In this study, a hybrid undesirable network data envelopment analysis model is developed for assessing the efficiency of social care systems. Studies investigating the performance of social care activities have mostly focused on a single social care type. To date, no study has proposed an integrated framework for assessing social care performance. To address this gap in the literature, the developed model incorporates four divisions for a comprehensive performance measurement: disability care, child and youth care, women care, and elderly care. In the model, the government’s expenditure on social care is the initial input, and the efficiency of social care activities in the aforementioned four divisions is evaluated in the second stage. Social care facilities and social care workers serve as the nonradial input and radial input, respectively. Care recipients and those affected by violence serve as the desirable output and undesirable output, respectively, in the second stage. The empirical results have several practical implications for Taiwan’s social care system.
{"title":"Using the hybrid undesirable network data envelopment analysis model to evaluate the efficiency of Taiwan’s social care system","authors":"Chin-wei Huang","doi":"10.1051/ro/2024156","DOIUrl":"https://doi.org/10.1051/ro/2024156","url":null,"abstract":"In this study, a hybrid undesirable network data envelopment analysis model is developed for assessing the efficiency of social care systems. Studies investigating the performance of social care activities have mostly focused on a single social care type. To date, no study has proposed an integrated framework for assessing social care performance. To address this gap in the literature, the developed model incorporates four divisions for a comprehensive performance measurement: disability care, child and youth care, women care, and elderly care. In the model, the government’s expenditure on social care is the initial input, and the efficiency of social care activities in the aforementioned four divisions is evaluated in the second stage. Social care facilities and social care workers serve as the nonradial input and radial input, respectively. Care recipients and those affected by violence serve as the desirable output and undesirable output, respectively, in the second stage. The empirical results have several practical implications for Taiwan’s social care system.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"11 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141803180","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}
In this paper, we investigate the robust reinsurance contracts under Stackelberg game and market equilibrium. Each reinsurance contract contains two decision makers, one insurer and one reinsurer. The insurer is ambiguity-neutral and adopts a loss-dependent premium principle to collect premium. The reinsurer is ambiguity-averse and is a Bayesian learner. By using the stochastic dynamic programming method and the inverse method, the analytical expressions of the optimal risk allocation proportion and reinsurance price are derived for the two types of reinsurance contracts. We shows that the loss-dependent premium principle has the penalty-reward nature. Both the reinsurance price and demand decrease as the extrapolative intensity increases. Learning has important significance and always puts down the reinsurance price and puts up the reinsurance demand. On the contrary, the reinsurer's ambiguity aversion raises the reinsurance price and decreases the reinsurance demand. Finally, numerical analysis reveals that the reinsurance price is greater under the Stackelberg game than that under the market equilibrium.
{"title":"Reinsurance contracts under Stackelberg game and market equilibrium","authors":"Duni Hu, Guomin Yang, Hailong Wang","doi":"10.1051/ro/2024155","DOIUrl":"https://doi.org/10.1051/ro/2024155","url":null,"abstract":"In this paper, we investigate the robust reinsurance contracts under Stackelberg game and market equilibrium. Each reinsurance contract contains two decision makers, one insurer and one reinsurer. The insurer is ambiguity-neutral and adopts a loss-dependent premium principle to collect premium. The reinsurer is ambiguity-averse and is a Bayesian learner. By using the stochastic dynamic programming method and the inverse method, the analytical expressions of the optimal risk allocation proportion and reinsurance price are derived for the two types of reinsurance contracts. We shows that the loss-dependent premium principle has the penalty-reward nature. Both the reinsurance price and demand decrease as the extrapolative intensity increases. Learning has important significance and always puts down the reinsurance price and puts up the reinsurance demand. On the contrary, the reinsurer's ambiguity aversion raises the reinsurance price and decreases the reinsurance demand. Finally, numerical analysis reveals that the reinsurance price is greater under the Stackelberg game than that under the market equilibrium.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"28 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141802921","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}
Han Song, Yuxin Shu, Ying Dai, Lin Zhou, Haiyan Li
