Pub Date : 2018-06-05DOI: 10.1504/IJMOR.2018.10008489
T. Singh, Pandit Jagatananda Mishra, Hadibandhu Pattanayak
This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.
{"title":"An EOQ inventory model for deteriorating items with time-dependent deterioration rate, ramp-type demand rate and shortages","authors":"T. Singh, Pandit Jagatananda Mishra, Hadibandhu Pattanayak","doi":"10.1504/IJMOR.2018.10008489","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10008489","url":null,"abstract":"This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123767693","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10010956
M. Kassem, M. El-Hadidy
In this paper, we present a new study to minimise the expected value of the first meeting time between one of the searchers and the randomly moving target in the space (case of the multiplicative search technique) from a viewpoint of computational optimisation. We introduce the dual problem for the fuzzy multiobjective nonlinear programming problem (FMONLP) with inequality constraints which is obtained in El-Hadidy [International Journal of Computational Methods, Vol. 13, No. 6 (2016) 1650038 (38 pages)]. For this problem, we generalise the following classes of the vector-valued functions for fuzzy sets: weak strictly pseudo-quasi type I, strong pseudo-quasi type I, weak quasi strictly type I and weak strictly pseudo type I. We provide the fuzzy forms of Mond-Weir and general Mond-Weir duals for the involved problem and consequently various duality results are derived.
{"title":"On duality of fuzzy multiobjective optimisation problems: application to a multiplicative search technique","authors":"M. Kassem, M. El-Hadidy","doi":"10.1504/IJMOR.2018.10010956","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010956","url":null,"abstract":"In this paper, we present a new study to minimise the expected value of the first meeting time between one of the searchers and the randomly moving target in the space (case of the multiplicative search technique) from a viewpoint of computational optimisation. We introduce the dual problem for the fuzzy multiobjective nonlinear programming problem (FMONLP) with inequality constraints which is obtained in El-Hadidy [International Journal of Computational Methods, Vol. 13, No. 6 (2016) 1650038 (38 pages)]. For this problem, we generalise the following classes of the vector-valued functions for fuzzy sets: weak strictly pseudo-quasi type I, strong pseudo-quasi type I, weak quasi strictly type I and weak strictly pseudo type I. We provide the fuzzy forms of Mond-Weir and general Mond-Weir duals for the involved problem and consequently various duality results are derived.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128051195","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10010953
Jayanth Kumar Thenepalle, Purusotham Singamsetty
This paper deals with a variant of minimum spanning tree problem with multiple constraints, which includes degree, weight and budgeting constraints simultaneously together. To model the problem, a zero-one programming is incorporated. An exact solution procedure called pattern recognition technique-based lexi-search algorithm is developed. A suitable numerical illustration is given to check the applicability of the developed algorithm. Furthermore, the algorithm is programmed in C and tested with randomly generated hard instances, computational results are also reported. The overall results reveal that the proposed algorithm is fairly proficient in the sense of both acquiring the optimal solutions and computational time.
{"title":"An exact algorithm for multi-constrained minimum spanning tree problem","authors":"Jayanth Kumar Thenepalle, Purusotham Singamsetty","doi":"10.1504/IJMOR.2018.10010953","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010953","url":null,"abstract":"This paper deals with a variant of minimum spanning tree problem with multiple constraints, which includes degree, weight and budgeting constraints simultaneously together. To model the problem, a zero-one programming is incorporated. An exact solution procedure called pattern recognition technique-based lexi-search algorithm is developed. A suitable numerical illustration is given to check the applicability of the developed algorithm. Furthermore, the algorithm is programmed in C and tested with randomly generated hard instances, computational results are also reported. The overall results reveal that the proposed algorithm is fairly proficient in the sense of both acquiring the optimal solutions and computational time.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"40 1-8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123375521","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10010958
M. Mohammadi
The simultaneous selection factory's problem has been recently proposed as a generalisation in distributed permutation flow shop setting. In this paper, a new generalisation of simultaneous lot-sizing and scheduling decisions in permutation flow shop problem to the distributed permutation flow shop has been studied. Under this generalisation, it is not necessary to use all existing factories and each product cannot be produced in more than one factory. An exact formulation of the problem provided as a mixed integer program. In order to solve the problem, a heuristic procedure has been developed. To test the accuracy of heuristic, a lower bound is developed and compared against the optimal solution.
