Pub Date : 2019-08-05DOI: 10.1504/IJMOR.2019.10022967
Sonu Rajak, P. Parthiban, R. Dhanalakshmi
Multi-depot vehicle routing problem with simultaneous deliveries and pickups (MDVRPSDP) is a variant of classical vehicle routing problem (VRP), which has often encountered in real-life scenarios of transportation logistics; Where, vehicles are required to simultaneously deliver the goods and also pick-up some goods from the customers. The current scenario importance of reverse logistics activities has increased. Therefore it is necessary to determine efficient and effective vehicle routes for simultaneous delivery and pick-up activities. MDVRPSDP, which is very well-known non-deterministic polynomial-hard (NP-hard) and combinatorial optimisation (CO) problem, which requires metaheuristics to solve this type of problems. In this context, this article presents a hybrid metaheuristic which combines simulated annealing (SA), ant colony optimisation (ACO) and along with long-arc-broken removal heuristic approach for solving the MDVRPSDP. The preliminary results show that the proposed algorithm can provide good solutions.
{"title":"A hybrid metaheuristics approach for a multi-depot vehicle routing problem with simultaneous deliveries and pickups","authors":"Sonu Rajak, P. Parthiban, R. Dhanalakshmi","doi":"10.1504/IJMOR.2019.10022967","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022967","url":null,"abstract":"Multi-depot vehicle routing problem with simultaneous deliveries and pickups (MDVRPSDP) is a variant of classical vehicle routing problem (VRP), which has often encountered in real-life scenarios of transportation logistics; Where, vehicles are required to simultaneously deliver the goods and also pick-up some goods from the customers. The current scenario importance of reverse logistics activities has increased. Therefore it is necessary to determine efficient and effective vehicle routes for simultaneous delivery and pick-up activities. MDVRPSDP, which is very well-known non-deterministic polynomial-hard (NP-hard) and combinatorial optimisation (CO) problem, which requires metaheuristics to solve this type of problems. In this context, this article presents a hybrid metaheuristic which combines simulated annealing (SA), ant colony optimisation (ACO) and along with long-arc-broken removal heuristic approach for solving the MDVRPSDP. The preliminary results show that the proposed algorithm can provide good solutions.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125574849","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 : 2019-08-05DOI: 10.1504/IJMOR.2019.10022968
M. Allahdadi
In this paper, we propose a new method for solving interval linear programming (ILP) problems. For solving the ILP problems, two important items should be considered: feasibility (i.e., solutions satisfy all constraints) and optimality (i.e., solutions are optimal for at least a characteristic model). In some methods, a part of the solution space is infeasible (i.e., it violates any constraints) such as the best and worst cases method (BWC) proposed by Tong in 1994 and two-step method (TSM) proposed by Huang et al. in 1995. In some methods, the solution space is completely feasible, but is not completely optimal (i.e., some points of the solution space are not optimal) such as modified ILP method (MILP) proposed by Zhou et al. in 2009 and improved TSM (ITSM) proposed by Wang and Huang in 2014. Firstly, basis stability for the ILP problems is reviewed. Secondly, the solving methods are analysed from the point of view of the feasibility and optimality conditions. Later, a new method which modifies the TSM by using the basis stability approach is presented. This method gives a solution space that is not only completely feasible, but also completely optimal.
{"title":"A modified two-step method for solving interval linear programming problems","authors":"M. Allahdadi","doi":"10.1504/IJMOR.2019.10022968","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022968","url":null,"abstract":"In this paper, we propose a new method for solving interval linear programming (ILP) problems. For solving the ILP problems, two important items should be considered: feasibility (i.e., solutions satisfy all constraints) and optimality (i.e., solutions are optimal for at least a characteristic model). In some methods, a part of the solution space is infeasible (i.e., it violates any constraints) such as the best and worst cases method (BWC) proposed by Tong in 1994 and two-step method (TSM) proposed by Huang et al. in 1995. In some methods, the solution space is completely feasible, but is not completely optimal (i.e., some points of the solution space are not optimal) such as modified ILP method (MILP) proposed by Zhou et al. in 2009 and improved TSM (ITSM) proposed by Wang and Huang in 2014. Firstly, basis stability for the ILP problems is reviewed. Secondly, the solving methods are analysed from the point of view of the feasibility and optimality conditions. Later, a new method which modifies the TSM by using the basis stability approach is presented. This method gives a solution space that is not only completely feasible, but also completely optimal.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129025409","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 : 2019-08-05DOI: 10.1504/IJMOR.2019.10022969
Barun Khara, J. Dey, S. Mondal
In this article, an economic production quantity (EPQ) model with partially imperfect production system has been considered where both perfect and imperfect quality items are produced and demand of the product has been assumed as a function of selling price, reliability of the product and advertisement. Perfect quality items are ready for sale but imperfect quality items are reworked at a cost to become perfect one. Reworking cost, reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the time dependent development cost and also by improving the quality of the raw material used in the production system. Under such circumstances, a profit function has been developed and maximised by optimising the reliability parameter of the manufacturing system, reliability of the product and duration of production. Finally, the model has been illustrated with some numerical examples.