The proliferation of digital technologies has revolutionized various industries, prompting enterprises to prioritize investment in big data analytics. Despite the associated value, enterprises must carefully assess the cost proposition of such investment. This study models a supply chain with a manufacturer and a retailer, investigating big data investment decisions and strategies of manufacturer as leader across varying scenarios. The results show that: if the manufacturer focus only on the big data service level, it will choose not to outsource. In the case of non-outsourcing, the pre-production big data service level, the pre-sale big data service level and the retailer’s profit are higher, however, the manufacturer’s profit depends on fixed cost. Moreover, the manufacturer has three options: it chooses non-outsourcing if the profits of supply chain members are decreased, it chooses outsourcing without coordination mechanism if only considers maximizing own profit, it chooses outsourcing with coordination mechanism if considers the profits of other members. If outsourcing is considered, the manufacturer can decide its cost-sharing rate according to different situations. When consumers need products with high satisfaction, they will improve the big data service level. And, the increased price is also acceptable to consumers. When consumers pay more attention to low price, appropriately reducing the big data service level can also satisfy consumers. In addition, this paper provides some management inspirations for decision-making and operation of supply chain.
{"title":"Big data service outsourcing and cost-sharing choices for the manufacturer","authors":"Han Song, Yuxin Shu, Ying Dai, Lin Zhou, Haiyan Li","doi":"10.1051/ro/2024154","DOIUrl":"https://doi.org/10.1051/ro/2024154","url":null,"abstract":"The proliferation of digital technologies has revolutionized various industries, prompting enterprises to prioritize investment in big data analytics. Despite the associated value, enterprises must carefully assess the cost proposition of such investment. This study models a supply chain with a manufacturer and a retailer, investigating big data investment decisions and strategies of manufacturer as leader across varying scenarios. The results show that: if the manufacturer focus only on the big data service level, it will choose not to outsource. In the case of non-outsourcing, the pre-production big data service level, the pre-sale big data service level and the retailer’s profit are higher, however, the manufacturer’s profit depends on fixed cost. Moreover, the manufacturer has three options: it chooses non-outsourcing if the profits of supply chain members are decreased, it chooses outsourcing without coordination mechanism if only considers maximizing own profit, it chooses outsourcing with coordination mechanism if considers the profits of other members. If outsourcing is considered, the manufacturer can decide its cost-sharing rate according to different situations. When consumers need products with high satisfaction, they will improve the big data service level. And, the increased price is also acceptable to consumers. When consumers pay more attention to low price, appropriately reducing the big data service level can also satisfy consumers. In addition, this paper provides some management inspirations for decision-making and operation of supply chain.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"101 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141802314","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}
A factor of a graph is a spanning subgraph. Spectral sufficient conditions are provided via spectral radius and signless Laplacian spectral radius for graphs with (i) a matching of given size (particularly, $1$-factor) containing any given edge, and (ii) a star factor with a component isomorphic to stars of order two or three containing any given edge, respectively.
{"title":"Spectral sufficient conditions for graph factors containing any edge","authors":"Jin Cai, Bo Zhou","doi":"10.1051/ro/2024153","DOIUrl":"https://doi.org/10.1051/ro/2024153","url":null,"abstract":"A factor of a graph is a spanning subgraph. Spectral sufficient conditions are provided via spectral radius and signless Laplacian spectral radius for graphs with (i) a matching of given size (particularly, $1$-factor) containing any given edge, and (ii) a star factor with a component isomorphic to stars of order two or three containing any given edge, respectively.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"35 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141808551","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}
Clarifying responsibility for wastewater discharges and enhancing reasonable allocation of wastewater emission permits are critical for controlling wastewater discharge in the context global sustainable development plans. The traditional wastewater allocation approach has several drawbacks, such as sub-regional "free-riding," imbalanced regional development and demand, and unfair allocation mechanism. This study developed a model based on cooperative game theory to allocate responsibility for wastewater discharge in China's Tuojiang River Basin. In this model, the level of impact of a watershed sub-region on the water environment is determined, according to which the wastewater discharge responsibility is assigned. The stronger the impact of upstream sub-regions on downstream wastewater discharge, the greater the responsibility for wastewater discharge. Furthermore, by implementing the wastewater cooperation model, sub-regions can monitor and incentivize each other, through which wastewater discharges can be reduced by 16.38%, compared to the baseline mechanism and overall discharges can be reduced by 5007.99 tons. This study provides recommendations for appropriate management authorities to improve the allocation of wastewater discharge responsibility at the watershed scale.