{"title":"Simultaneous selection factories, assignment products to factories, lot-sizing and scheduling in distributed permutation flow shop","authors":"M. Mohammadi","doi":"10.1504/IJMOR.2018.10010958","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010958","url":null,"abstract":"The simultaneous selection factory's problem has been recently proposed as a generalisation in distributed permutation flow shop setting. In this paper, a new generalisation of simultaneous lot-sizing and scheduling decisions in permutation flow shop problem to the distributed permutation flow shop has been studied. Under this generalisation, it is not necessary to use all existing factories and each product cannot be produced in more than one factory. An exact formulation of the problem provided as a mixed integer program. In order to solve the problem, a heuristic procedure has been developed. To test the accuracy of heuristic, a lower bound is developed and compared against the optimal solution.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115472878","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10010957
Nita H. Shah, Mrudul Y. Jani, U. Chaudhari
Nowadays, the use of the offer of delay payment is a very impressive tool to boost the market demand by attracting more customers. In this paper, we propose an inventory model, in which a retailer receives a permissible delay on the entire purchase expanse from the manufacturer (i.e., an up-stream full trade credit). In comparison, the retailer asks customers to pay some percent of purchasing cost at the time of receiving the product to reduce default risk (i.e., a down-stream partial trade credit). We consider the product with maximum fixed-life time deterioration and to reduce deterioration of the product, seller spends capital on preservation technology to preserve the item. Here, down-stream trade credit dependent quadratic demand is debated which is suitable for the products whose demand increases initially and afterward it starts to decrease. Industries like fashion and electronics most probably deals with this type of demand. The objective is to minimise the total relevant cost of retailer with respect to cycle time, down-stream trade credit and investment for preservation technology. The model is supported with numerical examples. Sensitivity analysis is done to derive insights for decision-maker. Graphical results, in three dimensions, are exhibited with supervisory decisions.
{"title":"Optimal ordering policy for deteriorating items under down-stream trade credit dependent quadratic demand with full up-stream trade credit and partial down-stream trade credit","authors":"Nita H. Shah, Mrudul Y. Jani, U. Chaudhari","doi":"10.1504/IJMOR.2018.10010957","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010957","url":null,"abstract":"Nowadays, the use of the offer of delay payment is a very impressive tool to boost the market demand by attracting more customers. In this paper, we propose an inventory model, in which a retailer receives a permissible delay on the entire purchase expanse from the manufacturer (i.e., an up-stream full trade credit). In comparison, the retailer asks customers to pay some percent of purchasing cost at the time of receiving the product to reduce default risk (i.e., a down-stream partial trade credit). We consider the product with maximum fixed-life time deterioration and to reduce deterioration of the product, seller spends capital on preservation technology to preserve the item. Here, down-stream trade credit dependent quadratic demand is debated which is suitable for the products whose demand increases initially and afterward it starts to decrease. Industries like fashion and electronics most probably deals with this type of demand. The objective is to minimise the total relevant cost of retailer with respect to cycle time, down-stream trade credit and investment for preservation technology. The model is supported with numerical examples. Sensitivity analysis is done to derive insights for decision-maker. Graphical results, in three dimensions, are exhibited with supervisory decisions.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120813480","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10010954
Deepali Khurana, R. Chaudhary
The objective of the present paper is to develop an inventory model for deteriorating products. In this paper the demand is a function of time and available stock level since the available stock level is an important tool to attract the customers. The shortages are allowed and partially backlogged. Depending on the rate of backlogging two different cases are developed. In the first case, the rate of backlogging is constant and in another case the backlogging rate is time dependent. Numerical example is given to illustrate the model and its significant feature. Sensitivity analysis is also carried out to study the effect of different parameters on total average cost.
{"title":"An order level inventory model for deteriorating stock product and time dependent demand under shortages","authors":"Deepali Khurana, R. Chaudhary","doi":"10.1504/IJMOR.2018.10010954","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010954","url":null,"abstract":"The objective of the present paper is to develop an inventory model for deteriorating products. In this paper the demand is a function of time and available stock level since the available stock level is an important tool to attract the customers. The shortages are allowed and partially backlogged. Depending on the rate of backlogging two different cases are developed. In the first case, the rate of backlogging is constant and in another case the backlogging rate is time dependent. Numerical example is given to illustrate the model and its significant feature. Sensitivity analysis is also carried out to study the effect of different parameters on total average cost.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130147590","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10004127
M. Lone, S. Mir, Imran Khan
Survey non-response refers to the failure to get a useable response from the respondent selected for the sample. Non-response may occur due to several reasons. The randomised response technique (RRT) presented by Warner (1965) used to estimate proportion of respondents to the sensitive questions without revealing his choice to the interviewer. In this article, the problem of optimal allocation in stratified sampling where RRT is used in presence of non-response, is formulated as an nonlinear programming problem (NLPP). The formulated problem is solved using branch and bound method and the results are obtained through LINGO.
