Hongwei Jiao, Wenjie Wang, Li Ge, P. Shen, Y. Shang
In this paper, we consider the min-max linear fractional programming problem (MLFP) which is NP-hard. We first introduce some auxiliary variables to derive an equivalent problem of the problem (MLFP). An outer space branch-and-bound algorithm is then designed by integrating some basic operations such as the linear relaxation method and branching rule. The global convergence of the proposed algorithm is proved by means of the subsequent solutions of a series of linear relaxation programming problems, and the computational complexity of the proposed algorithm is estimated based on the branching rule. Finally, numerical experimental results demonstrate the proposed algorithm can be used to efficiently compute the globally optimal solutions of test examples.
{"title":"Efficient algorithm for globally computing the min-max linear fractional programming problem","authors":"Hongwei Jiao, Wenjie Wang, Li Ge, P. Shen, Y. Shang","doi":"10.1051/ro/2023075","DOIUrl":"https://doi.org/10.1051/ro/2023075","url":null,"abstract":"In this paper, we consider the min-max linear fractional programming problem (MLFP) which is NP-hard. We first introduce some auxiliary variables to derive an equivalent problem of the problem (MLFP). An outer space branch-and-bound algorithm is then designed by integrating some basic operations such as the linear relaxation method and branching rule. The global convergence of the proposed algorithm is proved by means of the subsequent solutions of a series of linear relaxation programming problems, and the computational complexity of the proposed algorithm is estimated based on the branching rule. Finally, numerical experimental results demonstrate the proposed algorithm can be used to efficiently compute the globally optimal solutions of test examples.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82816369","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}
Customers are either eager or obliged to switch from a physical consultation firm to an online consultation platform. Considering customers' switching behavior and competition effect on bilateral users, the paper developed a three-echelon Stackelberg game framework where two consultation companies decide bilateral "pricing" (the service price and the wage), and the servicer decides service investment. In four scenarios combining two salary strategies (Employment or Sharing strategy) and two game sequences (firm as leader or follower), stakeholders' optimal decision-making and revenue were proved. We then theoretically analyzed the influence of some parameters on the equilibrium status and the gap between them and numerically simulated the joint effect of switching rate and parameters on the equilibrium revenue of stakeholders. It is deduced that in the consultation service market: (a) there is equilibrium status in all four scenarios when the switching rate, the servicer's sensitivity to current revenue, and the service cost coefficient on the firm satisfy certain conditions; (b) the servicer's potential market and the service investment cost coefficients negatively affect the optimal fixed wage set by the two companies and the servicer's revenue; (c) two consultation companies can achieve greater revenue when both adopt Sharing strategy; (d) servicer with higher perceived service cost are incented to devote more to servicing when both employ Employment strategy.
{"title":"Bilateral \"pricing\" for consultation companies' competition considering customers' switching behavior","authors":"Junchang Li, Jiantong Zhang, Hongzhen Song","doi":"10.1051/ro/2023076","DOIUrl":"https://doi.org/10.1051/ro/2023076","url":null,"abstract":"Customers are either eager or obliged to switch from a physical consultation firm to an online consultation platform. Considering customers' switching behavior and competition effect on bilateral users, the paper developed a three-echelon Stackelberg game framework where two consultation companies decide bilateral \"pricing\" (the service price and the wage), and the servicer decides service investment. In four scenarios combining two salary strategies (Employment or Sharing strategy) and two game sequences (firm as leader or follower), stakeholders' optimal decision-making and revenue were proved. We then theoretically analyzed the influence of some parameters on the equilibrium status and the gap between them and numerically simulated the joint effect of switching rate and parameters on the equilibrium revenue of stakeholders. It is deduced that in the consultation service market: (a) there is equilibrium status in all four scenarios when the switching rate, the servicer's sensitivity to current revenue, and the service cost coefficient on the firm satisfy certain conditions; (b) the servicer's potential market and the service investment cost coefficients negatively affect the optimal fixed wage set by the two companies and the servicer's revenue; (c) two consultation companies can achieve greater revenue when both adopt Sharing strategy; (d) servicer with higher perceived service cost are incented to devote more to servicing when both employ Employment strategy.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91207160","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}
B. Senthilkumar, M. Chellali, H. N. Kumar, Y. B. Venkatakrishnan
A vertex u of a graph G = ( V,E ), ve -dominates every edge incident to u , as well as every edge adjacent to these incident edges. A set S ⊆ V is a vertex-edge dominating set (or a ved–set for short) if every edge of E is ve- dominated by at least one vertex of S . The vertex-edge domination number is the minimum cardinality of a ved–set in G. In this paper, we investigate the graphs having unique minimum ved-sets that we will call UVED-graphs. We start by giving some basic properties of UVED-graphs. For the class of trees, we establish two equivalent conditions characterizing UVED-trees which we subsequently complete by providing a constructive characterization.
