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Single-machine scheduling with fixed energy recharging times to minimize the number of late jobs and the number of just-in-time jobs: A parameterized complexity analysis
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-02-03 DOI: 10.1016/j.ejor.2025.01.007
Renjie Yu, Daniel Oron
We study single-machine scheduling problems where processing each job requires both processing time and rechargeable energy. Subject to a predefined energy capacity, energy can be recharged after each job during a fixed recharging period. Our focus is on two due date-related scheduling criteria: minimizing the number of late jobs and maximizing the weighted number of jobs completed exactly at their due dates. This study aims to analyze the parameterized tractability of the two problems and develop fixed-parameter algorithms with respect to three natural parameters: the number of different due dates vd, the number of different processing times vp, and the number of different energy consumptions ve. Following the proofs of NP-hardness across several contexts, we demonstrate that both problems remain intractable when parameterized by vd and vp. To complement our results, we show that both problems become fixed-parameter tractable (FPT) when parameterized by ve and vd, and are solvable in polynomial time when both ve and vp are constant.
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引用次数: 0
Optimizing omnichannel assortments and inventory provisions under the multichannel attraction model
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-02-03 DOI: 10.1016/j.ejor.2025.01.035
Andrey Vasilyev, Sebastian Maier, Ralf W. Seifert
Assortment optimization presents a complex challenge for retailers, as it depends on numerous decision factors. Changes in assortment can result in demand redistribution with multi-layered consequences. This complexity is even more pronounced for omnichannel retailers, which have to manage assortments across multiple sales channels. Choice modeling has emerged as an effective method in assortment optimization, capturing customer shopping behavior and shifts in demand as assortments change. In this paper, we utilize the multichannel attraction model – a discrete choice model specifically designed for omnichannel environments – and generalize it for the case of a retailer managing both an online store and a network of physical stores. We integrate assortment decisions with optimal inventory decisions, assuming stochastic demand. Our model shows that overlooking the demand variability can result in suboptimal assortment decisions due to the demand pooling effect. We derive complexity results for the assortment optimization problem, which we formulate as a mixed-integer second-order cone program. We then develop two heuristic algorithms based on different relaxations of the formulated optimization problem. Furthermore, we conduct an extensive numerical analysis to provide managerial insights. We find that an increasing coefficient of variation of demand has a dual effect on optimal assortment sizes, initially causing a decrease in online assortment size due to rising costs, followed by an increase in online assortment size because of the demand pooling effect. Finally, we evaluate the potential benefits of omnichannel assortment optimization compared to assortment optimization in siloed channels.
{"title":"Optimizing omnichannel assortments and inventory provisions under the multichannel attraction model","authors":"Andrey Vasilyev, Sebastian Maier, Ralf W. Seifert","doi":"10.1016/j.ejor.2025.01.035","DOIUrl":"https://doi.org/10.1016/j.ejor.2025.01.035","url":null,"abstract":"Assortment optimization presents a complex challenge for retailers, as it depends on numerous decision factors. Changes in assortment can result in demand redistribution with multi-layered consequences. This complexity is even more pronounced for omnichannel retailers, which have to manage assortments across multiple sales channels. Choice modeling has emerged as an effective method in assortment optimization, capturing customer shopping behavior and shifts in demand as assortments change. In this paper, we utilize the multichannel attraction model – a discrete choice model specifically designed for omnichannel environments – and generalize it for the case of a retailer managing both an online store and a network of physical stores. We integrate assortment decisions with optimal inventory decisions, assuming stochastic demand. Our model shows that overlooking the demand variability can result in suboptimal assortment decisions due to the demand pooling effect. We derive complexity results for the assortment optimization problem, which we formulate as a mixed-integer second-order cone program. We then develop two heuristic algorithms based on different relaxations of the formulated optimization problem. Furthermore, we conduct an extensive numerical analysis to provide managerial insights. We find that an increasing coefficient of variation of demand has a dual effect on optimal assortment sizes, initially causing a decrease in online assortment size due to rising costs, followed by an increase in online assortment size because of the demand pooling effect. Finally, we evaluate the potential benefits of omnichannel assortment optimization compared to assortment optimization in siloed channels.","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":"5 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143477828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Goodness-of-fit in production models: A Bayesian perspective
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-31 DOI: 10.1016/j.ejor.2025.01.030
Mike Tsionas, Valentin Zelenyuk, Xibin Zhang
We propose a general approach for modeling production technologies, allowing for modeling both inefficiency and noise that are specific for each input and each output. The approach is based on amalgamating ideas from nonparametric activity analysis models for production and consumption theory with stochastic frontier models. We do this by effectively re-interpreting the activity analysis models as simultaneous equations models in Bayesian compression and artificial neural networks framework. We make minimal assumptions about noise in the data and we allow for flexible approximations to input- and output-specific slacks. We use compression to solve the problem of an exceeding number of parameters in general production technologies and also incorporate environmental variables in the estimation. We also present Monte Carlo simulation results and an empirical illustration of this approach for US banking data.
