Pub Date : 2021-04-20DOI: 10.1080/01966324.2021.1910886
José G. Sanabria-Rey, E. L. Solano-Charris, C. A. Vega-Mejía, C. L. Quintero-Araújo
Abstract During recent years, Last-mile deliveries (LMD) have become relevant due to its application in e-commerce, urban logistics, and food delivery among others. This work addresses an LMD denoted as a Vehicle Routing Problem with time windows (VRPTW) and aims to minimize total time of the distribution process (i.e., makespan). The LMD is an NP-Hard problem that refers to the delivery of goods from a consolidation center to a destination. For solving the problem, a spreadsheet-based solution that employs a multi-start algorithm based on the biased-randomized version of the nearest neighbor heuristic is introduced. Real historical data of last-mile deliveries for dairy products in Bogotá (Colombia) was considered for evaluating our proposed method. Computational experiments are carried out to show the competitiveness of our method in terms of makespan, number of vehicles, average vehicle occupancy, average load and costs. Some insights for future works are also provided.
{"title":"Solving Last-Mile Deliveries for Dairy Products Using a Biased Randomization-Based Spreadsheet. A Case Study","authors":"José G. Sanabria-Rey, E. L. Solano-Charris, C. A. Vega-Mejía, C. L. Quintero-Araújo","doi":"10.1080/01966324.2021.1910886","DOIUrl":"https://doi.org/10.1080/01966324.2021.1910886","url":null,"abstract":"Abstract During recent years, Last-mile deliveries (LMD) have become relevant due to its application in e-commerce, urban logistics, and food delivery among others. This work addresses an LMD denoted as a Vehicle Routing Problem with time windows (VRPTW) and aims to minimize total time of the distribution process (i.e., makespan). The LMD is an NP-Hard problem that refers to the delivery of goods from a consolidation center to a destination. For solving the problem, a spreadsheet-based solution that employs a multi-start algorithm based on the biased-randomized version of the nearest neighbor heuristic is introduced. Real historical data of last-mile deliveries for dairy products in Bogotá (Colombia) was considered for evaluating our proposed method. Computational experiments are carried out to show the competitiveness of our method in terms of makespan, number of vehicles, average vehicle occupancy, average load and costs. Some insights for future works are also provided.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"51 - 69"},"PeriodicalIF":0.0,"publicationDate":"2021-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1910886","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45131966","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}
Pub Date : 2021-04-19DOI: 10.1080/01966324.2021.1903369
M. Usha, S. Balamurali
Abstract In this paper, a method of designing quick switching sampling system for resubmitted lots for inspection of attribute quality characteristics based on the gamma-Poisson distribution is proposed. We determine the required parameters by using two-points on the operating characteristic curve approach such that both producer’s and the consumer’s risks are satisfied for some specified values of acceptable quality level and limiting quality level. Tables are constructed for optimal sample size and two acceptance numbers of the proposed sampling system. The relative efficiency of the proposed system over conventional plans is also discussed. In addition, an economic design of the above mentioned sampling system to minimize total cost is also investigated. Consequently, it is proved that the proposed system minimizes the total inspection cost and average total inspection.
{"title":"Economic Design of Quick Switching Sampling System for Resubmitted Lots under Gamma-Poisson Distribution","authors":"M. Usha, S. Balamurali","doi":"10.1080/01966324.2021.1903369","DOIUrl":"https://doi.org/10.1080/01966324.2021.1903369","url":null,"abstract":"Abstract In this paper, a method of designing quick switching sampling system for resubmitted lots for inspection of attribute quality characteristics based on the gamma-Poisson distribution is proposed. We determine the required parameters by using two-points on the operating characteristic curve approach such that both producer’s and the consumer’s risks are satisfied for some specified values of acceptable quality level and limiting quality level. Tables are constructed for optimal sample size and two acceptance numbers of the proposed sampling system. The relative efficiency of the proposed system over conventional plans is also discussed. In addition, an economic design of the above mentioned sampling system to minimize total cost is also investigated. Consequently, it is proved that the proposed system minimizes the total inspection cost and average total inspection.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"24 - 37"},"PeriodicalIF":0.0,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1903369","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45782721","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}
Pub Date : 2021-03-27DOI: 10.1080/01966324.2021.1903368
V. Agiwal, J. Jeevan Kumar, Narinder Kumar
Abstract In this paper, we develop an estimation procedure for an autoregressive model with polynomial time trend approximated by a spline function. Spline function has the advantage of approximating the non-linear time series in an appropriate degree of polynomial time trend model. For Bayesian parameter estimation, the conditional posterior distribution is obtained under two symmetric loss functions. Due to the complex form of the conditional posterior distribution, Markov Chain Monte Carlo (MCMC) approach is used to estimate the Bayes estimators. The performance of Bayes estimators is compared with that of the corresponding maximum likelihood estimators (MLEs) in terms of mean squared error (MSE) and average absolute bias (AB) via a simulation study. To illustrate the proposed study, import series of Brazil, Russia, India, China, and South Africa (BRICS) countries are analyzed.