{"title":"Incentive mechanism for allocating wastewater discharge responsibility based on cooperative game theory","authors":"Yue Li, Xudong Chen, Qiufeng Zhang, Yangxi Lv, Zixuan Zhang, Xue Feng","doi":"10.1051/ro/2024151","DOIUrl":"https://doi.org/10.1051/ro/2024151","url":null,"abstract":"Clarifying responsibility for wastewater discharges and enhancing reasonable allocation of wastewater emission permits are critical for controlling wastewater discharge in the context global sustainable development plans. The traditional wastewater allocation approach has several drawbacks, such as sub-regional \"free-riding,\" imbalanced regional development and demand, and unfair allocation mechanism. This study developed a model based on cooperative game theory to allocate responsibility for wastewater discharge in China's Tuojiang River Basin. In this model, the level of impact of a watershed sub-region on the water environment is determined, according to which the wastewater discharge responsibility is assigned. The stronger the impact of upstream sub-regions on downstream wastewater discharge, the greater the responsibility for wastewater discharge. Furthermore, by implementing the wastewater cooperation model, sub-regions can monitor and incentivize each other, through which wastewater discharges can be reduced by 16.38%, compared to the baseline mechanism and overall discharges can be reduced by 5007.99 tons. This study provides recommendations for appropriate management authorities to improve the allocation of wastewater discharge responsibility at the watershed scale.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"2 25","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141807473","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}
Service providers often provide chargeable extra waiting area value-added services (EWS) to enhance customers' waiting experiences, e.g., in VIP and business lounges at airports, train stations, luxury brand stores, etc., to improve profitability. The impact of EWS on customers' value perception is subject to their heterogeneous sensitivities and also depends on the reference effect due to EWS' observable status. This paper investigates the optimal level of EWS and price decisions for a service provider facing heterogeneous customers, namely the EWS-preferring (E-type) customers and ordinary (O-type) customers, considering the observable status (observable vs. unobservable) of EWS using pooled or dedicated capacities in operations through M/M/1 queue models. The optimal price and level are solved and the optimal profit is calculated under each scenario. It is found that customers' heterogeneous sensitivities play an important role in the price and intensity decisions. Offering observable EWS to leverage the reference effect in customers' value perception can lead to a higher profit. Furthermore, using pooled capacity in operations with EWS is more profitable when service costs are higher. These results offer significant managerial implications and provide practical guidelines for service providers regarding the intensity of EWS, service price, and whether EWS should be observable to customers through pooled or dedicated capacities.
