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Optimal exact design of double acceptance sampling plans by attributes

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2019年第17期89卷 3313-3329页

作者： Duarte, Belmiro P. M. Granjo, Jose F. O. Coimbra Polytech ISEC Dept Chem & Biol Engn R Pedro Nunes P-3030199 Coimbra Portugal Univ Coimbra Dept Chem Engn CIEPQPF Coimbra Portugal

The design of double acceptance sampling (AS) plans for attributes based on the operating characteristic curve paradigm is usually addressed by enumeration algorithms. These AS plans may be non optimal regarding the sample size to inspect as they were obtained without the requirement that the constraints at the OC curve controlled points are not violated for minimum Average Sample Number (ASN) scenarios. An approach based on mathematical programming is proposed to systematically design double AS plans for attributes, where the characteristics controlled are modelled by binomial or Poisson distributions. Specifically, mixed integer nonlinear programming (MINLP) formulations are developed and combined with an enumeration algorithm that allows finding ASN minimax optimal plans. A theoretical result is developed with the purpose of assuring the global optimum design is reached by iteration where a convenient solver is used to find local optima. To validate the algorithm, we compare our results with those of tables commonly used for practical purposes, consider different rates of risk, and setups commonly used in Lot Quality Assurance Plans (LQAS) for health monitoring programmes. Finally, we compare AS plans determined for processes described by binomial and Poisson distributions.

关键词： Acceptance sampling plan mixed integer nonlinear programming operating characteristic curve average sample number

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A hybrid differential evolution algorithm for a location-inventory problem in a closed-loop supply chain with product recovery

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COMPLEX & INTELLIGENT SYSTEMS 2023年第4期9卷 4123-4145页

作者： Guo, Hao Liu, Gang Zhang, Ying Zhang, Chunnan Xiong, Chuanhui Li, Wenli Wuhan Text Univ Sch Management Wuhan 430200 Hubei Peoples R China Hubei Univ Econ Collaborat Innovat Ctr Emiss Trading Syst Coconstr Wuhan 430200 Hubei Peoples R China Hubei Univ Econ Sch Business Adm Wuhan 430200 Hubei Peoples R China SUNY Buffalo Dept Ind & Syst Engn Buffalo NY 14260 USA State Univ New York Plattsburgh Dept Accounting Plattsburgh NY 12901 USA Univ North Carolina Pembroke Thomas Sch Business Pembroke NC 28372 USA Univ Hubei Prov Key Res Inst Humanities & Social Sci Res Ctr Enterprise Decis Support Wuhan 430200 Hubei Peoples R China

Product recovery is an important business because of its great economic, social, and environmental benefits in practice. In this paper, a location-inventory problem (LIP) in a closed-loop supply chain (CLSC) is investigated to optimize facility location and inventory control decisions by considering product recovery. The objective is to optimize facility location and inventory control decisions to minimize the total cost of business operations in a closed-loop supply chain system. We formulate this problem as a mixed-integer nonlinear programming model and design a modified hybrid differential evolution algorithm (MHDE) to solve it efficiently. Finally, numerical results are presented to validate the performance of the new algorithm. The results show that MHDE is more efficient and effective than Lingo and other algorithms for the research problem under study. Managerial insights are also derived for business managers to improve their supply chain performance.

关键词： Location-inventory problem Closed-loop supply chain mixed integer nonlinear programming Differential evolution Product recovery

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The nature of optimal policies for deterministic finite-horizon inventory models

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE-OPERATIONS & LOGISTICS 2022年第1期9卷 39-60页

作者： Benkherouf, Lakdere Gilding, Brian H. Kuwait Univ Coll Sci Dept Stat & Operat Res POB 5969 Safat 13060 Kuwait Kuwait Univ Coll Sci Dept Math Safat Kuwait

This paper concerns a general formulation for a longstanding problem. This is the problem of determining a replenishment schedule that minimises the total cost of stocking and holding an inventory in a deterministic finite-horizon inventory model. The formulation permits the treatment of seemingly unrelated models in a single framework. These include classical lot-size models, batching models, repair models, recovery models and others. Admissible control policies are restricted to a partition of some closed interval on the real line. The solution of a mixed integer nonlinear programming problem (MINLP) delivers the optimal partition. It is shown that the MINLP possesses an optimal solution under very mild conditions. The theory of submodular functions on a lattice is the key to handling the integer variable. This theory permits the recovery and generalisations of earlier results on the interleaving property of optimal partitions and a convexity property of the value of the objective function. Past intractable inventory models with demand driven by a general differential equation and in the absence and in the presence of shortages and inflation are solved. This generalises a number of existing results in the literature.