{"title":"Bayesian Estimation of the Polynomial Time Trend AR(1) Model through Spline Function","authors":"V. Agiwal, J. Jeevan Kumar, Narinder Kumar","doi":"10.1080/01966324.2021.1903368","DOIUrl":"https://doi.org/10.1080/01966324.2021.1903368","url":null,"abstract":"Abstract In this paper, we develop an estimation procedure for an autoregressive model with polynomial time trend approximated by a spline function. Spline function has the advantage of approximating the non-linear time series in an appropriate degree of polynomial time trend model. For Bayesian parameter estimation, the conditional posterior distribution is obtained under two symmetric loss functions. Due to the complex form of the conditional posterior distribution, Markov Chain Monte Carlo (MCMC) approach is used to estimate the Bayes estimators. The performance of Bayes estimators is compared with that of the corresponding maximum likelihood estimators (MLEs) in terms of mean squared error (MSE) and average absolute bias (AB) via a simulation study. To illustrate the proposed study, import series of Brazil, Russia, India, China, and South Africa (BRICS) countries are analyzed.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"13 - 23"},"PeriodicalIF":0.0,"publicationDate":"2021-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1903368","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41859572","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}
Pub Date : 2021-03-26DOI: 10.1080/01966324.2021.1899878
Manoj Chacko, Rakhi Mohan
Abstract The main drawback of progressive type-II censoring is that the time length of the experiment may be very large. This drawback of progressive type-II censoring scheme can be avoided if we consider progressively type-II hybrid censoring scheme, which is a mixture of progressive type-II and hybrid censoring schemes. In this paper, we consider the problem of estimation of parameters for a two-parameter Kumaraswamy-exponential distribution based on progressively type-II hybrid censored sample. The maximum likelihood estimators and Bayes estimators of the parameters are obtained using different loss functions such as squared error loss function, LINEX loss function and entropy loss function. For Bayes estimation we use importance sampling method. A simulation study is then performed for comparing various estimators developed in this paper. A real data set is also used for illustration.
{"title":"Estimation of Parameters of Kumaraswamy-Exponential Distribution Based on Progressively Type-II Hybrid Censored Data","authors":"Manoj Chacko, Rakhi Mohan","doi":"10.1080/01966324.2021.1899878","DOIUrl":"https://doi.org/10.1080/01966324.2021.1899878","url":null,"abstract":"Abstract The main drawback of progressive type-II censoring is that the time length of the experiment may be very large. This drawback of progressive type-II censoring scheme can be avoided if we consider progressively type-II hybrid censoring scheme, which is a mixture of progressive type-II and hybrid censoring schemes. In this paper, we consider the problem of estimation of parameters for a two-parameter Kumaraswamy-exponential distribution based on progressively type-II hybrid censored sample. The maximum likelihood estimators and Bayes estimators of the parameters are obtained using different loss functions such as squared error loss function, LINEX loss function and entropy loss function. For Bayes estimation we use importance sampling method. A simulation study is then performed for comparing various estimators developed in this paper. A real data set is also used for illustration.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"41 1","pages":"1 - 12"},"PeriodicalIF":0.0,"publicationDate":"2021-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1899878","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49552447","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}
Pub Date : 2021-03-19DOI: 10.1080/01966324.2021.1891999
K. R. Meena, Aditi Kar Gangopadhyay, Omer Abdalghani
Abstract The problem of estimation after selection can be seen in numerous statistical applications. Let be a random sample drawn from the population where Π i follows Pareto distribution with an unknown scale parameter θi and common known shape parameter β. This article is concerned with the problem of estimating θL (or θS ), the scale parameter of the selected Pareto population under the generalized Stein loss function. The uniformly minimum risk unbiased (UMRU) estimators of θL and θS , scale parameters of the largest and the smallest population respectively, are determined. For k = 2, we have obtained a sufficient condition of minimaxity of θS and showed that the generalized Bayes estimator of θS is a minimax estimator for k = 2. Also, a class of linear admissible estimators of the form of θL and θS is found, and a sufficient condition for inadmissibility is provided. Further, we demonstrate that the UMRU estimator of θS is inadmissible. A comparison between the proposed estimators is conducted using MATLAB software and a real data set is analyzed for illustrative purposes. Finally, conclusions and discussion are reported.
