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Partial reformulation-linearization based optimization models for the Golomb ruler problem 基于部分重拟线性化的戈隆尺问题优化模型
RAIRO - Operations Research Pub Date : 2024-06-04 DOI: 10.1051/ro/2024121
H. Ouzia
{"title":"Partial reformulation-linearization based optimization models for the Golomb ruler problem","authors":"H. Ouzia","doi":"10.1051/ro/2024121","DOIUrl":"https://doi.org/10.1051/ro/2024121","url":null,"abstract":"In this paper, we provide a straightforward proof of a conjecture proposed in cite{Duxbury2021} regarding the optimal solutions of a non-convex mathematical programming model of the Golomb ruler problem. Subsequently, we investigate the computational efficiency of four new binary mixed-integer linear programming models to compute optimal Golomb rulers. These models are derived from a well-known nonlinear integer model proposed in cite{Kocuk2019}, utilizing the reformulation-linearization technique. modif{Finally, we provide the correct outputs of the greedy heuristic proposed in cite{Duxbury2021} and correct some false conclusions stated or implied therein.}","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"6 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A double bootstrap data envelopment analysis model with stochastic reducible outputs and expandable inputs: An application to power plants 具有随机还原输出和可扩展输入的双引导数据包络分析模型:电厂应用
RAIRO - Operations Research Pub Date : 2024-06-04 DOI: 10.1051/ro/2024119
Alireza Amirteimoori, T. Allahviranloo, Asunur Cezar
{"title":"A double bootstrap data envelopment analysis model with stochastic reducible outputs and expandable inputs: An application to power plants","authors":"Alireza Amirteimoori, T. Allahviranloo, Asunur Cezar","doi":"10.1051/ro/2024119","DOIUrl":"https://doi.org/10.1051/ro/2024119","url":null,"abstract":"Clean production of electricity is not only cost-effective but also effective in reducing pollutants. Toward this end, the use of clean fuels is strongly recommended by environmentalists. Benchmarking techniques, especially data envelopment analysis, are an appropriate tool for measuring the relative efficiency of firms with environmental pollutants. In classic data envelopment analysis models, decision-makers are faced with production processes in which reducible inputs are used to produce expandable outputs. In this contribution, we consider production processes when the input and output data are given in stochastic form and some throughputs are reducible and some others are expandable. A stochastic directional distance function model is proposed to calculate the relative technical efficiency of firms. In order to evaluate firm-specific technical efficiency, we apply bootstrap DEA. We first calculate the technical efficiency scores of firms by classic DEA model. Then, the double bootstrap DEA model is applied to determine the impact of explanatory variables on firm efficiency. To demonstrate the applicability of the procedure, we present an empirical application wherein we employ power plants.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"10 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141267337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wolfe type duality on quasidifferentiable mathematical programs with vanishing constraints 具有消失约束条件的准微分数学程序的沃尔夫类型对偶性
RAIRO - Operations Research Pub Date : 2024-05-24 DOI: 10.1051/ro/2024115
Shashi Kant Mishra, Vandana Singh
{"title":"Wolfe type duality on quasidifferentiable mathematical programs with vanishing constraints","authors":"Shashi Kant Mishra, Vandana Singh","doi":"10.1051/ro/2024115","DOIUrl":"https://doi.org/10.1051/ro/2024115","url":null,"abstract":"This article is devoted to the study of duality results for optimization problems with vanishing constraints in nonsmooth case. We formulate Wolfe type dual and establish weak, strong, converse, restricted converse and strict converse duality results for mathematical programs with vanishing constraints involving quasidifferentiable functions. Under the assumption of invex and strictly invex functions with respect to a convex compact set","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"2 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141099225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Round-trip hub location problem 往返枢纽位置问题
RAIRO - Operations Research Pub Date : 2024-05-24 DOI: 10.1051/ro/2024116
Omar Kemmar, karim bouamrane, S. Gelareh