图G = (V,E)， ve -的顶点u支配着与u相关的每条边，以及与这些相关边相邻的每条边。若集合S的每条边都被S的至少一个顶点控制，则集S是一个点边控制集(简称为维集)。在本文中，我们研究了具有唯一最小维集的图，我们称之为ued图。我们首先给出uvid图的一些基本性质。对于这类树，我们建立了两个等价条件来描述uded树的特征，随后我们通过提供一个建设性的特征来完成这两个等价条件。
{"title":"Graphs with unique minimum vertex-edge dominating sets","authors":"B. Senthilkumar, M. Chellali, H. N. Kumar, Y. B. Venkatakrishnan","doi":"10.1051/ro/2023074","DOIUrl":"https://doi.org/10.1051/ro/2023074","url":null,"abstract":"A vertex u of a graph G = ( V,E ), ve -dominates every edge incident to u , as well as every edge adjacent to these incident edges. A set S ⊆ V is a vertex-edge dominating set (or a ved–set for short) if every edge of E is ve- dominated by at least one vertex of S . The vertex-edge domination number is the minimum cardinality of a ved–set in G. In this paper, we investigate the graphs having unique minimum ved-sets that we will call UVED-graphs. We start by giving some basic properties of UVED-graphs. For the class of trees, we establish two equivalent conditions characterizing UVED-trees which we subsequently complete by providing a constructive characterization.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75232679","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 aim of this study is to develop a multi-dimensional integrated efficiency analysis (MDIEA) model to be implemented when a pandemic breaks out. The first phase of the model involved the determination of input and output criteria that might affect the course of combat against the pandemic. Two methods were employed in the second phase: CRITIC method, which uses objective values to determine criteria weights; and, Fuzzy SWARA method, which is based on subjective values and decision makers’ opinions due to the assumption that the criteria might not be determined precisely and completely. The subjective and objective criteria weights obtained from these two methods were combined using SOWIA method so that integrated criteria weights could be determined. In the third phase, three separate efficiency rankings were obtained using EATWOS, OCRA and FDEA methods depending on the criteria weights. In the fourth phase, these efficiency rankings were combined by employing TPOP method in order to obtain one single precise ranking. The model proposed in this study determines countries’ efficiency by employing three different efficiency analysis methods together; i.e. it makes use of different point of views and different calculation procedures of different methods. The previous studies mostly analyzed the efficiency of countries by using one single efficiency method. Urban population ratio, prevalence rate of diabetes, population of people over 65 years old, number of beds in intensive care units and number of vaccination doses are the study-specific criteria that are different from other studies. The present study is expected to contribute to the literature since it is the first study that proposes a model to evaluate the performances of countries during pandemics. The proposed model was implemented to assess OECD countries’ efficiency in their fight against COVID-19, which was a prevailing crisis worldwide. When all the obtained results are considered, it is difficult to claim that one single criterion is effective in combating against the pandemic. Keeping the rate of infection – thus, the number of infected people- under control is crucial for an effective combat against the pandemic. It is also possible for countries to change their policies or prefer to adopt stricter policies so as to control the spread of the virus.