{"title":"On Estimating Scale Parameter of the Selected Pareto Population under the Generalized Stein Loss Function","authors":"K. R. Meena, Aditi Kar Gangopadhyay, Omer Abdalghani","doi":"10.1080/01966324.2021.1891999","DOIUrl":"https://doi.org/10.1080/01966324.2021.1891999","url":null,"abstract":"Abstract The problem of estimation after selection can be seen in numerous statistical applications. Let be a random sample drawn from the population where Π i follows Pareto distribution with an unknown scale parameter θi and common known shape parameter β. This article is concerned with the problem of estimating θL (or θS ), the scale parameter of the selected Pareto population under the generalized Stein loss function. The uniformly minimum risk unbiased (UMRU) estimators of θL and θS , scale parameters of the largest and the smallest population respectively, are determined. For k = 2, we have obtained a sufficient condition of minimaxity of θS and showed that the generalized Bayes estimator of θS is a minimax estimator for k = 2. Also, a class of linear admissible estimators of the form of θL and θS is found, and a sufficient condition for inadmissibility is provided. Further, we demonstrate that the UMRU estimator of θS is inadmissible. A comparison between the proposed estimators is conducted using MATLAB software and a real data set is analyzed for illustrative purposes. Finally, conclusions and discussion are reported.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"357 - 377"},"PeriodicalIF":0.0,"publicationDate":"2021-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1891999","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46642801","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}
Pub Date : 2021-03-05DOI: 10.1080/01966324.2021.1892000
John W. Glasser, R. Regis
Abstract The survival function method is a well-known alternative procedure for calculating the expectation of a nonnegative random variable with a continuous probability distribution. This paper proves a generalization of this method that can be used to calculate the expectation of a continuously differentiable function of a nonnegative random variable with a continuous, discrete or mixed probability distribution. A similar result is used in actuarial probability manuals, but proofs for the general case along with required assumptions are often not provided. Moreover, generalizations of the survival function method are typically not mentioned in probability textbooks. One of the main contributions of this paper is that it explores some technical conditions that guarantee that the method can be applied. This paper also provides an alternate proof of the generalized survival function method along with a different set of conditions under which the method can be proved to hold. Finally, examples of how the method can be applied to calculate expectations and moment-generating functions and to derive an integral identity are given.
