This study proposes a methodology to obtain an efficient solution for a programming model which is multi-objective quadratic fractional with pentagonal fuzzy numbers as coefficients in all the objective functions and constraints. The proposed approach consists of three stages. In the first stage, defuzzification of the coefficients is carried out using the mean method of α-cut. Then, in the second stage, a crisp multi-objective quadratic fractional programming model (MOQFP) is constructed to obtain a non-fractional model based on an iterative parametric approach. In the final stage, this multiobjective non-fractional model is transformed to obtain a model with a single objective by applying the ε-constraint method. This final model is then solved to get desired solution. Also, an algorithm and flowchart expressing the methodology are given to present a clear picture of the approach. Finally, a numerical example illustrating the complete approach is given.
{"title":"An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers","authors":"V. Goyal, N. Rani, D. Gupta","doi":"10.37190/ord220103","DOIUrl":"https://doi.org/10.37190/ord220103","url":null,"abstract":"This study proposes a methodology to obtain an efficient solution for a programming model which is multi-objective quadratic fractional with pentagonal fuzzy numbers as coefficients in all the objective functions and constraints. The proposed approach consists of three stages. In the first stage, defuzzification of the coefficients is carried out using the mean method of α-cut. Then, in the second stage, a crisp multi-objective quadratic fractional programming model (MOQFP) is constructed to obtain a non-fractional model based on an iterative parametric approach. In the final stage, this multiobjective non-fractional model is transformed to obtain a model with a single objective by applying the ε-constraint method. This final model is then solved to get desired solution. Also, an algorithm and flowchart expressing the methodology are given to present a clear picture of the approach. Finally, a numerical example illustrating the complete approach is given.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"45 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86700728","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 previous research, the Extended Order Scale (EOS) dedicated to risk assessment was analysed. It was characterised by a Numerical Order Scale (NOS) evaluated by trapezoidal oriented fuzzy numbers (TrOFNs). However, the research showed that EOS with two-stage orientation phases, was too complicated. Therefore, the main aim of our paper is to simplify a Complete Order Scale (COS) to a zero- or one-stage order scale and a hybrid approach. For this purpose, a way to calculate the scoring function is presented. The results show that changes in the COS structure influence the values of a scoring function. Replacing just one linguistic indicator gives different results. Another finding of the research is the method’s flexibility that allows an expert to individually choose the most suitable COS. The research proves that the boundary between various linguistic labels cannot be precisely defined. However, knowledge of a formal COS structure allows it to be transformed into a less complex one.
{"title":"Modifications of order scales for assessing debtors","authors":"Aleksandra Wójcicka-Wójtowicz, Krzysztof Piasecki","doi":"10.37190/ord220309","DOIUrl":"https://doi.org/10.37190/ord220309","url":null,"abstract":"In previous research, the Extended Order Scale (EOS) dedicated to risk assessment was analysed. It was characterised by a Numerical Order Scale (NOS) evaluated by trapezoidal oriented fuzzy numbers (TrOFNs). However, the research showed that EOS with two-stage orientation phases, was too complicated. Therefore, the main aim of our paper is to simplify a Complete Order Scale (COS) to a zero- or one-stage order scale and a hybrid approach. For this purpose, a way to calculate the scoring function is presented. The results show that changes in the COS structure influence the values of a scoring function. Replacing just one linguistic indicator gives different results. Another finding of the research is the method’s flexibility that allows an expert to individually choose the most suitable COS. The research proves that the boundary between various linguistic labels cannot be precisely defined. However, knowledge of a formal COS structure allows it to be transformed into a less complex one.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"24 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81357945","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}
Kateryna Czerniachowska, Marcin Hernes, Krzysztof Lutosławski
Shelf space is one of the essential resources in logistic decisions. Order picking is the most time-consuming and labour-intensive of the distribution processes in distribution centres. Current research investigates the allocation of shelf space on a rack in a distribution centre and a retail store. The retail store, as well as the distribution centre, offers a large number of shelf storage locations. In this research, multi-orientated capping as a product of the rack allocation method is investigated. Capping allows additional product items to be placed on the rack. We show the linearisation technique with the help of which the models with capping could be linearised and, therefore, an optimal solution could be obtained. The computational experiments compare the quality of results obtained by non-linear and linear models. The proposed technique does not increase the complexity of the initial non-linear problem.