{"title":"Goodness-of-fit in production models: A Bayesian perspective","authors":"Mike Tsionas, Valentin Zelenyuk, Xibin Zhang","doi":"10.1016/j.ejor.2025.01.030","DOIUrl":"https://doi.org/10.1016/j.ejor.2025.01.030","url":null,"abstract":"We propose a general approach for modeling production technologies, allowing for modeling both inefficiency and noise that are specific for each input and each output. The approach is based on amalgamating ideas from nonparametric activity analysis models for production and consumption theory with stochastic frontier models. We do this by effectively re-interpreting the activity analysis models as simultaneous equations models in Bayesian compression and artificial neural networks framework. We make minimal assumptions about noise in the data and we allow for flexible approximations to input- and output-specific slacks. We use compression to solve the problem of an exceeding number of parameters in general production technologies and also incorporate environmental variables in the estimation. We also present Monte Carlo simulation results and an empirical illustration of this approach for US banking data.","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":"9 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143477831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Deep Controlled Learning for Inventory Control
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-31 DOI: 10.1016/j.ejor.2025.01.026
Tarkan Temizöz, Christina Imdahl, Remco Dijkman, Douniel Lamghari-Idrissi, Willem van Jaarsveld
The application of Deep Reinforcement Learning (DRL) to inventory management is an emerging field. However, traditional DRL algorithms, originally developed for diverse domains such as game-playing and robotics, may not be well-suited for the specific challenges posed by inventory management. Consequently, these algorithms often fail to outperform established heuristics; for instance, no existing DRL approach consistently surpasses the capped base-stock policy in lost sales inventory control. This highlights a critical gap in the practical application of DRL to inventory management: the highly stochastic nature of inventory problems requires tailored solutions. In response, we propose Deep Controlled Learning (DCL), a new DRL algorithm designed for highly stochastic problems. DCL is based on approximate policy iteration and incorporates an efficient simulation mechanism, combining Sequential Halving with Common Random Numbers. Our numerical studies demonstrate that DCL consistently outperforms state-of-the-art heuristics and DRL algorithms across various inventory settings, including lost sales, perishable inventory systems, and inventory systems with random lead times. DCL achieves lower average costs in all test cases while maintaining an optimality gap of no more than 0.2%. Remarkably, this performance is achieved using the same hyperparameter set across all experiments, underscoring the robustness and generalizability of our approach. These findings contribute to the ongoing exploration of tailored DRL algorithms for inventory management, providing a foundation for further research and practical application in this area.
