadist & Invest Operat Tenerife 38071 Canary Islands Spain Inst Tecnol Metropolitano ITM Dept Calidad & Prod Medellin Antioquia Colombia Univ Puerto Rico Rio Piedras Dept Math San Juan PR 00931 USA Univ Puerto Rico Rio Piedras Ctr Biostat & Bioinformat San Juan PR 00931 USA

Unified Bayesian/frequentist approaches for the design of attributes sampling plans are introduced by minimizing and limiting a weighted-average of the classical or expected producer and consumer risks adopted by the decision maker. This change of paradigm in the construction of test plans for lot acceptance provides optimal inspection schemes from both frequentist and Bayesian perspectives. Classes of admissible test plans minimizing the weighted-average risks are first defined. Constrained optimization problems are then solved in order to determine sample sizes with smallest classical or expected weighted-average risks, as well as acceptance test plans with minimal inspection effort and controlled risks. The proposed methodology to determine optimal sample sizes and decision criteria for lot sentencing constitutes a plausible consensus between Frequentists and Bayesians. Moreover, the use of prior information on the fraction defective allows the practitioners to appreciably reduce the required sample size for lot screening. Optimal lot inspection schemes can also be easily updated using past performance of the sampling plans. Besides the advantages the suggested approach has for hypothesis testing, namely large sample consistency and reproducible results, it permits to make a trade-off between the opposite goals of customers and manufacturers. Some applications in reliability demonstration testing and industrial quality control are presented for illustrative purposes. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Quality control Constrained optimization Lot sampling inspection integer nonlinear programming Reliability demonstration testing

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