{"title":"A linearisation approach to solving a non-linear shelf space allocation problem with multi-oriented capping in retail store and distribution centre","authors":"Kateryna Czerniachowska, Marcin Hernes, Krzysztof Lutosławski","doi":"10.37190/ord220403","DOIUrl":"https://doi.org/10.37190/ord220403","url":null,"abstract":"Shelf space is one of the essential resources in logistic decisions. Order picking is the most time-consuming and labour-intensive of the distribution processes in distribution centres. Current research investigates the allocation of shelf space on a rack in a distribution centre and a retail store. The retail store, as well as the distribution centre, offers a large number of shelf storage locations. In this research, multi-orientated capping as a product of the rack allocation method is investigated. Capping allows additional product items to be placed on the rack. We show the linearisation technique with the help of which the models with capping could be linearised and, therefore, an optimal solution could be obtained. The computational experiments compare the quality of results obtained by non-linear and linear models. The proposed technique does not increase the complexity of the initial non-linear problem.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"114 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82818576","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}
Barter exchange has been growing in popularity during the coronavirus pandemic. This article considers bartering introduced to the newsvendor model with multiplicative demand. The objective of the model is to specify the order quantity and retail price to maximize the expected profit. We distinguish cases with the co-movement of prices of exchanged products and without it. In the first case, we calculate a precise optimal solution to the problem. In the latter case, we prove the existence of an optimal solution and give the conditions under which it is unique. We examine the sensitivity analysis of the results which is illustrated in numerical examples. The analysis revealed that the greater the commission, the lower the optimal profit. We make a conclusion that barter exchange can help the retailer to improve the profit.
{"title":"Barter exchange as the way to deal with excess inventory: newsvendor problem with multiplicative demand","authors":"M. Bieniek","doi":"10.37190/ord220304","DOIUrl":"https://doi.org/10.37190/ord220304","url":null,"abstract":"Barter exchange has been growing in popularity during the coronavirus pandemic. This article considers bartering introduced to the newsvendor model with multiplicative demand. The objective of the model is to specify the order quantity and retail price to maximize the expected profit. We distinguish cases with the co-movement of prices of exchanged products and without it. In the first case, we calculate a precise optimal solution to the problem. In the latter case, we prove the existence of an optimal solution and give the conditions under which it is unique. We examine the sensitivity analysis of the results which is illustrated in numerical examples. The analysis revealed that the greater the commission, the lower the optimal profit. We make a conclusion that barter exchange can help the retailer to improve the profit.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"28 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89919662","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 the present business environment, rapidly developing technology and the competitive world market pose challenges to the available assets of industries. Hence, industries need to allocate and use available assets at the optimum level. Thus, industrialists must create a good decision plan to guide their performance in the production sector. As a result, the present study applies the Meta-Goal Programming technique to attain several objectives simultaneously in the textile production sector. The importance of this study lies in pursuing different objectives simultaneously, which has been almost ignored till now. The production scheduling problem in a textile firm is used to illustrate the practicability and mathematical validity of the suggested approach. Analysis of the results obtained demonstrates that the solution met all three meta-goals with some original goals being met partially. An analysis of the sensitivity of the approach to the weights of the preferences was conducted.
{"title":"Application of goal programming in the textile apparel industry to resolve production planning problems a meta-goal programming technique using weights","authors":"Zahid Amin Malik, Rakesh Kumar, G. Pathak, H. Roy","doi":"10.37190/ord220205","DOIUrl":"https://doi.org/10.37190/ord220205","url":null,"abstract":"In the present business environment, rapidly developing technology and the competitive world market pose challenges to the available assets of industries. Hence, industries need to allocate and use available assets at the optimum level. Thus, industrialists must create a good decision plan to guide their performance in the production sector. As a result, the present study applies the Meta-Goal Programming technique to attain several objectives simultaneously in the textile production sector. The importance of this study lies in pursuing different objectives simultaneously, which has been almost ignored till now. The production scheduling problem in a textile firm is used to illustrate the practicability and mathematical validity of the suggested approach. Analysis of the results obtained demonstrates that the solution met all three meta-goals with some original goals being met partially. An analysis of the sensitivity of the approach to the weights of the preferences was conducted.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"21 5","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72583214","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}
Herbert Mukalazi, T. Larsson, Juma Kasozi, Fred Mayambala
We study the Parliamentary Pension Scheme of Uganda, a hybrid cash balance scheme which is contributory. It has two categories of members, the staff of the Parliamentary Commission and the Members of Parliament. A long term projection of the scheme’s demographic and financial evolution is done to assess its sustainability and fairness with respect to the two categories of members. The projection of the scheme’s future members is done using non-linear regression. The distribution of future members by age states is done by Markov model using frequencies of state transition of the scheme members. We project the future contributions, accumulated funds, benefits, asset and liability values together with associated funding ratios. The results show that the fund is neither sustainable nor fair with respect to the two categories of members.