{"title":"Deep Controlled Learning for Inventory Control","authors":"Tarkan Temizöz, Christina Imdahl, Remco Dijkman, Douniel Lamghari-Idrissi, Willem van Jaarsveld","doi":"10.1016/j.ejor.2025.01.026","DOIUrl":"https://doi.org/10.1016/j.ejor.2025.01.026","url":null,"abstract":"The application of Deep Reinforcement Learning (DRL) to inventory management is an emerging field. However, traditional DRL algorithms, originally developed for diverse domains such as game-playing and robotics, may not be well-suited for the specific challenges posed by inventory management. Consequently, these algorithms often fail to outperform established heuristics; for instance, no existing DRL approach consistently surpasses the capped base-stock policy in lost sales inventory control. This highlights a critical gap in the practical application of DRL to inventory management: the highly stochastic nature of inventory problems requires tailored solutions. In response, we propose Deep Controlled Learning (DCL), a new DRL algorithm designed for highly stochastic problems. DCL is based on approximate policy iteration and incorporates an efficient simulation mechanism, combining Sequential Halving with Common Random Numbers. Our numerical studies demonstrate that DCL consistently outperforms state-of-the-art heuristics and DRL algorithms across various inventory settings, including lost sales, perishable inventory systems, and inventory systems with random lead times. DCL achieves lower average costs in all test cases while maintaining an optimality gap of no more than 0.2%. Remarkably, this performance is achieved using the same hyperparameter set across all experiments, underscoring the robustness and generalizability of our approach. These findings contribute to the ongoing exploration of tailored DRL algorithms for inventory management, providing a foundation for further research and practical application in this area.","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":"75 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143385311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sequential product launches with post-sale updates
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-30 DOI: 10.1016/j.ejor.2025.01.018
Monire Jalili, Michael S. Pangburn, Euthemia Stavrulaki, Shubin Xu
As technology evolves, a seller may offer sequential releases of its product over time, with new versions offering superior performance. Beyond offering new product releases over time, sellers now increasingly have the option of offering post-sale software updates, thereby potentially extending product longevity. The potential to change product life cycles via software updates is of strategic importance, particularly since past and future product releases are interrelated. Considering stochastic technology evolution and strategic consumers, we study the strategy of augmenting paid product releases with free product updates. By contrasting this strategy against two benchmark product-launch policies without free updates, we show that offering free updates can generate nontrivial profit gains and optimally lengthen the seller’s new-product introduction cycles. We explore the sensitivity of the seller’s optimal release decisions and profit to key drivers, including costs and technology uncertainty. We also investigate the impact of consumer heterogeneity, distinct time-discount rates between the seller and consumers, and allowing multiple updates per product release. Our results show that while free updates ostensibly appear to favor consumers and do deliver utility to customers, they also are an effective mechanism for a seller to increase profits.
{"title":"Sequential product launches with post-sale updates","authors":"Monire Jalili, Michael S. Pangburn, Euthemia Stavrulaki, Shubin Xu","doi":"10.1016/j.ejor.2025.01.018","DOIUrl":"https://doi.org/10.1016/j.ejor.2025.01.018","url":null,"abstract":"As technology evolves, a seller may offer sequential releases of its product over time, with new versions offering superior performance. Beyond offering new product releases over time, sellers now increasingly have the option of offering post-sale software updates, thereby potentially extending product longevity. The potential to change product life cycles via software updates is of strategic importance, particularly since past and future product releases are interrelated. Considering stochastic technology evolution and strategic consumers, we study the strategy of augmenting paid product releases with free product updates. By contrasting this strategy against two benchmark product-launch policies without free updates, we show that offering free updates can generate nontrivial profit gains and optimally lengthen the seller’s new-product introduction cycles. We explore the sensitivity of the seller’s optimal release decisions and profit to key drivers, including costs and technology uncertainty. We also investigate the impact of consumer heterogeneity, distinct time-discount rates between the seller and consumers, and allowing multiple updates per product release. Our results show that while free updates ostensibly appear to favor consumers and do deliver utility to customers, they also are an effective mechanism for a seller to increase profits.","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":"3 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143385313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A branch-and-price algorithm for fast and equitable last-mile relief aid distribution
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-30 DOI: 10.1016/j.ejor.2025.01.032
Mahdi Mostajabdaveh, F. Sibel Salman, Walter J. Gutjahr
The distribution of relief supplies to shelters is a critical aspect of post-disaster humanitarian logistics. In major disasters, prepositioned supplies often fall short of meeting all demands. We address the problem of planning vehicle routes from a distribution center to shelters while allocating limited relief supplies. To balance efficiency and equity, we formulate a bi-objective problem: minimizing a Gini-index-based measure of inequity in unsatisfied demand for fair distribution and minimizing total travel time for timely delivery. We propose a Mixed Integer Programming (MIP) model and use the ϵ-constraint method to handle the bi-objective nature. By deriving mathematical properties of the optimal solution, we introduce valid inequalities and design an algorithm for optimal delivery allocations given feasible vehicle routes. A branch-and-price (B&P) algorithm is developed to solve the problem efficiently. Computational tests on realistic datasets from a past earthquake in Van, Turkey, and predicted data for Istanbul’s Kartal region show that the B&P algorithm significantly outperforms commercial MIP solvers.Our bi-objective approach reduces aid distribution inequity by 34% without compromising efficiency. Results indicate that when time constraints are very loose or tight, lexicographic optimization prioritizing demand coverage over fairness is effective. For moderately restrictive time constraints, a balanced approach is essential to avoid inequitable outcomes.