关键词： Inventory model finite time horizon optimal schedule mixed integer nonlinear programming submodular function

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Multi-venue location optimization with overlapping audience reach areas

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OPERATIONAL RESEARCH 2024年第4期24卷 65页

作者： Shams-Shoaaee, Shervin Dept Natl Def 60 Moodie Dr Ottawa ON K1A 0K2 Canada

The Canadian Armed Forces (CAF) is currently facing recruitment challenges. Similar to target market advertising in other industries, military recruitment can be optimized by aiming recruitment efforts at populations with high enrolment success potential. Using historical data, geographical regions with high potential for recruitment can be identified. This can be used to optimize the reach of recruitment events to high potential geographical regions. This paper looks at applications of facility location optimization in recruitment attraction event planning activities where there are intersections in regions each venue can attract audiences from (venue reach areas), and the probability that the events will attract targeted audience varies by geographical location. This study models the problem as a mixed integer nonlinear problem (MINLP) and provides an exact solution method. This is followed by a case study applying the model to the CAF's recruitment events for a sample geographical area of the Canadian National Capital Region (NCR).

关键词： Military recruitment optimization Facilities' location selection optimization mixed integer nonlinear programming Linear integer programming Discrete optimization

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Robust delay-constrained routing in telecommunications

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ANNALS OF OPERATIONS RESEARCH 2013年第1期206卷 163-181页

作者： Hijazi, Hassan Bonami, Pierre Ouorou, Adam Orange Labs R&D CORE MCN F-92794 Issy Les Moulineaux 9 France CNRS Aix Marseille Univ LIF Marseille France

In telecommunications, operators usually use market surveys and statistical models to estimate traffic evolution in networks or to approximate queuing delay functions in routing strategies. Many research activities concentrated on handling traffic uncertainty in network design. Measurements on real world networks have shown significant errors in delay approximations, leading to weak management decisions in network planning. In this work, we introduce elements of robust optimization theory for delay modeling in routing problems. Different types of data uncertainty are considered and linked to corresponding robust models. We study a special case of constraints featuring separable additive functions. Specifically, we consider that each term of the sum is disturbed by a random parameter. These constraints are frequent in network based problems, where functions reflecting real world measurements on links are summed up over end-to-end paths. While classical robust formulations have to deal with the introduction of new variables, we show that, under specific hypotheses, the deterministic robust counterpart can be formulated in the space of original variables. This offers the possibility of constructing tractable robust models. Starting from Soyster's conservative model, we write and compare different uncertainty sets and formulations offering each a different protection level for the delay constrained routing problem. Computational experiments are developed in order to evaluate the "price of robustness" and to assess the quality of the new formulations.

关键词： Robust optimization mixed integer nonlinear programming Delay constrained routing problem

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Identification of groundwater contamination sources using a statistical algorithm based on an improved Kalman filter and simulation optimization

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HYDROGEOLOGY JOURNAL 2019年第8期27卷 2919-2931页

作者： Li, Jiuhui Lu, Wenxi Wang, Han Fan, Yue Jilin Univ Key Lab Groundwater Resources & Environm Minist Educ Changchun 130021 Jilin Peoples R China Jilin Univ Coll New Energy & Environm Changchun 130021 Jilin Peoples R China

Identification of groundwater contamination sources, as a solution to an inverse problem, is mainly based on simulation optimization methods. However, the establishment and solution of an optimization model are extremely complicated for the inverse problem, where many decision variables need to be identified. Combining simulation optimization methods with other mathematical methods can effectively avoid this shortcoming. In order to identify features of contamination sources, the Kalman filter is combined with a mixed-integer nonlinear programming optimization model (MINLP). Firstly, the Kalman filter is improved by U-D decomposition (a matrix decomposition method) to identify the number and approximate locations of real contamination sources among potential contamination sources. A 0-1 MINLP solution is then employed to identify the accurate location and release history of the contamination source. Kriging is used to produce a surrogate model for the numerical simulation model. The surrogate model approximates the numerical simulation model, which can be embedded in the 0-1 MINLP instead of the numerical simulation model and it can be called directly during the iteration of the optimization model, thereby avoiding manually coupling the numerical simulation model with the optimization model during the solution process. Results demonstrate that the improved Kalman filter exhibits better numerical stability, where it can effectively avoid the filter divergence problem as well as solve the number and approximate locations of contamination sources in the inverse identification problem. The accurate location and release history of the contamination source can be effectively identified by using the 0-1 MINLP.