{"title":"Determining the effectiveness of countries in combating pandemics: COVID-19 case","authors":"Zeynep Büsra Keskin, E. Delice","doi":"10.1051/ro/2023077","DOIUrl":"https://doi.org/10.1051/ro/2023077","url":null,"abstract":"The aim of this study is to develop a multi-dimensional integrated efficiency analysis (MDIEA) model to be implemented when a pandemic breaks out. The first phase of the model involved the determination of input and output criteria that might affect the course of combat against the pandemic. Two methods were employed in the second phase: CRITIC method, which uses objective values to determine criteria weights; and, Fuzzy SWARA method, which is based on subjective values and decision makers’ opinions due to the assumption that the criteria might not be determined precisely and completely. The subjective and objective criteria weights obtained from these two methods were combined using SOWIA method so that integrated criteria weights could be determined. In the third phase, three separate efficiency rankings were obtained using EATWOS, OCRA and FDEA methods depending on the criteria weights. In the fourth phase, these efficiency rankings were combined by employing TPOP method in order to obtain one single precise ranking. The model proposed in this study determines countries’ efficiency by employing three different efficiency analysis methods together; i.e. it makes use of different point of views and different calculation procedures of different methods. The previous studies mostly analyzed the efficiency of countries by using one single efficiency method. Urban population ratio, prevalence rate of diabetes, population of people over 65 years old, number of beds in intensive care units and number of vaccination doses are the study-specific criteria that are different from other studies. The present study is expected to contribute to the literature since it is the first study that proposes a model to evaluate the performances of countries during pandemics. The proposed model was implemented to assess OECD countries’ efficiency in their fight against COVID-19, which was a prevailing crisis worldwide. When all the obtained results are considered, it is difficult to claim that one single criterion is effective in combating against the pandemic. Keeping the rate of infection – thus, the number of infected people- under control is crucial for an effective combat against the pandemic. It is also possible for countries to change their policies or prefer to adopt stricter policies so as to control the spread of the virus.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91510319","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}
This article focuses on optimality conditions for a robust fractional interval-valued optimization problem with uncertain inequality constraints (RNFIVP) based on convexificators. Using the tools of convexity, an example of sufficient optimality conditions is demonstrated. Robust parametric duality for (RNFIVP) is formulated and utilizing the concept of convexity, usual duality results between the primal and dual problems are investigated. Further, the equivalence between the saddle point criteria of a Lagrangian type function and a robust LU-optimal solution for (RNFIVP) with convexity is also examined.
{"title":"Optimality, duality and saddle point criteria for a robust fractional interval-valued optimization problem with uncertain inequality constraints via convexificators","authors":"K. Kummari, Rekha R. Jaichander, I. Ahmad","doi":"10.1051/ro/2023070","DOIUrl":"https://doi.org/10.1051/ro/2023070","url":null,"abstract":"This article focuses on optimality conditions for a robust\u0000fractional interval-valued optimization problem with uncertain inequality\u0000constraints (RNFIVP) based on convexificators. Using the tools\u0000of convexity, an example of sufficient optimality conditions is demonstrated.\u0000Robust parametric duality for (RNFIVP) is formulated and\u0000utilizing the concept of convexity, usual duality results between the\u0000primal and dual problems are investigated. Further, the equivalence\u0000between the saddle point criteria of a Lagrangian type function and a\u0000robust LU-optimal solution for (RNFIVP) with convexity is also examined.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74915520","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}
Facing the rapid value decline issue in the fast fashion product (FFP) industry, improving quick response (QR) capability will allow a FFP supply chain to deliver products to customers faster and capture more value. On this basis, the value compensate through QR effort and the coordination strategy for a FFP supply chain in an omnichannel context is investigated. Characterizing the regularity of product value attenuation and also QR effort as the key decision variable in a FFP omnichannel, five differential game theoretical decision models are formulated, solved and compared, including: (i) without cost sharing model under a decentralized decision; (ii) manufacturer-led unilateral cost sharing model under a decentralized decision; (iii) retailer-led unilateral cost sharing model under a decentralized decision; (iv) bilateral cost sharing under a decentralized decision; (v) bilateral cost sharing model under a coordination decision. The corresponding numerical and sensitivity analyses are conducted on a calibrated real-world fast fashion product, and have found that, in order to achieve higher total profit, a cost sharing contract mechanism is better than a without cost sharing contract mechanism; a bilateral mechanism is better than a unilateral mechanism; and a coordination mechanism is better than a decentralized mechanism. The theoretical themes developed in this study imply that FFP omnichannel practitioners should put more resource and energy in coordinating their QR efforts in the supply chain. Importantly, they should collaborate closely to confine the cost of QR effort investment through a smart selection of the right QR technologies and a better utilization of these technologies to develop and support a highly sense-and-respond supply chain operation method.