{"title":"Long term projection of the demographic and financial evolution of the parliamentary pension scheme of Uganda","authors":"Herbert Mukalazi, T. Larsson, Juma Kasozi, Fred Mayambala","doi":"10.37190/ord220307","DOIUrl":"https://doi.org/10.37190/ord220307","url":null,"abstract":"We study the Parliamentary Pension Scheme of Uganda, a hybrid cash balance scheme which is contributory. It has two categories of members, the staff of the Parliamentary Commission and the Members of Parliament. A long term projection of the scheme’s demographic and financial evolution is done to assess its sustainability and fairness with respect to the two categories of members. The projection of the scheme’s future members is done using non-linear regression. The distribution of future members by age states is done by Markov model using frequencies of state transition of the scheme members. We project the future contributions, accumulated funds, benefits, asset and liability values together with associated funding ratios. The results show that the fund is neither sustainable nor fair with respect to the two categories of members.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"19 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75346452","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 paper considers a four-dimensional multi-objective multi-item transportation problem (4DMOMITP), where all the parameters are regarded as uncertain variables. In this paper, three mathematical models, namely expected value model (EVM), optimistic value model (OVM) and dependent optimistic-constrained model (DOCM), are discussed for the uncertain model of 4DMOMITP.Thesemodels are converted into their corresponding deterministic forms using different ranking criteria from uncertainty theory. These deterministic models are then solved by using the Lingo 18.0 software, utilizing three different classical approaches for obtaining a solution. A numerical example is given to illustrate the application of the model and the solution algorithm. A sensitivity analysis for the OVM and DOCM models has also been performed with respect to the confidence levels.
{"title":"Four-dimensional uncertain multi-objective multi-item transportation problem","authors":"Vandana Kakran Kakran, J. Dhodiya","doi":"10.37190/ord220204","DOIUrl":"https://doi.org/10.37190/ord220204","url":null,"abstract":"This paper considers a four-dimensional multi-objective multi-item transportation problem (4DMOMITP), where all the parameters are regarded as uncertain variables. In this paper, three mathematical models, namely expected value model (EVM), optimistic value model (OVM) and dependent optimistic-constrained model (DOCM), are discussed for the uncertain model of 4DMOMITP.Thesemodels are converted into their corresponding deterministic forms using different ranking criteria from uncertainty theory. These deterministic models are then solved by using the Lingo 18.0 software, utilizing three different classical approaches for obtaining a solution. A numerical example is given to illustrate the application of the model and the solution algorithm. A sensitivity analysis for the OVM and DOCM models has also been performed with respect to the confidence levels.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"30 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72588601","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 most recent big reform of the Polish health system took place in 2017 and introduced a basic hospital service provision system. Hospitals were able to be included in the network and receive flat-rate financing from the National Health Fund. The current paper aims to assess how the relative situation of hospitals changed between 2015 and 2018. This study is based on multicriteria rankings which take into account the values of profit/loss on sales, the contract with the NHF, the income from health services outside the NHF, the income from rental and lease, the employment of doctors, the employment of nurses, liabilities, operating costs, and interns and residents per hospital bed. The similarity of rankings constructed using different methods is shown. Based on the results of the Chi-squared test, it can be concluded that the inclusion in the network does not affect whether the relative situation of a hospital between 2015 and 2018 improved or not. In the regression analysis, the dummy variable for level 1 hospital was negatively related to the median rank; however, this impact was not statistically significant.