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引用次数: 0
Monitoring bank risk around the world using unsupervised learning
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-28 DOI: 10.1016/j.ejor.2025.01.036
Mathieu Mercadier, Amine Tarazi, Paul Armand, Jean-Pierre Lardy
This paper provides a transparent and dynamic decision support tool that ranks clusters of listed banks worldwide by riskiness. It is designed to be flexible in updating and editing the values and quantities of banks, indicators, and clusters. For constructing this tool, a large set of stand-alone and systemic risk indicators are computed and reduced to fewer representative factors. These factors are set as features for an adjusted version of a nested k-means algorithm that handles missing data. This algorithm gathers banks per clusters of riskiness and ranks them. The results of the individual banks' multidimensional clustering are also aggregable per country and region, enabling the identification of areas of fragility. Empirically, we rank five clusters of 256 listed banks and compute 72 indicators, which are reduced to 12 components based on 10 main factors, over the 2004–2024 period. The findings emphasize the importance of giving special consideration to the ambiguous impact of banks' size on systemic risk measures.
{"title":"Monitoring bank risk around the world using unsupervised learning","authors":"Mathieu Mercadier, Amine Tarazi, Paul Armand, Jean-Pierre Lardy","doi":"10.1016/j.ejor.2025.01.036","DOIUrl":"https://doi.org/10.1016/j.ejor.2025.01.036","url":null,"abstract":"This paper provides a transparent and dynamic decision support tool that ranks clusters of listed banks worldwide by riskiness. It is designed to be flexible in updating and editing the values and quantities of banks, indicators, and clusters. For constructing this tool, a large set of stand-alone and systemic risk indicators are computed and reduced to fewer representative factors. These factors are set as features for an adjusted version of a nested k-means algorithm that handles missing data. This algorithm gathers banks per clusters of riskiness and ranks them. The results of the individual banks' multidimensional clustering are also aggregable per country and region, enabling the identification of areas of fragility. Empirically, we rank five clusters of 256 listed banks and compute 72 indicators, which are reduced to 12 components based on 10 main factors, over the 2004–2024 period. The findings emphasize the importance of giving special consideration to the ambiguous impact of banks' size on systemic risk measures.","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":"14 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077784","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic model for physician staffing and scheduling in emergency departments with multiple treatment stages
IF 6.4 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-26 DOI: 10.1016/j.ejor.2025.01.027
Janaina F. Marchesi, Silvio Hamacher, Igor Tona Peres
We propose a new solution for the Emergency Department (ED) staffing and scheduling problem, considering uncertainty in patient arrival patterns, multiple treatment stages, and resource capacity. A two-stage stochastic mathematical programming model was developed. We employed a Sample Average Approximation (SAA) method to generate scenarios and a discrete event simulation to evaluate the results. The model was applied in a large hospital, with 72,988 medical encounters and 85 physicians in a ten-month period. Compared to the hospital’s actual scheduling, we obtained an overall average waiting time reduction from 54.6 (54.0–55.1) to 16.8 (16.7–17.0) minutes and an average Length of Stay reduction from 102.1 (101.7–102.4) to 64.3 (64.2–64.5) minutes. Therefore, this study offers a stochastic model that effectively addresses uncertainties in EDs, aligning physician schedules with patient arrivals and potentially improving the quality of service by reducing waiting times.