{"title":"Quick response in fast fashion omnichannel: exploring cost sharing effect","authors":"Danli Chen, Shong-Iee Ivan Su, Zhisong Chen","doi":"10.1051/ro/2023071","DOIUrl":"https://doi.org/10.1051/ro/2023071","url":null,"abstract":"Facing the rapid value decline issue in the fast fashion product (FFP) industry, improving quick response (QR) capability will allow a FFP supply chain to deliver products to customers faster and capture more value. On this basis, the value compensate through QR effort and the coordination strategy for a FFP supply chain in an omnichannel context is investigated. Characterizing the regularity of product value attenuation and also QR effort as the key decision variable in a FFP omnichannel, five differential game theoretical decision models are formulated, solved and compared, including: (i) without cost sharing model under a decentralized decision; (ii) manufacturer-led unilateral cost sharing model under a decentralized decision; (iii) retailer-led unilateral cost sharing model under a decentralized decision; (iv) bilateral cost sharing under a decentralized decision; (v) bilateral cost sharing model under a coordination decision. The corresponding numerical and sensitivity analyses are conducted on a calibrated real-world fast fashion product, and have found that, in order to achieve higher total profit, a cost sharing contract mechanism is better than a without cost sharing contract mechanism; a bilateral mechanism is better than a unilateral mechanism; and a coordination mechanism is better than a decentralized mechanism. The theoretical themes developed in this study imply that FFP omnichannel practitioners should put more resource and energy in coordinating their QR efforts in the supply chain. Importantly, they should collaborate closely to confine the cost of QR effort investment through a smart selection of the right QR technologies and a better utilization of these technologies to develop and support a highly sense-and-respond supply chain operation method.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73268327","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}
Mohammed Boukedroun, D. Duvivier, Abdessamad Ait El Cadi, V. Poirriez, Moncef Abbas
Job-shop scheduling problems are among most studied problems in last years because of their importance for industries and manufacturing processes. They are classified as NP-hard problems in the strong sense. In order to tackle these problems several models and methods have been used. In this paper, we propose a hybrid metaheuristic composed of a genetic algorithm and a tabu search algorithm to solve the stochastic job-shop scheduling problem. Our contribution is based on a study of the perturbations that affect the processing times of the jobs. These perturbations, due to machine failures, occur according to a Poisson process; the results of our approach are validated on a set of instances originating from the OR-Library [14]. On the basis of these instances, the hybrid metaheuristic is used to solve the stochastic jobshop scheduling problem with the objective of minimizing the makespan as first objective and the number of critical operations as second objective during the robustness analysis. Indeed, the results show that a high value of the number of critical operations is linked to high variations of the makespan of the perturbed schedules, or in other words to a weak robustness of the relating GA’s best schedule. Consequently, critical operations are not only good targets for optimizing a schedule, but also a clue of its goodness when considering stochastic and robustness aspects: the less critical operations it contains, the better it is.