{"title":"Effects of product reliability dependent demand in an EPQ model considering partially imperfect production","authors":"Barun Khara, J. Dey, S. Mondal","doi":"10.1504/IJMOR.2019.10022969","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022969","url":null,"abstract":"In this article, an economic production quantity (EPQ) model with partially imperfect production system has been considered where both perfect and imperfect quality items are produced and demand of the product has been assumed as a function of selling price, reliability of the product and advertisement. Perfect quality items are ready for sale but imperfect quality items are reworked at a cost to become perfect one. Reworking cost, reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the time dependent development cost and also by improving the quality of the raw material used in the production system. Under such circumstances, a profit function has been developed and maximised by optimising the reliability parameter of the manufacturing system, reliability of the product and duration of production. Finally, the model has been illustrated with some numerical examples.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129938481","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 : 2019-08-05DOI: 10.1504/IJMOR.2019.10022964
A. Manocha, G. Taneja, Sukhvir Singh, R. Rishi
Stochastic model for a two-unit hot standby database system comprising of one operative (primary unit) and one hot standby unit has been developed. The primary unit acts as production unit which is synchronised with hot standby unit through online transfer of archive redo logs. The data being saved in the primary unit gets simultaneously stored in the hot standby unit. The different modes of failure of primary database have been considered. To avoid loss of data, random inspection of the standby unit is carried out by a database administrator (DBA) to see as to whether redo log files are created/updated in standby unit or not. The repair of the failed unit and creation/updation of redo log files are also done by the DBA. The system is analysed using semi-Markov process and regenerative point technique. Mathematical expressions for various performance measures of the system have been obtained along with cost-benefit analysis of the system. Numerical analysis has been done to validate the derived results. Bounds for various parameters have also been obtained with regard to profitability of the system.
{"title":"Modelling and analysis of two-unit hot standby database system with random inspection of standby unit","authors":"A. Manocha, G. Taneja, Sukhvir Singh, R. Rishi","doi":"10.1504/IJMOR.2019.10022964","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022964","url":null,"abstract":"Stochastic model for a two-unit hot standby database system comprising of one operative (primary unit) and one hot standby unit has been developed. The primary unit acts as production unit which is synchronised with hot standby unit through online transfer of archive redo logs. The data being saved in the primary unit gets simultaneously stored in the hot standby unit. The different modes of failure of primary database have been considered. To avoid loss of data, random inspection of the standby unit is carried out by a database administrator (DBA) to see as to whether redo log files are created/updated in standby unit or not. The repair of the failed unit and creation/updation of redo log files are also done by the DBA. The system is analysed using semi-Markov process and regenerative point technique. Mathematical expressions for various performance measures of the system have been obtained along with cost-benefit analysis of the system. Numerical analysis has been done to validate the derived results. Bounds for various parameters have also been obtained with regard to profitability of the system.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"40 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133022342","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 : 2019-08-05DOI: 10.1504/IJMOR.2019.10022963
S. Jeyakumar, E. Rameshkumar
A single server model, after completion of a bulk service, if there is no breakdown with probability (1 − ψ) and queue length (queue) ≥ 'a', then the bulk service continues, otherwise, the server performs closedown work is analysed. At the end of bulk service, if there is a breakdown occurs with probability (ψ), then the server performs renovation process. After that, if the queue is ≥ 'a', then he performs bulk service otherwise the server perform closedown work follows a vacation. After that, if the queue is less than 'a', then he takes at most 'M' vacations successively. After 'M' vacations, if the queue is still less than 'a', then he remains in the system. However, the customers enter the service station with probability 'p' (0 ≤ p ≤ 1) during multiple adaptive vacations. The probability generating function (PGF) of queue size and performance measures are obtained and cost model is developed.