{"title":"Changes in the relative situation of district hospitals in Poland after the introduction of a system of basic hospital service provision in 2017","authors":"A. Sielska","doi":"10.37190/ord220308","DOIUrl":"https://doi.org/10.37190/ord220308","url":null,"abstract":"The most recent big reform of the Polish health system took place in 2017 and introduced a basic hospital service provision system. Hospitals were able to be included in the network and receive flat-rate financing from the National Health Fund. The current paper aims to assess how the relative situation of hospitals changed between 2015 and 2018. This study is based on multicriteria rankings which take into account the values of profit/loss on sales, the contract with the NHF, the income from health services outside the NHF, the income from rental and lease, the employment of doctors, the employment of nurses, liabilities, operating costs, and interns and residents per hospital bed. The similarity of rankings constructed using different methods is shown. Based on the results of the Chi-squared test, it can be concluded that the inclusion in the network does not affect whether the relative situation of a hospital between 2015 and 2018 improved or not. In the regression analysis, the dummy variable for level 1 hospital was negatively related to the median rank; however, this impact was not statistically significant.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"14 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74902949","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}
For the past few decades, control and building engineering communities have been focusing on thermal comfort as a key factor in designing sustainable building evaluation methods and tools. However, estimating the indoor air temperature of buildings is a complicated task due to the nonlinear and complex building dynamics characterised by the time-varying environment with disturbances. The primary focus of this paper is designing a predictive and probabilistic room temperature model of buildings using Gaussian processes (GPs) and incorporating it into model predictive control (MPC) to minimise energy consumption and provide thermal comfort satisfaction. The full probabilistic capabilities of GPs are exploited from two perspectives: the mean prediction is used for the room temperature model, while the uncertainty is involved in the MPC objective not to lose the desired performance and design a robust controller. We illustrated the potential of the proposed method in a numerical example with simulation results.
{"title":"Supervisory optimal control using machine learning for building thermal comfort","authors":"Shokhjakhon Abdufattokhov, Nurilla Mahamatov, Kamila Ibragimova, Dilfuza Gulyamova, Dilyorjon Yuldashev","doi":"10.37190/ord220401","DOIUrl":"https://doi.org/10.37190/ord220401","url":null,"abstract":"For the past few decades, control and building engineering communities have been focusing on thermal comfort as a key factor in designing sustainable building evaluation methods and tools. However, estimating the indoor air temperature of buildings is a complicated task due to the nonlinear and complex building dynamics characterised by the time-varying environment with disturbances. The primary focus of this paper is designing a predictive and probabilistic room temperature model of buildings using Gaussian processes (GPs) and incorporating it into model predictive control (MPC) to minimise energy consumption and provide thermal comfort satisfaction. The full probabilistic capabilities of GPs are exploited from two perspectives: the mean prediction is used for the room temperature model, while the uncertainty is involved in the MPC objective not to lose the desired performance and design a robust controller. We illustrated the potential of the proposed method in a numerical example with simulation results.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"307 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78356777","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}
We consider Markovian differentiated hiatuses queues with bulk entries. With the help of the matrix geometric method, we discuss the stability condition for the existence of the steady-state solution of our model and we obtain the stationary system size by using a probability generating function. The stochastic decomposition form of stationary system size and the waiting time distribution of an arbitrary beneficiary are also analysed. Furthermore, we perform the expense analysis using the particle swarm optimization technique and we obtain the optimality of service rate and hiatus rate. Finally, we study the effects of changes in the parameters on some important performance measures of the system through numerical observations.
{"title":"A discussion on the optimality of bulk entry queue with differentiated hiatuses","authors":"M. Vadivukarasi, K. Kalidass","doi":"10.37190/ord220209","DOIUrl":"https://doi.org/10.37190/ord220209","url":null,"abstract":"We consider Markovian differentiated hiatuses queues with bulk entries. With the help of the matrix geometric method, we discuss the stability condition for the existence of the steady-state solution of our model and we obtain the stationary system size by using a probability generating function. The stochastic decomposition form of stationary system size and the waiting time distribution of an arbitrary beneficiary are also analysed. Furthermore, we perform the expense analysis using the particle swarm optimization technique and we obtain the optimality of service rate and hiatus rate. Finally, we study the effects of changes in the parameters on some important performance measures of the system through numerical observations.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":"43 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80864513","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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