{"title":"The optimal decision of service provider considering extra waiting area value-added services---pooled or dedicated?","authors":"Wentao Zhan, Jida Liu, Xuchuan Yuan, Xiaotong Huang, Minghui Jiang","doi":"10.1051/ro/2024152","DOIUrl":"https://doi.org/10.1051/ro/2024152","url":null,"abstract":"Service providers often provide chargeable extra waiting area value-added services (EWS) to enhance customers' waiting experiences, e.g., in VIP and business lounges at airports, train stations, luxury brand stores, etc., to improve profitability. The impact of EWS on customers' value perception is subject to their heterogeneous sensitivities and also depends on the reference effect due to EWS' observable status. This paper investigates the optimal level of EWS and price decisions for a service provider facing heterogeneous customers, namely the EWS-preferring (E-type) customers and ordinary (O-type) customers, considering the observable status (observable vs. unobservable) of EWS using pooled or dedicated capacities in operations through M/M/1 queue models. The optimal price and level are solved and the optimal profit is calculated under each scenario. It is found that customers' heterogeneous sensitivities play an important role in the price and intensity decisions. Offering observable EWS to leverage the reference effect in customers' value perception can lead to a higher profit. Furthermore, using pooled capacity in operations with EWS is more profitable when service costs are higher. These results offer significant managerial implications and provide practical guidelines for service providers regarding the intensity of EWS, service price, and whether EWS should be observable to customers through pooled or dedicated capacities.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"53 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141806824","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}
With the diversity of shopping styles, reference prices have become a consideration in consumers’ purchasing decisions. It is critical to understand how manufacturers and retailers make optimal decisions based on consumer behavior. To this end, we develop a manufacturer-led Stackelberg (M-Stackelberg) game model to investigate the impact of consumer proportion, reference price effect (RPE), and the channel preference coefficient on the decision of the remanufacturing supply chain (RSC) in dual-channel structures. Through comparing different game scenario models, we find that when the reference price coefficient is relatively small, the optimal decisions for the manufacturer and the retailer are the same regardless of whether the RPE is considered. The manufacturer and E-tailer always benefit from RPE, while the traditional retailer (T-retailer) is uncertain. The numerical analysis revealed that the profits of supply chain members are inversely proportional to the proportion of consumers. The smaller the proportion of primary consumers, the more favorable the supply chain. In particular, the higher the channel preference coefficient, the higher the profits of the manufacturer and E-tailer, while the lower the benefit of the T-retailer. Further, in the dynamic game, the total supply chain profit is highest when the T-retailer prices earlier than the E-tailer.
随着购物方式的多样化，参考价格已成为消费者购买决策的一个考虑因素。了解制造商和零售商如何根据消费者行为做出最优决策至关重要。为此，我们建立了一个制造商主导的斯塔克尔伯格（M-Stackelberg）博弈模型，研究消费者比例、参考价格效应（RPE）和渠道偏好系数对双渠道结构中再制造供应链（RSC）决策的影响。通过比较不同的博弈情景模型，我们发现当参考价格系数相对较小时，无论是否考虑参考价格效应，制造商和零售商的最优决策都是相同的。制造商和网络零售商总是能从 RPE 中获益，而传统零售商（T-零售商）则不确定。数值分析表明，供应链成员的利润与消费者比例成反比。初级消费者比例越小，供应链越有利。其中，渠道偏好系数越高，制造商和网络零售商的利润越高，而 T 型零售商的收益越低。此外，在动态博弈中，当 T 型零售商比 E 型零售商更早定价时，供应链总利润最高。
{"title":"Models for dual-channel remanufacturing supply chain with reference price effect under static and dynamic games","authors":"Lili Dai, T. Shu, Yanyan Zheng, Shouyang Wang","doi":"10.1051/ro/2024148","DOIUrl":"https://doi.org/10.1051/ro/2024148","url":null,"abstract":"With the diversity of shopping styles, reference prices have become a consideration in consumers’ purchasing decisions. It is critical to understand how manufacturers and retailers make optimal decisions based on consumer behavior. To this end, we develop a manufacturer-led Stackelberg (M-Stackelberg) game model to investigate the impact of consumer proportion, reference price effect (RPE), and the channel preference coefficient on the decision of the remanufacturing supply chain (RSC) in dual-channel structures. Through comparing different game scenario models, we find that when the reference price coefficient is relatively small, the optimal decisions for the manufacturer and the retailer are the same regardless of whether the RPE is considered. The manufacturer and E-tailer always benefit from RPE, while the traditional retailer (T-retailer) is uncertain. The numerical analysis revealed that the profits of supply chain members are inversely proportional to the proportion of consumers. The smaller the proportion of primary consumers, the more favorable the supply chain. In particular, the higher the channel preference coefficient, the higher the profits of the manufacturer and E-tailer, while the lower the benefit of the T-retailer. Further, in the dynamic game, the total supply chain profit is highest when the T-retailer prices earlier than the E-tailer.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"55 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141813306","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}