{"title":"Stochastic model for physician staffing and scheduling in emergency departments with multiple treatment stages","authors":"Janaina F. Marchesi, Silvio Hamacher, Igor Tona Peres","doi":"10.1016/j.ejor.2025.01.027","DOIUrl":"https://doi.org/10.1016/j.ejor.2025.01.027","url":null,"abstract":"We propose a new solution for the Emergency Department (ED) staffing and scheduling problem, considering uncertainty in patient arrival patterns, multiple treatment stages, and resource capacity. A two-stage stochastic mathematical programming model was developed. We employed a Sample Average Approximation (SAA) method to generate scenarios and a discrete event simulation to evaluate the results. The model was applied in a large hospital, with 72,988 medical encounters and 85 physicians in a ten-month period. Compared to the hospital’s actual scheduling, we obtained an overall average waiting time reduction from 54.6 (54.0–55.1) to 16.8 (16.7–17.0) minutes and an average Length of Stay reduction from 102.1 (101.7–102.4) to 64.3 (64.2–64.5) minutes. Therefore, this study offers a stochastic model that effectively addresses uncertainties in EDs, aligning physician schedules with patient arrivals and potentially improving the quality of service by reducing waiting times.","PeriodicalId":55161,"journal":{"name":"European Journal of Operational Research","volume":"61 1","pages":""},"PeriodicalIF":6.4,"publicationDate":"2025-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143077785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
From collaborative filtering to deep learning: Advancing recommender systems with longitudinal data in the financial services industry
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-25 DOI: 10.1016/j.ejor.2025.01.022
Stephanie Beyer Díaz, Kristof Coussement, Arno De Caigny
Recommender systems (RS) are highly relevant for multiple domains, allowing to construct personalized suggestions for consumers. Previous studies have strongly focused on collaborative filtering approaches, but the inclusion of longitudinal data (LD) has received limited attention. To address this gap, we investigate the impact of incorporating LD for recommendations, comparing traditional collaborative filtering approaches, multi-label classifier (MLC) algorithms, and a deep learning model (DL) in the form of gated recurrent units (GRU). Additional analysis for the best performing model is provided through SHapley Additive exPlanations (SHAP), to uncover relations between the different recommended products and features. Thus, this article contributes to operational research literature by (1) comparing several MLC techniques and RS, including state-of-the-art DL models in a real-life scenario, (2) the comparison of various featurization techniques to assess the impact of incorporating LD on MLC performance, (3) the evaluation of LD as sequential input through the use of DL models, (4) offering interpretable model insights to improve the understanding of RS with LD. The results uncover that DL models are capable of extracting information from longitudinal features for overall higher and statistically significant performance. Further, SHAP values reveal that LD has the higher impact on model output and managerial relevant temporal patterns emerge across product categories.
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引用次数: 0
Trade-off between utility and fairness in two-agent single-machine scheduling
IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE Pub Date : 2025-01-25 DOI: 10.1016/j.ejor.2025.01.025
Alessandro Agnetis , Mario Benini , Gaia Nicosia , Andrea Pacifici
We consider the problem arising when two agents, each owning a set of jobs, compete to schedule their jobs on a common processing resource. Each schedule implies a certain utility for each agent and an overall system utility. We are interested in solutions that incorporate some criterion of fairness for the agents and, at the same time, are satisfactory from the viewpoint of system utility. More precisely, we investigate the trade-off between fairness and system utility when both agents want to minimize the total completion time of their respective jobs. We analyze the structure of the set of such trade-off solutions, and propose an exact algorithm for their computation, based on the Lagrangian relaxation of a MILP formulation of the problem. A large set of computational experiments has been carried out to show the viability of the approach. Moreover, the results show that in most cases a solution having a high degree of fairness can be obtained by sacrificing a very limited amount of system utility.
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引用次数: 0
期刊
European Journal of Operational Research
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