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":null,"pages":null},"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}
The awareness of making decisions in an imprecise environment has resulted in considering the inventory system under a fuzzy approach. The effects of uncertain demand have been finding increased application in many inventory systems. Un-certainty creates complicated situations for the manufacturer in making decisions. Markets have become more competitive as a result of technological advancements. The effect of inflation on the overall cost of the inventory system is useful in providing a tool for the analysis of inventory decisions. This study intended to estimate the effect of different fuzzy numbers on a manufacturer's annual joint expected total cost. The comparative study of this proposed model has been considered for two different fuzzy numbers with the defuzzification technique as the centroid method. The optimization technique has been used to minimize the producer’s joint expected total cost under the condition mentioned earlier, and the model is validated numerically.
{"title":"Optimization of an EPQ model in an imprecise environment with defuzzification by the centroid method under inflation","authors":"R. Arora, A. Chauhan, Renu Sharma, A. Singh","doi":"10.37190/ord220303","DOIUrl":"https://doi.org/10.37190/ord220303","url":null,"abstract":"The awareness of making decisions in an imprecise environment has resulted in considering the inventory system under a fuzzy approach. The effects of uncertain demand have been finding increased application in many inventory systems. Un-certainty creates complicated situations for the manufacturer in making decisions. Markets have become more competitive as a result of technological advancements. The effect of inflation on the overall cost of the inventory system is useful in providing a tool for the analysis of inventory decisions. This study intended to estimate the effect of different fuzzy numbers on a manufacturer's annual joint expected total cost. The comparative study of this proposed model has been considered for two different fuzzy numbers with the defuzzification technique as the centroid method. The optimization technique has been used to minimize the producer’s joint expected total cost under the condition mentioned earlier, and the model is validated numerically.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88786544","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 the research is comparison between average order picking times obtained using the analytical model and simulation methods for shared storage systems. We also compare the results obtained with the results obtained for dedicated storage. We assume the random and ABC-class storage (with within and across aisle storage policies). We select the locations by means of the TOPSIS method for two take-out strategies: quantity adjustment (QA) and priority of partial units (PPU). We determine the route by using s-shape and return heuristics. In most cases, the simulated average order picking times are shorter than the analytical ones. It results from not considering the criteria’ weights in calculation of the analytical order picking time. Also, the results for shared storage with QA strategy are in most cases better than for dedicated storage. This might imply an advantage of shared over dedicated storage, but needs further confirmation.
{"title":"Analytical and simulation determination of order picking time in a low storage warehouse for shared storage systems","authors":"K. Dmytrów","doi":"10.37190/ord220203","DOIUrl":"https://doi.org/10.37190/ord220203","url":null,"abstract":"The aim of the research is comparison between average order picking times obtained using the analytical model and simulation methods for shared storage systems. We also compare the results obtained with the results obtained for dedicated storage. We assume the random and ABC-class storage (with within and across aisle storage policies). We select the locations by means of the TOPSIS method for two take-out strategies: quantity adjustment (QA) and priority of partial units (PPU). We determine the route by using s-shape and return heuristics. In most cases, the simulated average order picking times are shorter than the analytical ones. It results from not considering the criteria’ weights in calculation of the analytical order picking time. Also, the results for shared storage with QA strategy are in most cases better than for dedicated storage. This might imply an advantage of shared over dedicated storage, but needs further confirmation.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84608938","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 intuitionistic fuzzy sets (IFSs) have a more significant contribution to describing and dealing with uncertainty. The intuitionistic fuzzy measure is a significant consideration in the field of IFSs theory. However, Pythagorean fuzzy sets (PFSs) are an extension of the IFSs. PFSs are more capable of modelling uncertainties than IFSs in real-world decision-making scenarios. The majority of PFSs research has concentrated on establishing decision-making frameworks. A similarity measure is a key concept which measures the closeness of PFSs. IFSs-based similarity measures have been proposed in the literature. This type of similarity measure, however, has a drawback since it cannot satisfy the axiomatic definition of similarity by offering counter-intuitive examples. For this study, a similarity-based on logarithmic function for Pythagorean fuzzy sets (PFSs) is proposed as a solution to the problem. A decision-making approach is presented to ascertain the suitability of careers for aspirants. Additionally, numerical illustration is applied to determine the strength and validity of the proposed similarity measures. The application of the proposed similarity measures is also presented in this article. A comparison of the suggested measures with the existing ones is also demonstrated to ensure the reliability of the measures. The results show that the proposed similarity measures are efficient and reasonable from both numerical and realistic assessments.