{"title":"Round-trip hub location problem","authors":"Omar Kemmar, karim bouamrane, S. Gelareh","doi":"10.1051/ro/2024116","DOIUrl":"https://doi.org/10.1051/ro/2024116","url":null,"abstract":"In this paper, we introduce a novel network design for the Hub Location Problem, inspired by the round-trip structure commonly used by transport service providers. Our design integrates spoke nodes assigned to a central hub node, creating round-trips where the hub node serves as the starting point, visits all assigned spoke nodes, and returns to the hub. To enhance transportation services and provide additional redundancy, we introduce a new type of nodes called runaway nodes to the network. The motivation for this research arises from two real-life cases encountered during consultancy projects, underscoring the necessity for an optimized network design in transportation services.\u0000To address the proposed problem, we introduce a mixed-integer linear programming (MIP) mathematical model. However, due to the problem's complexity, the feasibility of the MIP model is limited to small-scale instances. To tackle medium and large-scale instances, we introduce two hyper-heuristic approaches based on reinforcement learning. These hyper-heuristic approaches harness the power of reinforcement learning to guide the selection of low-level heuristics and improve solution quality. We conduct extensive computational experiments to evaluate the efficiency and effectiveness of the proposed approaches.\u0000The results of our experiments affirm the efficiency of the proposed hyper-heuristic approaches, showcasing their ability to discover high-quality solutions for the Hub Location Problem.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"1 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141101182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-choice conic goal programming model-based network data envelopment analysis 基于多选圆锥目标编程模型的网络数据包络分析
RAIRO - Operations Research Pub Date : 2024-05-24 DOI: 10.1051/ro/2024117
Derya Deliktaş, O. Ustun, Ezgi Aktar Demirtaş, Rifat Aykut Arapoglu
{"title":"Multi-choice conic goal programming model-based network data envelopment analysis","authors":"Derya Deliktaş, O. Ustun, Ezgi Aktar Demirtaş, Rifat Aykut Arapoglu","doi":"10.1051/ro/2024117","DOIUrl":"https://doi.org/10.1051/ro/2024117","url":null,"abstract":"In multi-stage processes, classical Data Envelopment Analysis (DEA) acts like a black box and measures the efficiency of decision-making units (DMUs) without considering the internal structure of the system. Unlike classical DEA, recent studies have shown that the overall system efficiency scores are more meaningful if researched using the Network DEA (NDEA) methodology. NDEA performs simultaneous efficiency evaluations of sub-processes and the entire system. Recently, the composition method integrated with multi-objective programming (MOP) has been preferred by many authors to alleviate the drawbacks of earlier methods such as decomposition, slack-based measure (SBM) and the system-centric approach. This study proposes a novel approach incorporating Multi-Choice Conic Goal Programming into the NDEA (MCCGP-NDEA). It provides a more accurate representation of the Pareto front by revealing potential Pareto optimal solutions which are overlooked by the composition methods. Due to its ability to modify stage weights based on the decision makers' (DMs) preferences, it is likely to gather more samples from the Pareto surface. Computational results on available benchmark problems confirm that the proposed MCCGP-NDEA is a viable alternative to existing methods.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"3 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141099568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher-order optimality conditions with separated derivatives and sensitivity analysis for set-valued optimization 带分离导数的高阶最优条件和集值优化的敏感性分析
RAIRO - Operations Research Pub Date : 2024-05-24 DOI: 10.1051/ro/2024118
Tian Tang, Guolin Yu