{"title":"A hybrid genetic algorithm for stochastic job-shop scheduling problems","authors":"Mohammed Boukedroun, D. Duvivier, Abdessamad Ait El Cadi, V. Poirriez, Moncef Abbas","doi":"10.1051/ro/2023067","DOIUrl":"https://doi.org/10.1051/ro/2023067","url":null,"abstract":"Job-shop scheduling problems are among most studied\u0000problems in last years because of their importance for industries and\u0000manufacturing processes. They are classified as NP-hard problems in\u0000the strong sense. In order to tackle these problems several models and\u0000methods have been used. In this paper, we propose a hybrid metaheuristic\u0000composed of a genetic algorithm and a tabu search algorithm\u0000to solve the stochastic job-shop scheduling problem. Our contribution is\u0000based on a study of the perturbations that affect the processing times of\u0000the jobs. These perturbations, due to machine failures, occur according\u0000to a Poisson process; the results of our approach are validated on a set\u0000of instances originating from the OR-Library [14]. On the basis of these\u0000instances, the hybrid metaheuristic is used to solve the stochastic jobshop\u0000scheduling problem with the objective of minimizing the makespan\u0000as first objective and the number of critical operations as second objective\u0000during the robustness analysis. Indeed, the results show that a high\u0000value of the number of critical operations is linked to high variations of\u0000the makespan of the perturbed schedules, or in other words to a weak\u0000robustness of the relating GA’s best schedule. Consequently, critical operations\u0000are not only good targets for optimizing a schedule, but also a\u0000clue of its goodness when considering stochastic and robustness aspects:\u0000the less critical operations it contains, the better it is.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78425575","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}
This research examines the reliability characteristics of a broad series-parallel system. Complex system, having elements in series and parallel configuration is considered here to compute the reliability. Due to the failure of component, the system can either breakdown or can work with reduced frequency. To analyze the effect of component failure, sensitivity of the system with respect to reliability parameters is analyzed. In this study, generally distributed and exponentially distributed repair rates are taken into consideration from failed state to the working state of the system. The mathematical model of the designed structure is developed using Markov process and supplementary variable technique. The comparative study of the system availability and its sensitivity with respect to general distribution and general as well as exponential distribution has been examined. The Gumbel-Hougaard family of copula is used to analyze the effect of both the distributions together. For a better explanation of this work, a numerical example has been provided and shown the results graphically.
{"title":"Analysis of series-parallel system's sensitivity in context of components failures","authors":"Shivani, M. Ram, Nupur Goyal, Akshay Kumar","doi":"10.1051/ro/2023068","DOIUrl":"https://doi.org/10.1051/ro/2023068","url":null,"abstract":"This research examines the reliability characteristics of a broad series-parallel system. Complex system, having elements in series and parallel configuration is considered here to compute the reliability. Due to the failure of component, the system can either breakdown or can work with reduced frequency. To analyze the effect of component failure, sensitivity of the system with respect to reliability parameters is analyzed. In this study, generally distributed and exponentially distributed repair rates are taken into consideration from failed state to the working state of the system. The mathematical model of the designed structure is developed using Markov process and supplementary variable technique. The comparative study of the system availability and its sensitivity with respect to general distribution and general as well as exponential distribution has been examined. The Gumbel-Hougaard family of copula is used to analyze the effect of both the distributions together. For a better explanation of this work, a numerical example has been provided and shown the results graphically.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83604177","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}
Let G be a connected graph of even order n. An odd [1,b]-factor of G is a spanning subgraph F of G such that dF(v) ∈ {1,3,5,··· ,b} for any v ∈ V (G), where b is positive odd integer. The distance matrix D(G) of G is a symmetric real matrix with (i,j)-entry being the distance between the vertices vi and vj. The distance signless Laplacian matrix Q(G) of G is defined by Q(G) = Tr(G) + D(G), where Tr(G) is the diagonal matrix of the vertex transmissions in G. The largest eigenvalue η1(G) of Q(G) is called the distance signless Laplacian spectral radius of G. In this paper, we verify sharp upper bounds on the distance signless Laplacian spectral radius to guarantee the existence of an odd [1,b]-factor in a graph; we provide some graphs to show that the bounds are optimal.