The integration of online trading has emerged as a crucial driver of operational efficiency in the reverse supply chain. This study expands the recycling model to include three distinct scenarios: basic-offline recycling (BR), single-platform recycling (SR), and dual-platform recycling (DR). The research delves into the implications of varying platform numbers, profit-sharing contracts, consumer recycling preferences, and recycling price adjustment speeds on supply chain stability within a multi-period decision-making framework. Findings reveal that the SR model is not always yield higher profits for remanufacturers through lower revenue allocation proportions to platforms, in stark contrast to the DR model. Furthermore, rapid decision adjustments do not consistently enhance the stability of the recycling system across multiple decision cycles. Remanufacturers' expansion strategies are significantly impacted by the costs associated with acquiring e-waste from individual recyclers. Importantly, an excess of platforms does not always result in favorable outcomes. Conversely, the SR model proves superior to the DR model in practical contexts that may arise. These insights offer valuable guidance to remanufacturers seeking to develop viable expansion strategies that foster mutually beneficial relationships among individual recyclers, remanufacturers, and platforms.
在线交易的整合已成为提高逆向供应链运营效率的重要驱动力。本研究将回收模型扩展到三种不同的情景：基本离线回收（BR）、单平台回收（SR）和双平台回收（DR）。研究在多期决策框架内深入探讨了不同平台数量、利润分享合同、消费者回收偏好和回收价格调整速度对供应链稳定性的影响。研究结果表明，与 DR 模式形成鲜明对比的是，SR 模式并不总能通过降低平台的收入分配比例为再制造商带来更高的利润。此外，在多个决策周期中，快速决策调整并不能持续增强回收系统的稳定性。再制造商的扩张战略受到从单个回收商处收购电子废弃物的相关成本的显著影响。重要的是，过多的平台并不总能带来有利的结果。相反，在可能出现的实际情况中，SR 模式被证明优于 DR 模式。这些见解为再制造商提供了宝贵的指导，帮助他们制定可行的扩张战略，促进个体回收商、再制造商和平台之间的互利关系。
{"title":"Expand or not? Trade-offs of the remanufacturer on recycling channels\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 ","authors":"Xin Qi, Tao Zhang","doi":"10.1051/ro/2024150","DOIUrl":"https://doi.org/10.1051/ro/2024150","url":null,"abstract":"The integration of online trading has emerged as a crucial driver of operational efficiency in the reverse supply chain. This study expands the recycling model to include three distinct scenarios: basic-offline recycling (BR), single-platform recycling (SR), and dual-platform recycling (DR). The research delves into the implications of varying platform numbers, profit-sharing contracts, consumer recycling preferences, and recycling price adjustment speeds on supply chain stability within a multi-period decision-making framework. Findings reveal that the SR model is not always yield higher profits for remanufacturers through lower revenue allocation proportions to platforms, in stark contrast to the DR model. Furthermore, rapid decision adjustments do not consistently enhance the stability of the recycling system across multiple decision cycles. Remanufacturers' expansion strategies are significantly impacted by the costs associated with acquiring e-waste from individual recyclers. Importantly, an excess of platforms does not always result in favorable outcomes. Conversely, the SR model proves superior to the DR model in practical contexts that may arise. These insights offer valuable guidance to remanufacturers seeking to develop viable expansion strategies that foster mutually beneficial relationships among individual recyclers, remanufacturers, and platforms.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"5 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141810167","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}
Profit contributed by take-away service has become an increasingly essential element of the restaurant operating revenue. Since take-away service usually relies on the third-party platform and there are many differences between the cost of take-away service and that of sit-down service. We focus on the restaurant which provides both sit-down service and take-away service, the service system is modeled as a two-stage tandem queueing system. We study the restaurant’s optimal capacity level for each stage. Besides, as there exist price difference between the two services, inequity aversion is also investigaed in our model. We study symmetrical and asymmetrical inequity aversion according to consumers’elasity of demand. Through analysis of theoretical model, we get some conclusions: first, the optimal service capacity consists of two parts, base capacity and safety capacity. And the loss resulted from waiting time lag is equal to the waste of resources caused by fluctuations in arrival rate. Second, when customers really long for the restaurant, even if high price will lead to severe inequity aversion, restaurant can always earn more by raising the price in service channel with high revenue. While when customers are indifferent of the restaurant and the others, the price gap is meant to result in revenue decrease. Third, reduction in customers’ susceptibility can help to enhance operation profit in general. Market environment plays a decisive role in choosing the optimal service level.