{"title":"Logarithmic similarity measures on Pythagorean fuzzy sets in the admission process","authors":"Haritika Arora, Anjali Naithani","doi":"10.37190/ord220101","DOIUrl":"https://doi.org/10.37190/ord220101","url":null,"abstract":"The intuitionistic fuzzy sets (IFSs) have a more significant contribution to describing and dealing with uncertainty. The intuitionistic fuzzy measure is a significant consideration in the field of IFSs theory. However, Pythagorean fuzzy sets (PFSs) are an extension of the IFSs. PFSs are more capable of modelling uncertainties than IFSs in real-world decision-making scenarios. The majority of PFSs research has concentrated on establishing decision-making frameworks. A similarity measure is a key concept which measures the closeness of PFSs. IFSs-based similarity measures have been proposed in the literature. This type of similarity measure, however, has a drawback since it cannot satisfy the axiomatic definition of similarity by offering counter-intuitive examples. For this study, a similarity-based on logarithmic function for Pythagorean fuzzy sets (PFSs) is proposed as a solution to the problem. A decision-making approach is presented to ascertain the suitability of careers for aspirants. Additionally, numerical illustration is applied to determine the strength and validity of the proposed similarity measures. The application of the proposed similarity measures is also presented in this article. A comparison of the suggested measures with the existing ones is also demonstrated to ensure the reliability of the measures. The results show that the proposed similarity measures are efficient and reasonable from both numerical and realistic assessments.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86198728","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. Adhikari, A. Behera, Rabindra Mahapatra, H. Das
Bikes are becoming an increasingly popular and reliable mode of transportation in developing countries because of their efficiency and ability to navigate through rough terrain and narrow roadways. Bikes are more vulnerable to road accidents and their riders’ safety is the main concern at present days. Hence, it is essential to reduce the possibility of accidents caused by bike riders. The main reason for bike accidents is bike rider behaviours in the form of traffic rules violations. The paper’s main aim is to categorize the importance of seven attributes on traffic rules violations, including bike rider behaviours, road features, ambient conditions, driving skills, type of license, bike age/tenure and riding without a safety device (helmet). Bike riders’ violations that can lead to an accident and the impact of attributes have been analyzed using the structural equation modelling (SEM) technique. To analyze these attributes, 450 bike riders have been interviewed in Bhubaneswar, India. It has been concluded that bike rider behaviours are the most significant attribute of violations. Since most bike riders are young, with low income and education, paying more attention to their training and education before issuing a driving license is necessary. In addition, those who do not use safety devices (helmets) are more susceptible to committing violations. This relates to the lack of enough control and enforcement in developing cities. Also, it shows that the current traffic fines for not using safety devices (helmets) are not enforced enough. Finally, considering this research’s outcomes can help minimize traffic rules violations among bike riders, which is a step towards safer roads.
{"title":"Analysis of traffic rule violations among bike riders. A structural equation model","authors":"B. Adhikari, A. Behera, Rabindra Mahapatra, H. Das","doi":"10.37190/ord220302","DOIUrl":"https://doi.org/10.37190/ord220302","url":null,"abstract":"Bikes are becoming an increasingly popular and reliable mode of transportation in developing countries because of their efficiency and ability to navigate through rough terrain and narrow roadways. Bikes are more vulnerable to road accidents and their riders’ safety is the main concern at present days. Hence, it is essential to reduce the possibility of accidents caused by bike riders. The main reason for bike accidents is bike rider behaviours in the form of traffic rules violations. The paper’s main aim is to categorize the importance of seven attributes on traffic rules violations, including bike rider behaviours, road features, ambient conditions, driving skills, type of license, bike age/tenure and riding without a safety device (helmet). Bike riders’ violations that can lead to an accident and the impact of attributes have been analyzed using the structural equation modelling (SEM) technique. To analyze these attributes, 450 bike riders have been interviewed in Bhubaneswar, India. It has been concluded that bike rider behaviours are the most significant attribute of violations. Since most bike riders are young, with low income and education, paying more attention to their training and education before issuing a driving license is necessary. In addition, those who do not use safety devices (helmets) are more susceptible to committing violations. This relates to the lack of enough control and enforcement in developing cities. Also, it shows that the current traffic fines for not using safety devices (helmets) are not enforced enough. Finally, considering this research’s outcomes can help minimize traffic rules violations among bike riders, which is a step towards safer roads.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80421828","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}
Electricity producers and traders are exposed to various risks, among which price and volume risk play very important roles. This research considers portfolio-building strategies that enable the proportion of electricity traded in different electricity markets (day-ahead and intraday) to be chosen dynamically. Two types of approaches are considered: a simple strategy, which assumes that these proportions are fixed, and a data-driven strategy, in which the ratios fluctuate. To explore the market information, a structural vector autoregressive model is applied, which allows one to estimate the relationship between the variables of interest and simulate their future distribution. The approach is evaluated using data from the electricity market in Germany. The outcomes indicate that data-driven strategies increase revenue and reduce trading risk. These financial gains may encourage energy traders to apply advanced statistical methods in their portfolio-building process.