在单服务器模型中，批量服务完成后，如果不出现故障(概率为(1−ψ)且队列长度(queue)≥' A ')，则批量服务继续进行，否则分析服务器执行关闭工作。在批量服务结束时，如果发生故障的概率(ψ)，则服务器执行修复过程。之后，如果队列≥a，则执行批量服务，否则服务器在休假后执行关闭工作。之后，如果队列小于a，则他最多连续休假M次。在'M'假期之后，如果排队人数仍然少于'a'，则他仍留在系统中。但在多个自适应假期中，顾客进入服务站的概率为p(0≤p≤1)。得到了队列大小和性能指标的概率生成函数(PGF)，建立了成本模型。
{"title":"A study on MX/G(a, b)/1 queue with server breakdown without interruption and controllable arrivals during multiple adaptive vacations","authors":"S. Jeyakumar, E. Rameshkumar","doi":"10.1504/IJMOR.2019.10022963","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022963","url":null,"abstract":"A single server model, after completion of a bulk service, if there is no breakdown with probability (1 − ψ) and queue length (queue) ≥ 'a', then the bulk service continues, otherwise, the server performs closedown work is analysed. At the end of bulk service, if there is a breakdown occurs with probability (ψ), then the server performs renovation process. After that, if the queue is ≥ 'a', then he performs bulk service otherwise the server perform closedown work follows a vacation. After that, if the queue is less than 'a', then he takes at most 'M' vacations successively. After 'M' vacations, if the queue is still less than 'a', then he remains in the system. However, the customers enter the service station with probability 'p' (0 ≤ p ≤ 1) during multiple adaptive vacations. The probability generating function (PGF) of queue size and performance measures are obtained and cost model is developed.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124966204","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 : 2019-08-02DOI: 10.1504/IJMOR.2019.101612
N. Tahat, E. S. Ismail, A. Aljammal
A cryptosystem allows a sender to send any confidential or private message using a receiver's public key and the receiver next confirms the integrity and validity of the received message using his own secret key. Cryptosystem algorithms can be categorised based on the type of security suppositions, for example discrete logarithm, factorisation, and elliptic curve hard problems, which are all currently believed to be unsolvable in a reasonable time of period. Recently, cryptosystems based on chaotic maps have been proposed. Due to some subtle and close relationship between the properties of traditional cryptosystems and chaotic-based systems, the idea of using chaotic in cryptography has received a great deal of attention from many cryptography's researchers. Therefore, to enhance system security, we explore the implementation of a cryptosystem algorithm based on both cryptographic and chaotic system characteristics. We also provide security against known cryptographic attacks and discuss the performance analysis of the developed system.
{"title":"A cryptosystem based on chaotic maps and factoring problems","authors":"N. Tahat, E. S. Ismail, A. Aljammal","doi":"10.1504/IJMOR.2019.101612","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.101612","url":null,"abstract":"A cryptosystem allows a sender to send any confidential or private message using a receiver's public key and the receiver next confirms the integrity and validity of the received message using his own secret key. Cryptosystem algorithms can be categorised based on the type of security suppositions, for example discrete logarithm, factorisation, and elliptic curve hard problems, which are all currently believed to be unsolvable in a reasonable time of period. Recently, cryptosystems based on chaotic maps have been proposed. Due to some subtle and close relationship between the properties of traditional cryptosystems and chaotic-based systems, the idea of using chaotic in cryptography has received a great deal of attention from many cryptography's researchers. Therefore, to enhance system security, we explore the implementation of a cryptosystem algorithm based on both cryptographic and chaotic system characteristics. We also provide security against known cryptographic attacks and discuss the performance analysis of the developed system.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"156 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130650560","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 : 2019-08-02DOI: 10.1504/IJMOR.2019.10022832
Nurul Huda Mohamed, S. Salhi, G. Nagy, N. A. Mohamed
The split delivery vehicle routing problem (SDVRP) is a relaxed version of the classical VRP where customers can be visited more than once. The SDVRP is also applicable for problems where one or more of the customers require a demand larger than the vehicle capacity. Constructive heuristics adapted from the parallel savings and the sweep methods are first proposed to generate a set of solutions which is then used in the new and more efficient set covering-based formulation which we put forward. An effective repair mechanism to remedy any infeasibility due to the set covering problem is presented. A reduced set of promising routes is used in our model, instead of the original set of routes, proposing and using well defined reduction schemes. This set covering-based approach is tested on large datasets from the literature with encouraging results. In brief, seven best solutions including ties are found among the 137 SDVRP instances.