{"title":"Take-away and sit-down service operations under inequity aversion","authors":"Sijia Zeng, Wei Hu, Xiaochen Sun","doi":"10.1051/ro/2024149","DOIUrl":"https://doi.org/10.1051/ro/2024149","url":null,"abstract":"Profit contributed by take-away service has become an increasingly essential element of the restaurant operating revenue. Since take-away service usually relies on the third-party platform and there are many differences between the cost of take-away service and that of sit-down service. We focus on the restaurant which provides both sit-down service and take-away service, the service system is modeled as a two-stage tandem queueing system. We study the restaurant’s optimal capacity level for each stage. Besides, as there exist price difference between the two services, inequity aversion is also investigaed in our model. We study symmetrical and asymmetrical inequity aversion according to consumers’elasity of demand. Through analysis of theoretical model, we get some conclusions: first, the optimal service capacity consists of two parts, base capacity and safety capacity. And the loss resulted from waiting time lag is equal to the waste of resources caused by fluctuations in arrival rate. Second, when customers really long for the restaurant, even if high price will lead to severe inequity aversion, restaurant can always earn more by raising the price in service channel with high revenue. While when customers are indifferent of the restaurant and the others, the price gap is meant to result in revenue decrease. Third, reduction in customers’ susceptibility can help to enhance operation profit in general. Market environment plays a decisive role in choosing the optimal service level.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"21 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141813745","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}
In this paper, we have extended SEIR model of COVID- 19. The model incorporates two vital aspects in the form of vaccine compartment and constant time delay. The vaccination and time delay provide the information about immune protection and actual existence of the infection among the individuals, respectively. The model is analysed numerically and numerical simulation are executed for three different initial histories and constant time delays which affirm the biological relevance of the system. The analysis includes disease-free equilibrium (DFE), endemic equilibrium, and the basic reproduction number. The stability analysis is performed which reveal the asymptotic stability of the DFE when the basic reproduction number R0 < 1. The study addresses the boundedness and positivity of the solution as the time delay approaches zero. In addition, sensitivity analysis and contour plots for R0 with different parameters offer deeper insights into the model. The impact of vaccination and vaccine inefficacy on the model dynamics is explored.
{"title":"A delay differential equation model on Covid-19 with vaccination strategy\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000\u0000 ","authors":"Gaurang Sharma, Amit Sharma","doi":"10.1051/ro/2024147","DOIUrl":"https://doi.org/10.1051/ro/2024147","url":null,"abstract":"In this paper, we have extended SEIR model of COVID- 19. The model incorporates two vital aspects in the form of vaccine compartment and constant time delay. The vaccination and time delay provide the information about immune protection and actual existence of the infection among the individuals, respectively. The model is analysed numerically and numerical simulation are executed for three different initial histories and constant time delays which affirm the biological relevance of the system. The analysis includes disease-free equilibrium (DFE), endemic equilibrium, and the basic reproduction number. The stability analysis is performed which reveal the asymptotic stability of the DFE when the basic reproduction number R0 < 1. The study addresses the boundedness and positivity of the solution as the time delay approaches zero. In addition, sensitivity analysis and contour plots for R0 with different parameters offer deeper insights into the model. The impact of vaccination and vaccine inefficacy on the model dynamics is explored.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"121 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141820909","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}
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