{"title":"Characterizing an odd [1, b]-factor on the distance signless Laplacian spectral radius","authors":"Sizhong Zhou, Hong-xia Liu","doi":"10.1051/ro/2023069","DOIUrl":"https://doi.org/10.1051/ro/2023069","url":null,"abstract":"Let G be a connected graph of even order n. An odd [1,b]-factor of G is a spanning subgraph F of G such that dF(v) ∈ {1,3,5,··· ,b} for any v ∈ V (G), where b is positive odd integer. The distance matrix D(G) of G is a symmetric real matrix with (i,j)-entry being the distance between the vertices vi and vj. The distance signless Laplacian matrix Q(G) of G is defined by Q(G) = Tr(G) + D(G), where Tr(G) is the diagonal matrix of the vertex transmissions in G. The largest eigenvalue η1(G) of Q(G) is called the distance signless Laplacian spectral radius of G. In this paper, we verify sharp upper bounds on the distance signless Laplacian spectral radius to guarantee the existence of an odd [1,b]-factor in a graph; we provide some graphs to show that the bounds are optimal.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80942096","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}
Technology improvements in the retail industry influence the buying behaviours of customers. In the retail industry, it has been observed that the selling price of goods and promotional efforts influence a customer's choice. In the retail sector, the popularity of financing schemes i.e., trade credit offered by suppliers rather than financial institutions has also grown. Taking such a scenario into consideration and with reference to the retail sector, an inventory model has been developed for non-instantaneous deteriorating items. Effect of inflation also incorporated in model. Customers' demand is affected by the selling price of the product and the retailer's promotional efforts. During a shortage period, the backlogging rate of demand is considered a function of the waiting period. The retailer can also take advantage of a trade credit facility provided by the supplier. Furthermore, holding cost is time-dependent, and an investment is made to reduce ordering cost. Various theoretical results are obtained that maximize the retailer's total profit. To gain better managerial insights, sensitive analysis and numerical examples are provided. The results indicate that the retailer’s profit increases as the trade credit period increases. Further, the profit of the retailer increases if the retailer deals in products with a longer non-deteriorating period. Time-dependent holding cost shows a significant impact on the profit of retail. In addition to this, different existing papers in literature show the special case of the current model.
{"title":"Joint effect of selling price and promotional efforts on retailer's inventory control policy with trade credit, time-dependent holding cost, and partial backlogging under inflation","authors":"Sharad Kumar, S.R. Singh, Seema Agarwal, D. Yadav","doi":"10.1051/ro/2023066","DOIUrl":"https://doi.org/10.1051/ro/2023066","url":null,"abstract":"Technology improvements in the retail industry influence the buying behaviours of customers. In the retail industry, it has been observed that the selling price of goods and promotional efforts influence a customer's choice. In the retail sector, the popularity of financing schemes i.e., trade credit offered by suppliers rather than financial institutions has also grown. Taking such a scenario into consideration and with reference to the retail sector, an inventory model has been developed for non-instantaneous deteriorating items. Effect of inflation also incorporated in model. Customers' demand is affected by the selling price of the product and the retailer's promotional efforts. During a shortage period, the backlogging rate of demand is considered a function of the waiting period. The retailer can also take advantage of a trade credit facility provided by the supplier. Furthermore, holding cost is time-dependent, and an investment is made to reduce ordering cost. Various theoretical results are obtained that maximize the retailer's total profit. To gain better managerial insights, sensitive analysis and numerical examples are provided. The results indicate that the retailer’s profit increases as the trade credit period increases. Further, the profit of the retailer increases if the retailer deals in products with a longer non-deteriorating period. Time-dependent holding cost shows a significant impact on the profit of retail. In addition to this, different existing papers in literature show the special case of the current model.","PeriodicalId":20872,"journal":{"name":"RAIRO Oper. Res.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89903890","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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