{"title":"A matheuristic approach for the split delivery vehicle routing problem: an efficient set covering-based model with guided route generation schemes","authors":"Nurul Huda Mohamed, S. Salhi, G. Nagy, N. A. Mohamed","doi":"10.1504/IJMOR.2019.10022832","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022832","url":null,"abstract":"The split delivery vehicle routing problem (SDVRP) is a relaxed version of the classical VRP where customers can be visited more than once. The SDVRP is also applicable for problems where one or more of the customers require a demand larger than the vehicle capacity. Constructive heuristics adapted from the parallel savings and the sweep methods are first proposed to generate a set of solutions which is then used in the new and more efficient set covering-based formulation which we put forward. An effective repair mechanism to remedy any infeasibility due to the set covering problem is presented. A reduced set of promising routes is used in our model, instead of the original set of routes, proposing and using well defined reduction schemes. This set covering-based approach is tested on large datasets from the literature with encouraging results. In brief, seven best solutions including ties are found among the 137 SDVRP instances.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134230882","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 : 2019-08-02DOI: 10.1504/IJMOR.2019.10022827
G. Ayyappan, T. Deepa
This paper studies an M[x]/G(a, b)/1 queuing system with additional optional service, multiple vacation and setup time. After completing the first service, the customers may opt for the second service with probability α or leave the system with probability 1 ‒ α. After completing a bulk service, if the queue size is less than 'α', then the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than 'α', he leaves for another vacation and so on. This process continues until he finds at least 'α' customer in the queue. After a vacation, if the server finds at least 'α' customer waiting for service, he requires a setup time 'G' to start the service. After this setup, he serves a batch of ξ customers (a ≤ ξ ≤ b). Using supplementary variable technique, the probability generating function (PGF) of the queue size, expected queue length, expected waiting time, expected busy period and expected idle period are derived. Numerical illustrations are presented to visualise the effect of system parameters.
{"title":"Analysis of batch arrival bulk service queue with additional optional service multiple vacation and setup time","authors":"G. Ayyappan, T. Deepa","doi":"10.1504/IJMOR.2019.10022827","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022827","url":null,"abstract":"This paper studies an M[x]/G(a, b)/1 queuing system with additional optional service, multiple vacation and setup time. After completing the first service, the customers may opt for the second service with probability α or leave the system with probability 1 ‒ α. After completing a bulk service, if the queue size is less than 'α', then the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than 'α', he leaves for another vacation and so on. This process continues until he finds at least 'α' customer in the queue. After a vacation, if the server finds at least 'α' customer waiting for service, he requires a setup time 'G' to start the service. After this setup, he serves a batch of ξ customers (a ≤ ξ ≤ b). Using supplementary variable technique, the probability generating function (PGF) of the queue size, expected queue length, expected waiting time, expected busy period and expected idle period are derived. Numerical illustrations are presented to visualise the effect of system parameters.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124637608","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 : 2019-08-02DOI: 10.1504/IJMOR.2019.10022828
Imdat Kara, B. Kara
The paper 'polynomial formulation and heuristic-based approach for the k-travelling repairman problem' claims to present the first polynomial formulation for the k-travelling repairman problem (k-TRP). We first make some corrections on this formulation and we show that the first polynomial size formulation for k-TRP is the one proposed by Kara et al. (2008).
{"title":"Comments on the 'polynomial formulation and heuristic-based approach for the k-travelling repairman problem'","authors":"Imdat Kara, B. Kara","doi":"10.1504/IJMOR.2019.10022828","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.10022828","url":null,"abstract":"The paper 'polynomial formulation and heuristic-based approach for the k-travelling repairman problem' claims to present the first polynomial formulation for the k-travelling repairman problem (k-TRP). We first make some corrections on this formulation and we show that the first polynomial size formulation for k-TRP is the one proposed by Kara et al. (2008).","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132032900","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 : 2019-08-02DOI: 10.1504/IJMOR.2019.101616
D. Alexiou
A vehicle routing problem (VRP) is dealt with, where a fleet of vehicles serve (distribution/pickup) a given subset of demand locations in an urban network. A service time priority degree is given to a subset of demand locations. The aim of this paper is to find the least possible overall service time for vehicles to all the demand locations and particularly those that have a high degree of priority. The problem is dealt with in the context of graph theory and a corresponding method is proposed. The paper incorporates a numerical example of the proposed method.
{"title":"Minimising vehicle distribution duration considering service priority","authors":"D. Alexiou","doi":"10.1504/IJMOR.2019.101616","DOIUrl":"https://doi.org/10.1504/IJMOR.2019.101616","url":null,"abstract":"A vehicle routing problem (VRP) is dealt with, where a fleet of vehicles serve (distribution/pickup) a given subset of demand locations in an urban network. A service time priority degree is given to a subset of demand locations. The aim of this paper is to find the least possible overall service time for vehicles to all the demand locations and particularly those that have a high degree of priority. The problem is dealt with in the context of graph theory and a corresponding method is proposed. The paper incorporates a numerical example of the proposed method.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129115534","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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