{"title":"Higher-order optimality conditions with separated derivatives and sensitivity analysis for set-valued optimization","authors":"Tian Tang, Guolin Yu","doi":"10.1051/ro/2024118","DOIUrl":"https://doi.org/10.1051/ro/2024118","url":null,"abstract":"In this paper, we establish optimality conditions and sensitivity analysis of set-valued optimization problems in terms of higher-order radial derivatives. First, we obtain the optimality conditions with separated derivatives for a set-valued optimization problem, here separated derivatives means the derivatives of objective and constraint functions are different. Then, some duality theorems for a mixed type of primal-dual set-valued optimization problem are gained. Finally, several results concerning higher-order sensitivity analysis are presented. The main results of this paper are illustrated by some concrete examples.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"3 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141100681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Distinct sizes of maximal independent sets on graphs with restricted girth 周长受限图上最大独立集的不同大小
RAIRO - Operations Research Pub Date : 2024-05-15 DOI: 10.1051/ro/2024110
Márcia Cappelle, Julliano Nascimento, Vinícius Santos
{"title":"Distinct sizes of maximal independent sets on graphs with restricted girth","authors":"Márcia Cappelle, Julliano Nascimento, Vinícius Santos","doi":"10.1051/ro/2024110","DOIUrl":"https://doi.org/10.1051/ro/2024110","url":null,"abstract":"Let $G$ be a graph. If $G$ has exactly $r$ distinct sizes of maximal independent sets, $G$ belongs to a collection called $mathcal{M}_r$. If $G in mathcal{M}_{r}$ and the distinct values of its maximal independent sets are consecutive, then $G$ belongs to  $mathcal{I}_{r}$. The independence gap of $G$ is the difference between the maximum and the minimum sizes of a maximal independent set in $G$.  In this paper, we show that recognizing graphs in $mathcal{I}_r$ is $mathcal{NP}$-complete, for every integer $r geq 3$. On the other hand, we show that recognizing trees in $mathcal{M}_r$ can be done in polynomial time, for every $r geq 1$.\u0000Also, we present characterizations of some graphs with girth at least 6 with independence gap at least 1, including graphs with independence gap $r-1$, for $rgeq 2$, belonging to $mathcal{I}_r$. Moreover, we present a characterization of some trees in $mathcal{I}_3$.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"66 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Marginal profit maximization estimation of supply chains by waste energy decrement: a case study of the power industry 通过废能递减估算供应链边际利润最大化:电力行业案例研究
RAIRO - Operations Research Pub Date : 2024-05-15 DOI: 10.1051/ro/2024103
M. Pouralizadeh
{"title":"Marginal profit maximization estimation of supply chains by waste energy decrement: a case study of the power industry","authors":"M. Pouralizadeh","doi":"10.1051/ro/2024103","DOIUrl":"https://doi.org/10.1051/ro/2024103","url":null,"abstract":"Economic growth and excessive fossil energy consumption have direct effects on environmental destruction and greenhouse gas increments. The existing appropriate pattern for economic performance increase as well as pollution emissions abatement is a basic issue in industry activities. In this paper, a data envelopment analysis (DEA) model is introduced for estimating the directional marginal profit maximization of supply chain divisions based on wasted energy and power losses. The purpose of this study is to estimate the directional marginal productivity in the supply chain, which enables us to find the optimal direction of efficient divisions on the frontier. This makes the allocation of resources create a marginal profit increase and the pollution emissions be abated simultaneously. Indeed, the proposed model considers the synergistic effects of each input on MP estimation in predetermined directions. The model is able to estimate the marginal profit maximization of desirable output and undesirable output decrease for each input simultaneously. The results suggested that the gas field division of one of the supply chains had fundamental capacities for energy production increments and flare gas decrements. Furthermore, the gas field division of this supply chain also had a considerable structure for the marginal profit maximization of outputs based on flare gas decreases. Additionally, the distribution lines of 0.80% supply chains provided wasted energy reduction by adding one extra unit to the line's capacity in the determined direction. Especially, there were supply chains that had investment opportunities for an acceptable abatement of power losses. This not only enables divisions to respond to fluctuations in demand as they produce more energy in critical situations like climate change but also decreases harmful emissions as wasted energy in supply chain divisions.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"32 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140974205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Realizability problem of distance-edge-monitoring numbers 距离边缘监测数的可实现性问题