{"title":"A Generalized Survival Function Method for the Expectation of Functions of Nonnegative Random Variables","authors":"John W. Glasser, R. Regis","doi":"10.1080/01966324.2021.1892000","DOIUrl":"https://doi.org/10.1080/01966324.2021.1892000","url":null,"abstract":"Abstract The survival function method is a well-known alternative procedure for calculating the expectation of a nonnegative random variable with a continuous probability distribution. This paper proves a generalization of this method that can be used to calculate the expectation of a continuously differentiable function of a nonnegative random variable with a continuous, discrete or mixed probability distribution. A similar result is used in actuarial probability manuals, but proofs for the general case along with required assumptions are often not provided. Moreover, generalizations of the survival function method are typically not mentioned in probability textbooks. One of the main contributions of this paper is that it explores some technical conditions that guarantee that the method can be applied. This paper also provides an alternate proof of the generalized survival function method along with a different set of conditions under which the method can be proved to hold. Finally, examples of how the method can be applied to calculate expectations and moment-generating functions and to derive an integral identity are given.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"378 - 390"},"PeriodicalIF":0.0,"publicationDate":"2021-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1892000","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45749184","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}
Pub Date : 2021-02-26DOI: 10.1080/01966324.2021.1884920
C. Kumar, S. Harisankar
Abstract Here we introduce a bivariate version of the extended Yule distribution (EYD) of Martinez-Rodriguez et al (Computational Statistics and Data Analysis, 2011). The EYD has been found suitable for heavy tailed distributions. For emphasizing the practical relevance of the model, it is shown that the proposed distribution can be viewed as the distribution of the random sum of independently and identically distributed bivariate Bernoulli random variables. It is also observed that the proposed bivariate distribution is a very flexible distribution and it includes the bivariate geometric distribution as its special case. A genesis of the distribution and explicit closed form expressions for its probability mass function, factorial moments and the probability generating function of its conditional distributions are derived. Certain recurrence relations for probabilities, raw moments and factorial moments of the BEYD are also obtained. The method of maximum likelihood estimation is employed for estimating the parameters of the distribution. Some examples of application using data from different fields are included in order to illustrate all these procedures.
本文引入Martinez-Rodriguez等人(Computational Statistics and Data Analysis, 2011)的扩展Yule分布(EYD)的双变量版本。已发现EYD适合于重尾分布。为了强调模型的实际意义，表明所提出的分布可以看作是独立和同分布的二元伯努利随机变量的随机和的分布。我们还观察到，所提出的二元分布是一个非常灵活的分布，它将二元几何分布作为它的特例。推导了该分布的起源及其概率质量函数、阶乘矩及其条件分布的概率生成函数的显式封闭表达式。得到了BEYD的概率、原始矩和阶乘矩的递归关系。采用极大似然估计方法对分布参数进行估计。为了说明所有这些过程，包括使用来自不同领域的数据的一些应用程序示例。
{"title":"Bivariate Extended Yule Distribution","authors":"C. Kumar, S. Harisankar","doi":"10.1080/01966324.2021.1884920","DOIUrl":"https://doi.org/10.1080/01966324.2021.1884920","url":null,"abstract":"Abstract Here we introduce a bivariate version of the extended Yule distribution (EYD) of Martinez-Rodriguez et al (Computational Statistics and Data Analysis, 2011). The EYD has been found suitable for heavy tailed distributions. For emphasizing the practical relevance of the model, it is shown that the proposed distribution can be viewed as the distribution of the random sum of independently and identically distributed bivariate Bernoulli random variables. It is also observed that the proposed bivariate distribution is a very flexible distribution and it includes the bivariate geometric distribution as its special case. A genesis of the distribution and explicit closed form expressions for its probability mass function, factorial moments and the probability generating function of its conditional distributions are derived. Certain recurrence relations for probabilities, raw moments and factorial moments of the BEYD are also obtained. The method of maximum likelihood estimation is employed for estimating the parameters of the distribution. Some examples of application using data from different fields are included in order to illustrate all these procedures.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"340 - 356"},"PeriodicalIF":0.0,"publicationDate":"2021-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1884920","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48645670","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}
Pub Date : 2021-02-13DOI: 10.1080/01966324.2021.1875087
M. Sadegh
Abstract This article considers the stress-strength modeling for calculating of the stress-strength reliability of a coherent system as a function of the stress-strength reliabilities of its components. The system components may experience the same or different stress levels. We have found some mistakes in examples given by Bhattacharya and Roychowdhury (2013) due to misapplication of the system reliability when the system components were subjected to a common stress level. We show that the stress-strength reliability of a system with different stress levels does not include the case when the system components are subjected to a common stress level as a special case and give a correct argument. Their result for the case of different stress levels is correct.