{"title":"Allocation problem in the presence of non-response: a mathematical programming approach","authors":"M. Lone, S. Mir, Imran Khan","doi":"10.1504/IJMOR.2018.10004127","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10004127","url":null,"abstract":"Survey non-response refers to the failure to get a useable response from the respondent selected for the sample. Non-response may occur due to several reasons. The randomised response technique (RRT) presented by Warner (1965) used to estimate proportion of respondents to the sensitive questions without revealing his choice to the interviewer. In this article, the problem of optimal allocation in stratified sampling where RRT is used in presence of non-response, is formulated as an nonlinear programming problem (NLPP). The formulated problem is solved using branch and bound method and the results are obtained through LINGO.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126483195","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10010955
Deo Datta Aarya, Mukesh Kumar
In the proposed paper we develop an inventory model for instantaneous deteriorating items with multi variate function of demand rate. Generally, we observe that the demand for any product depends on so many factors, out of which the available stock and selling price are the main factors. So in this paper we have assumed that the demand rate is a function of stock and selling price. The production rate is taken as a function of demand rate. The shortages are allowed and it is assumed that the occurring shortages will be backlogged for which the backlogging rate is a function of waiting time. The numerical example and sensitivity exploration with respect to various parameters are also cited to illustrate the study.
{"title":"A production inventory model with selling price and stock sensitive demand under partial backlogging","authors":"Deo Datta Aarya, Mukesh Kumar","doi":"10.1504/IJMOR.2018.10010955","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010955","url":null,"abstract":"In the proposed paper we develop an inventory model for instantaneous deteriorating items with multi variate function of demand rate. Generally, we observe that the demand for any product depends on so many factors, out of which the available stock and selling price are the main factors. So in this paper we have assumed that the demand rate is a function of stock and selling price. The production rate is taken as a function of demand rate. The shortages are allowed and it is assumed that the occurring shortages will be backlogged for which the backlogging rate is a function of waiting time. The numerical example and sensitivity exploration with respect to various parameters are also cited to illustrate the study.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"231 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130621960","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 : 2018-03-29DOI: 10.1504/IJMOR.2018.10010952
B. Kumar
This paper deals with MX/G/1 queueing system in which arriving units join a single waiting line. Server provides the first essential service and one of the optional services among m available optional services, to all arriving units. After completion of both phases of services of each unit the server may take optional vacation with probability p. It is assumed that during any phase of service, server may stop working due to random failure and is sent for repair. Further it is assumed that arriving units may balk from the system when server is busy, vacation and under repair with probability -b = 1 – b. Using the probability generating functions we derive the queue size distribution at different time points as well as waiting time distribution. Finally numerical illustration is provided to analyse the sensitivity of different parameters on various performance measures.
{"title":"Unreliable bulk queueing model with optional services, Bernoulli vacation schedule and balking","authors":"B. Kumar","doi":"10.1504/IJMOR.2018.10010952","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010952","url":null,"abstract":"This paper deals with MX/G/1 queueing system in which arriving units join a single waiting line. Server provides the first essential service and one of the optional services among m available optional services, to all arriving units. After completion of both phases of services of each unit the server may take optional vacation with probability p. It is assumed that during any phase of service, server may stop working due to random failure and is sent for repair. Further it is assumed that arriving units may balk from the system when server is busy, vacation and under repair with probability -b = 1 – b. Using the probability generating functions we derive the queue size distribution at different time points as well as waiting time distribution. Finally numerical illustration is provided to analyse the sensitivity of different parameters on various performance measures.","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127714781","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 : 2018-02-08DOI: 10.1504/IJMOR.2018.10010220
T. Yen, Kuo-Hsiung Wang
The cloud computing is an emerging new computing paradigm which provides high reliability, high availability, and QoS-guaranteed computing services. The reliability and stability of power supply is one of the most important factors in successful cloud computing. In this paper, we compare three different configurations with imperfect coverage and standby switching failures based on system reliability and availability. The time-to-repair and the time-to-failure for each of the primary and warm standby components are assumed to be exponentially distributed. We derive the explicit expressions for mean time-to-failure, MTTF, and steady-state availability, AT(∞), for three configurations and perform a comparative analysis. Three configurations are ranked based on MTTF, AT(∞), and cost/benefit where benefit is either MTTF or AT(∞).
{"title":"Cost benefit analysis of three systems with imperfect coverage and standby switching failures","authors":"T. Yen, Kuo-Hsiung Wang","doi":"10.1504/IJMOR.2018.10010220","DOIUrl":"https://doi.org/10.1504/IJMOR.2018.10010220","url":null,"abstract":"The cloud computing is an emerging new computing paradigm which provides high reliability, high availability, and QoS-guaranteed computing services. The reliability and stability of power supply is one of the most important factors in successful cloud computing. In this paper, we compare three different configurations with imperfect coverage and standby switching failures based on system reliability and availability. The time-to-repair and the time-to-failure for each of the primary and warm standby components are assumed to be exponentially distributed. We derive the explicit expressions for mean time-to-failure, MTTF, and steady-state availability, AT(∞), for three configurations and perform a comparative analysis. Three configurations are ranked based on MTTF, AT(∞), and cost/benefit where benefit is either MTTF or AT(∞).","PeriodicalId":306451,"journal":{"name":"Int. J. Math. Oper. Res.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126317806","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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