RAIRO - Operations Research Pub Date : 2024-05-15 DOI: 10.1051/ro/2024106
Zhen Ji, Yaping Mao, Eddie Cheng, Xiaoyan Zhang
{"title":"Realizability problem of distance-edge-monitoring numbers","authors":"Zhen Ji, Yaping Mao, Eddie Cheng, Xiaoyan Zhang","doi":"10.1051/ro/2024106","DOIUrl":"https://doi.org/10.1051/ro/2024106","url":null,"abstract":"Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$.  For a set $M$ of vertices and an edge $e$ of a graph $G$, let $P(M, e)$ be the set of pairs $(x, y)$ with a vertex $x$ of $M$ and a vertex\u0000$y$ of $V(G)$ such that $d_{G}(x, y)neq d_{G-e}(x, y)$.\u0000%For a vertex $x$, let $EM(x)$ be the set of edges $e$ such that there exists a vertex $v$ in $G$ with $(x, v)in P({x}, e)$. If $e in EM(x)$, then we say that $e$ can be monitored by the vertex $x$.\u0000Given a vertex $x$, an edge $e$ is said to be monitored by $x$ if there exists a vertex $v$ in $G$ such that $(x, v)in P({x}, e)$, and the collection of such edges is $EM(x)$.\u0000A set $M$ of vertices of a graph $G$ is distance-edge-monitoring (DEM for short) set if every edge $e$ of $G$ is monitored by some vertex of $M$, that is, the set $P(M, e)$ is nonempty. The\u0000DEM number $operatorname{dem}(G)$ of a graph $G$ is defined as the smallest size of such a set in $G$.\u0000The vertices\u0000of $M$ represent distance probes in a network modeled by $G$; when the edge $e$ fails, the\u0000distance from $x$ to $y$ increases, and thus we are able to detect the failure.\u0000In this paper, we first give some bounds or exact values of line graphs of trees, grids, complete bipartite graphs, and\u0000obtain the exact values of DEM numbers for some graphs and their line graphs, including the friendship and wheel graphs.\u0000Next, for each $n, m>1$, we obtain that there exists a graph $G_{n,m}$ such that $operatorname{dem}(G_{n,m})=n$ and $operatorname{dem}(L(G_{n,m}))=4 or 2n+t$, for each integer $tgeq 0$. In the end, the DEM number for the line graph of a small world network (DURT) is given.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"53 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Joint optimization of the inventory routing problem considering the recycling of broken bikes in the bike-sharing system 考虑到共享单车系统中的破损单车回收问题,联合优化库存路由问题
RAIRO - Operations Research Pub Date : 2024-05-15 DOI: 10.1051/ro/2024109
Aigui Wu
{"title":"Joint optimization of the inventory routing problem considering the recycling of broken bikes in the bike-sharing system","authors":"Aigui Wu","doi":"10.1051/ro/2024109","DOIUrl":"https://doi.org/10.1051/ro/2024109","url":null,"abstract":"Bike-sharing system has become an indispensable element of sustainable urban transportation, effectively resolving the \"last mile\" transportation challenge for city dwellers. A major daily operational task in these systems is planning a fleet to rebalance the bikes over time, ensuring the optimal availability of bikes and docks to users. Recycling is also a daily work with the an increase in the number of broken bikes. However, rebalancing or recycling operation is always regarded as an independent tasks. They are separately studied in existing papers. Thus, this paper develops an operational strategy for recycling broken bikes during the rebalancing process, and studies the combination of the station inventory and vehicle routing problems. First, an inventory routing model is constructed with the aim of minimizing the total costs including procurement, expected user loss, inventory and transportation costs. Then, a two-stage iterative algorithm is developed with both exact and heuristic algorithms. We use real-world data from Capital Bikeshare to test our proposed model and approach, which shows the two-stage iterative algorithm is efficient and outperforms existing solutions in reducing total costs. Finally, the sensitivity analysis is performed on key parameters such as the vehicle’s capacity, unit penalty costs for customer dissatisfaction events, unit inventory holding costs and the observation period of rebalancing. It shows that enterprises can reduce the total cost by altering vehicle’s capacity, reducing the unit inventory holding costs or changing the observation period of rebalancing.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"74 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140973863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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