{"title":"Erratum to: Reliability of a Coherent System in a Multicomponent Stress-Strength Model","authors":"M. Sadegh","doi":"10.1080/01966324.2021.1875087","DOIUrl":"https://doi.org/10.1080/01966324.2021.1875087","url":null,"abstract":"Abstract This article considers the stress-strength modeling for calculating of the stress-strength reliability of a coherent system as a function of the stress-strength reliabilities of its components. The system components may experience the same or different stress levels. We have found some mistakes in examples given by Bhattacharya and Roychowdhury (2013) due to misapplication of the system reliability when the system components were subjected to a common stress level. We show that the stress-strength reliability of a system with different stress levels does not include the case when the system components are subjected to a common stress level as a special case and give a correct argument. Their result for the case of different stress levels is correct.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"336 - 339"},"PeriodicalIF":0.0,"publicationDate":"2021-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2021.1875087","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47661616","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}
Pub Date : 2020-12-26DOI: 10.1080/01966324.2020.1860840
P. Pundir, Rohit Patawa, P. Gupta
Abstract Characteristics of a two non-identical unit system with a cold standby facility are studied from Bayesian point of view with different type of priors assumed for unknown parameters. Time to failure and time to repair of the operating units are assumed to follow Lindley distribution. Several measures of system effectiveness, such as reliability, MTSF, steady state availability, expected profit etc. are obtained by using regenerative point technique. At the end, a numerical illustration is also carried out, for validation of the proposed system model.
{"title":"Analysis of Two Non-Identical Unit Cold Standby System in Presence of Prior Information","authors":"P. Pundir, Rohit Patawa, P. Gupta","doi":"10.1080/01966324.2020.1860840","DOIUrl":"https://doi.org/10.1080/01966324.2020.1860840","url":null,"abstract":"Abstract Characteristics of a two non-identical unit system with a cold standby facility are studied from Bayesian point of view with different type of priors assumed for unknown parameters. Time to failure and time to repair of the operating units are assumed to follow Lindley distribution. Several measures of system effectiveness, such as reliability, MTSF, steady state availability, expected profit etc. are obtained by using regenerative point technique. At the end, a numerical illustration is also carried out, for validation of the proposed system model.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"320 - 335"},"PeriodicalIF":0.0,"publicationDate":"2020-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1860840","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49640856","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}
Pub Date : 2020-12-17DOI: 10.1080/01966324.2020.1854137
P. Srivastava, D. Bisht
Abstract The primary issues in the solution of fuzzy transportation problems are loss of information, violation of the basic trading rule, and incomplete fuzzy information. This research article is a successful effort to overcome these issues. Here, a new method to solve the triangular fuzzy transportation problem by segregating it into three classical transportation problems has been developed without the use of any ranking technique. The minimum demand supply method is used to obtain an initial basic feasible solution of all three transportation problems individually. Then, the stepping stone method is applied to check the optimality of the solution. The classical solutions obtained are clubbed to get the fuzzy optimal solution of the triangular fuzzy transportation problem. This procedure is demonstrated with the help of numerical examples. A comparison of results from this procedure with the other existing methods confirms the applicability of the segregated approach. This approach can be helpful in the decision-making problems where data is given in the form of fuzzy numbers and can also be extended to an unbalanced fuzzy transportation problem.
{"title":"A Segregated Advancement in the Solution of Triangular Fuzzy Transportation Problems","authors":"P. Srivastava, D. Bisht","doi":"10.1080/01966324.2020.1854137","DOIUrl":"https://doi.org/10.1080/01966324.2020.1854137","url":null,"abstract":"Abstract The primary issues in the solution of fuzzy transportation problems are loss of information, violation of the basic trading rule, and incomplete fuzzy information. This research article is a successful effort to overcome these issues. Here, a new method to solve the triangular fuzzy transportation problem by segregating it into three classical transportation problems has been developed without the use of any ranking technique. The minimum demand supply method is used to obtain an initial basic feasible solution of all three transportation problems individually. Then, the stepping stone method is applied to check the optimality of the solution. The classical solutions obtained are clubbed to get the fuzzy optimal solution of the triangular fuzzy transportation problem. This procedure is demonstrated with the help of numerical examples. A comparison of results from this procedure with the other existing methods confirms the applicability of the segregated approach. This approach can be helpful in the decision-making problems where data is given in the form of fuzzy numbers and can also be extended to an unbalanced fuzzy transportation problem.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"40 1","pages":"134 - 144"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2020.1854137","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43573372","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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