关键词： Contamination Improved Kalmer filter mixed integer nonlinear programming Numerical modeling Surrogate model

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Reverse engineering genetic networks using nonlinear saturation kinetics

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BIOSYSTEMS 2019年 182卷 30-41页

作者： Youseph, Ahammed Sherief Kizhakkethil Chetty, Madhu Karmakar, Gour Monash Univ Fac Informat Technol Clayton Vic 3800 Australia Federat Univ Australia Sch Sci Engn & Informat Technol Gippsland 3842 Australia

A gene regulatory network (GRN) represents a set of genes along with their regulatory interactions. Cellular behavior is driven by genetic level interactions. Dynamics of such systems show nonlinear saturation kinetics which can be best modeled by Michaelis-Menten (MM) and Hill equations. Although MM equation is being widely used for modeling biochemical processes, it has been applied rarely. for reverse engineering GRNs. In this paper, we develop a complete framework for a novel model for GRN inference using MM kinetics. A set of coupled equations is first proposed for modeling GRNs. In the coupled model, Michaelis-Menten constant associated with regulation by a gene is made invariant irrespective of the gene being regulated. The parameter estimation of the proposed model is carried out using an evolutionary optimization method, namely, trigonometric differential evolution (TDE). Subsequently, the model is further improved and the regulations of different genes by a given gene are made distinct by allowing varying values of Michaelis-Menten constants for each regulation. Apart from making the model more relevant biologically, the improvement results in a decoupled GRN model with fast estimation of model parameters. Further, to enhance exploitation of the search, we propose a local search algorithm based on hill climbing heuristics. A novel mutation operation is also proposed to avoid population stagnation and premature convergence. Real life benchmark data sets generated in vivo are used for validating the proposed model. Further, we also analyze realistic in silico datasets generated using GeneNetweaver. The comparison of the performance of proposed model with other existing methods shows the potential of the proposed model.

关键词： Gene regulatory network Michaelis-Menten kinetics Reverse engineering mixed integer nonlinear programming Trigonometric differential evolution Local search

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Simulation of mass exchange networks using modified genetic algorithms

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KOREAN JOURNAL OF CHEMICAL ENGINEERING 2011年第2期28卷 332-341页

作者： Thunyawart, Jutamart Srinophakun, Thongchai Henwatthana, Waranya Kasetsart Univ Dept Chem Engn Bangkok 10900 Thailand King Mongkuts Univ Technol Thonburi Dept Chem Engn Bangkok 10140 Thailand Natl Ctr Excellence Petr Petrochem & Adv Mat Bangkok 10330 Thailand

The optimum water usage network leads to both a minimum of freshwater consumption and a minimum of generated wastewater. This work is to develop a mass-exchange networks (MENs) module for a minimum freshwater usage target. This module works as an interface to retrieve supplemental data of chemical processes from a process simulator and to communicate this to the genetic algorithm optimizer. A reuse system and a regeneration/recyclingsystem with a single contaminant are considered as approaches for freshwater minimization. In the formulated model, as mixed integer nonlinear programming (MINLP), all of the variables are divided into independent and dependent variables. The values of independent variables come from randomization,whereas the values of dependent variables come from simultaneous solutions of a set of equality constraints after assigning the values of independent variables. This method is applied to the steps of initialization, crossover and mutation. The MENs module is validated with a tricresylphosphate process consisting of five unit operations. Water is used to remove a fixed content of cresol. From the result, the module gives a reliable solution for freshwater minimization, which can satisfy mass balance and constraints. The results show that reuse and regeneration/recycling strategies can reduce freshwater consumption, including wastewater generated. Reuse cannot decrease the mass load of the contaminant, while regeneration/recycling can. In addition, regeneration requires less freshwater than the reuse process.

关键词： Wastewater Minimization Genetic Algorithm mixed integer nonlinear programming

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Generating convex polynomial inequalities for mixed 0-1 programs

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JOURNAL OF GLOBAL OPTIMIZATION 2002年第3期24卷 311-332页

作者： Stubbs, RA Mehrotra, S Northwestern Univ Dept Ind Engn & Management Sci Evanston IL 60208 USA

We develop a method for generating valid convex quadratic inequalities for mixed 0-1 convex programs. We also show how these inequalities can be generated in the linear case by defining cut generation problems using a projection cone. The basic results for quadratic inequalities are extended to generate convex polynomial inequalities.

关键词： mixed integer programming convex programming semidefinite programming mixed integer nonlinear programming mixed integer convex programming

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Determination of Network Configuration Considering Inventory Cost in a Supply Chain

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JOURNAL OF APPLIED RESEARCH AND TECHNOLOGY 2014年第4期12卷 674-683页

作者： Hernandez Gonzalez, N. M. Alvarez Socarras, A. Mata Perez, M. Univ Autonoma Nuevo Leon San Nicolas De Los Garza Nuevo Leon Mexico

In this paper we show the importance of applying mathematical optimization when designing the distribution network in a supply chain, specifically in making decisions related location of facilities and inventory management, which are associated with different levels of planning but are closely related. The addressed problem is an extension of the classic capacitated facility location problem. The distinguishing features are: the inventory management, the presence of multiple plants, and the single source constraints in both echelons. A key issue is that demand at each distribution center is a function of the demands at the retailers assigned, which is a random variable whose value is not known at the time of designing the network. We focus on the mathematical modeling of the problem and the evaluation of the performance of the developed models, so, it can be observed the troubles that arise when modeling supply chains that consider different types of decisions.

关键词： Supply chain location and inventory problem mixed integer nonlinear programming mixed integer linear programming

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