{"title":"Portfolio management of a small RES utility with a structural vector autoregressive model of electricity markets in Germany","authors":"K. Maciejowska","doi":"10.37190/ord220405","DOIUrl":"https://doi.org/10.37190/ord220405","url":null,"abstract":"Electricity producers and traders are exposed to various risks, among which price and volume risk play very important roles. This research considers portfolio-building strategies that enable the proportion of electricity traded in different electricity markets (day-ahead and intraday) to be chosen dynamically. Two types of approaches are considered: a simple strategy, which assumes that these proportions are fixed, and a data-driven strategy, in which the ratios fluctuate. To explore the market information, a structural vector autoregressive model is applied, which allows one to estimate the relationship between the variables of interest and simulate their future distribution. The approach is evaluated using data from the electricity market in Germany. The outcomes indicate that data-driven strategies increase revenue and reduce trading risk. These financial gains may encourage energy traders to apply advanced statistical methods in their portfolio-building process.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83277493","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}
S. Nasrollahi, H. Hosseini-Nasab, Mohamad Bagher Fakhrzad, M. Honarvar
The paper addresses the location-allocation and transportation problems in designing a cross-docking distribution network that consists of suppliers, cross-docks, and plants. A developed mixed-integer non-linear model is proposed for a post-distribution cross-docking strategy with multiple cross-docks and products that cross-docks can be connected. The objective function is to minimise the total cost comprising the cost of established cross-docks and transportation costs. To obtain this model, first, two models are introduced and compared (basic non-linear model 1 and non-linear model 2 with the possibility of connections between cross-docks). Results indicate that the total cost is decreased when the connection between cross-docks exists. So, model 2 is more efficient and suitable than model 1. Then, consolidation of plant orders is added to model 2, and the developed model is formulated. Finally, some problems with different sizes are generated randomly and solved by GAMS software to evaluate the model accuracy.
{"title":"A developed nonlinear model for the location-allocation and transportation problems in a cross-docking distribution network","authors":"S. Nasrollahi, H. Hosseini-Nasab, Mohamad Bagher Fakhrzad, M. Honarvar","doi":"10.37190/ord220107","DOIUrl":"https://doi.org/10.37190/ord220107","url":null,"abstract":"The paper addresses the location-allocation and transportation problems in designing a cross-docking distribution network that consists of suppliers, cross-docks, and plants. A developed mixed-integer non-linear model is proposed for a post-distribution cross-docking strategy with multiple cross-docks and products that cross-docks can be connected. The objective function is to minimise the total cost comprising the cost of established cross-docks and transportation costs. To obtain this model, first, two models are introduced and compared (basic non-linear model 1 and non-linear model 2 with the possibility of connections between cross-docks). Results indicate that the total cost is decreased when the connection between cross-docks exists. So, model 2 is more efficient and suitable than model 1. Then, consolidation of plant orders is added to model 2, and the developed model is formulated. Finally, some problems with different sizes are generated randomly and solved by GAMS software to evaluate the model accuracy.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81510671","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 article, the optimal loading of homogeneous marine cargo is considered. A mathematical formulation in terms of a mixed-integer linear program can be given. Still, the level of complexity turns out to be too high to perform full-scale computations. On the one hand, the reasons for this are the multitude of variables and constraints. On the other hand, feasible solutions to such problems may often be economically unacceptable or simply empty. Therefore, a heuristic is presented, according to which the relaxation of the limiting conditions influencing the solution’s feasibility and its economic profitability was parametrized. Under this heuristic, shifting the deadlines of selected orders is allowed. Also, the assignment of orders to vessels is separated from the allocation of vessels to piers in loading and unloading ports. The solution presented can be easily generalized by adding additional restrictions or features like indirect vessels, founding cost, or differentiation between materials.
