Systems of components with increasing failure rates are considered. Switching from an operating component on standby can be performed at each instant of time. Optimal switching strategies, maximizing the time to the first failure of a component and to the total failure of a system are investigated. A new type of a strategy: the limit strategy is introduced. It is proved that this strategy is optimal, when there is no additional information on the state of the system. Some simple examples are considered.
{"title":"On some optimal switching strategies","authors":"M. Finkelstein","doi":"10.5784/17-0-186","DOIUrl":"https://doi.org/10.5784/17-0-186","url":null,"abstract":"Systems of components with increasing failure rates are considered. Switching from an operating component on standby can be performed at each instant of time. Optimal switching strategies, maximizing the time to the first failure of a component and to the total failure of a system are investigated. A new type of a strategy: the limit strategy is introduced. It is proved that this strategy is optimal, when there is no additional information on the state of the system. Some simple examples are considered.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75270779","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 is a personal account of marketing and selling Operations Research (OR) in South Africa. The author reflects on this activity that has occupied him over the past ten to fifteen years. The traditional marketing mix is possibly not ideal for selling a consulting service such as OR. The author shows how he used ingredients such as able people, physical evidence and process in selling the services of the group he represented. The main elements of being successful are: one or more success stories, credibility, a network of people (potential clients), quality staff, a sense of urgency within the group and a recognition that the client is always king.
{"title":"Tips, tricks and techniques in practicing OR - a different twist!","authors":"H. Ittmann","doi":"10.5784/17-0-189","DOIUrl":"https://doi.org/10.5784/17-0-189","url":null,"abstract":"This paper is a personal account of marketing and selling Operations Research (OR) in South Africa. The author reflects on this activity that has occupied him over the past ten to fifteen years. The traditional marketing mix is possibly not ideal for selling a consulting service such as OR. The author shows how he used ingredients such as able people, physical evidence and process in selling the services of the group he represented. The main elements of being successful are: one or more success stories, credibility, a network of people (potential clients), quality staff, a sense of urgency within the group and a recognition that the client is always king.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73900389","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}
A common replacement policy for technical systems consists in replacing a system by a new one after its economic lifetime, i.e. at that moment when its long-run maintenance cost rate is minimal. However, the strict application of the economic lifetime does not take into account the individual deviations of maintenance cost rates of single systems from the average cost development. Hence, Beichet proposed the total repair cost limit replacement policy: the system is replaced by a new one as soon as its total repair cost reaches or exceeds a given level. He modelled the repair cost development by functions of the Wiener process with drift. Here the same policy is considered under the assumption that the one-dimensional probability distribution of the process describing the repair cost development is given. In the examples analysed, applying the total repair cost limit replacement policy instead of the economic life-time leads to cost savings of between 4% and 30%. Finally, it is illustrated how to include the reliability aspect into the policy.
{"title":"A general approach to total repair cost limit replacement policies","authors":"F. Beichelt","doi":"10.5784/15-0-417","DOIUrl":"https://doi.org/10.5784/15-0-417","url":null,"abstract":"A common replacement policy for technical systems consists in replacing a system by a new one after its economic lifetime, i.e. at that moment when its long-run maintenance cost rate is minimal. However, the strict application of the economic lifetime does not take into account the individual deviations of maintenance cost rates of single systems from the average cost development. Hence, Beichet proposed the total repair cost limit replacement policy: the system is replaced by a new one as soon as its total repair cost reaches or exceeds a given level. He modelled the repair cost development by functions of the Wiener process with drift. Here the same policy is considered under the assumption that the one-dimensional probability distribution of the process describing the repair cost development is given. In the examples analysed, applying the total repair cost limit replacement policy instead of the economic life-time leads to cost savings of between 4% and 30%. Finally, it is illustrated how to include the reliability aspect into the policy.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74194890","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}
Stochastic analysis of a two unit system with vacation period for the repair facility after the completion of m repairs is studied. All the underlying distributions are assumed to be non-Markovian. The reliability and availability analysis for such a system is studied. A numerical illustration is given.
{"title":"Stochastic analysis of a two unit system with vacation for the repair facility after M repairs","authors":"J. P. S. Yadavalli, M. Botha","doi":"10.5784/16-2-408","DOIUrl":"https://doi.org/10.5784/16-2-408","url":null,"abstract":"Stochastic analysis of a two unit system with vacation period for the repair facility after the completion of m repairs is studied. All the underlying distributions are assumed to be non-Markovian. The reliability and availability analysis for such a system is studied. A numerical illustration is given.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83122471","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}
An overview is given of Community Operations Research and of the connection between OR and development. The RDP is the main framework for development in South Africa, and its present state is described. Some suggestions are made as to ways in which ORSSA could support the RDP and development in South Africa.