{"title":"A heuristic approach to optimizing the loading of homogeneous marine cargo","authors":"Michał Bernardelli","doi":"10.37190/ord220201","DOIUrl":"https://doi.org/10.37190/ord220201","url":null,"abstract":"In this article, the optimal loading of homogeneous marine cargo is considered. A mathematical formulation in terms of a mixed-integer linear program can be given. Still, the level of complexity turns out to be too high to perform full-scale computations. On the one hand, the reasons for this are the multitude of variables and constraints. On the other hand, feasible solutions to such problems may often be economically unacceptable or simply empty. Therefore, a heuristic is presented, according to which the relaxation of the limiting conditions influencing the solution’s feasibility and its economic profitability was parametrized. Under this heuristic, shifting the deadlines of selected orders is allowed. Also, the assignment of orders to vessels is separated from the allocation of vessels to piers in loading and unloading ports. The solution presented can be easily generalized by adding additional restrictions or features like indirect vessels, founding cost, or differentiation between materials.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78058760","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}
M. Nasrollahi, Javaneh Ramezani, Mahmoud Sadraei, M. Fathi
Multi-criteria decision-making (MCDM) methods have been implemented in many fields. In the meantime, several methods have been proposed to obtain the weight of the criteria determined by various methods in different ways. In this paper, a new approach, called simultaneous interpretive structural modelling and weighting (SISMW), is proposed to solve a multi-criterion decision-making (MCDM) problem. Using SISMW, the weight of the criteria and the relationship between them could be determined simultaneously. In this approach, like the ISM method, pair comparison between criteria was made by the decision-maker to determine the relationships among the different criteria. With the help of this data, the weight of the criteria, as well as the causal (cause and effect) relationships between them, were determined in 12 steps. The main advantage of this method is that only one stage of data collection is required for obtaining weights and modelling, and so the research process may be faster. This may increase the reliability of the collected data because, in a one-step survey, the impact of time is minimized. This process can be useful for conceptualizing and developing theories to help decision makers understand the problem better.
{"title":"Simultaneous interpretive structural modelling and weighting (SISMW)","authors":"M. Nasrollahi, Javaneh Ramezani, Mahmoud Sadraei, M. Fathi","doi":"10.37190/ord220106","DOIUrl":"https://doi.org/10.37190/ord220106","url":null,"abstract":"Multi-criteria decision-making (MCDM) methods have been implemented in many fields. In the meantime, several methods have been proposed to obtain the weight of the criteria determined by various methods in different ways. In this paper, a new approach, called simultaneous interpretive structural modelling and weighting (SISMW), is proposed to solve a multi-criterion decision-making (MCDM) problem. Using SISMW, the weight of the criteria and the relationship between them could be determined simultaneously. In this approach, like the ISM method, pair comparison between criteria was made by the decision-maker to determine the relationships among the different criteria. With the help of this data, the weight of the criteria, as well as the causal (cause and effect) relationships between them, were determined in 12 steps. The main advantage of this method is that only one stage of data collection is required for obtaining weights and modelling, and so the research process may be faster. This may increase the reliability of the collected data because, in a one-step survey, the impact of time is minimized. This process can be useful for conceptualizing and developing theories to help decision makers understand the problem better.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89785229","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}
Z. Moazenzadeh, S. Saati, R. F. Saen, R. Matin, Sevan Sohraee
Although Data Envelopment Analysis (DEA) assumes that inputs and outputs take non-negative real values, in some realworld cases, data are integer-valued. In some situations, rounding a fractional value to the closest integer can lead to a misleading evaluation of efficiency and in some cases may lead to an infeasible projection point. To date, various radial and non-radial models have been presented. This paper proposes a slacks-based non-linear model that guarantees an integer-valued reference point for all integer targets. Also, the reference point of each target is feasible under the proposed model. The lack of a need to round answers to the closest whole value is an advantage of this method. In addition, the results of this model are compared with other models. An example is used to clarify the suggested method.
{"title":"A slacks-based nonlinear DEA model with integer data: an application to departments of the Islamic Azad University, Karaj Branch in Iran","authors":"Z. Moazenzadeh, S. Saati, R. F. Saen, R. Matin, Sevan Sohraee","doi":"10.37190/ord220306","DOIUrl":"https://doi.org/10.37190/ord220306","url":null,"abstract":"Although Data Envelopment Analysis (DEA) assumes that inputs and outputs take non-negative real values, in some realworld cases, data are integer-valued. In some situations, rounding a fractional value to the closest integer can lead to a misleading evaluation of efficiency and in some cases may lead to an infeasible projection point. To date, various radial and non-radial models have been presented. This paper proposes a slacks-based non-linear model that guarantees an integer-valued reference point for all integer targets. Also, the reference point of each target is feasible under the proposed model. The lack of a need to round answers to the closest whole value is an advantage of this method. In addition, the results of this model are compared with other models. An example is used to clarify the suggested method.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85725792","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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