{"title":"Community OR and OR for development","authors":"P. Fourie","doi":"10.5784/15-0-416","DOIUrl":"https://doi.org/10.5784/15-0-416","url":null,"abstract":"An overview is given of Community Operations Research and of the connection between OR and development. The RDP is the main framework for development in South Africa, and its present state is described. Some suggestions are made as to ways in which ORSSA could support the RDP and development in South Africa.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78715172","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 paper, a stochastic network is an undirected graph with unreliable edges and absolutely reliable nodes. Its connectedness probability is determined by reliability preserving network reduction. The principle of this method consists in splitting the underlying deterministic graph of the stochastic network into two edge-disjoint subgraphs via a separating node set. One of the subgraphs is replaced with a simpler structured graph (replacement graph) in such a way that the interesting reliability criterion of the original stochastic network is retained. Special attention is given to the construction of suitable replacement graphs. The case of a 3-point separating node set is considered in more detail.
{"title":"Combinatorial methods in netwotk reliability analysis","authors":"F. Beichelt","doi":"10.5784/16-1-412","DOIUrl":"https://doi.org/10.5784/16-1-412","url":null,"abstract":"In this paper, a stochastic network is an undirected graph with unreliable edges and absolutely reliable nodes. Its connectedness probability is determined by reliability preserving network reduction. The principle of this method consists in splitting the underlying deterministic graph of the stochastic network into two edge-disjoint subgraphs via a separating node set. One of the subgraphs is replaced with a simpler structured graph (replacement graph) in such a way that the interesting reliability criterion of the original stochastic network is retained. Special attention is given to the construction of suitable replacement graphs. The case of a 3-point separating node set is considered in more detail.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78745773","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 many studies where data are collected on several variables, there is a motivation to find if fewer variables would provide almost as much information. Variance of a variable about its mean is the common statistical measure of information content, and that is used here. We are interested whether the variability in one variable is sufficiently correlated with that in one or more of the other variables that the first variable is redundant. We wish to find one or more ‘principal variables’ that sufficiently reflect the information content in all the original variables. The paper explains the method of principal variables and reports experiments using the technique to see if just a few variables are sufficient to reflect the information in 11 socioeconomic variables on 130 countries from a World Bank (WB) database. While the method of principal variables is highly successful in a statistical sense, the WB data varies greatly from year to year, demonstrating that fewer variables wo uld be inadequate for this data.
{"title":"An experiment on selecting most informative variables in socio-economic data","authors":"L. Jenkins","doi":"10.5784/19-0-181","DOIUrl":"https://doi.org/10.5784/19-0-181","url":null,"abstract":"In many studies where data are collected on several variables, there is a motivation to find if fewer variables would provide almost as much information. Variance of a variable about its mean is the common statistical measure of information content, and that is used here. We are interested whether the variability in one variable is sufficiently correlated with that in one or more of the other variables that the first variable is redundant. We wish to find one or more ‘principal variables’ that sufficiently reflect the information content in all the original variables. The paper explains the method of principal variables and reports experiments using the technique to see if just a few variables are sufficient to reflect the information in 11 socioeconomic variables on 130 countries from a World Bank (WB) database. While the method of principal variables is highly successful in a statistical sense, the WB data varies greatly from year to year, demonstrating that fewer variables wo uld be inadequate for this data.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"88 2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84051775","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}
Financial economists and actuaries do not always talk the same language. One particular difference of concern to actuaries is the method of treatment (or non-treatment) of the liabilities of an investor in the portfolio selection problem. Another difference relates to the way in which liabilities are valued. In this paper, these differences are discussed and possible way forward are suggested.
{"title":"Assets, liabilities and risks","authors":"R. Thomson","doi":"10.5784/17-0-188","DOIUrl":"https://doi.org/10.5784/17-0-188","url":null,"abstract":"Financial economists and actuaries do not always talk the same language. One particular difference of concern to actuaries is the method of treatment (or non-treatment) of the liabilities of an investor in the portfolio selection problem. Another difference relates to the way in which liabilities are valued. In this paper, these differences are discussed and possible way forward are suggested.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"25 5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88879836","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 article gives an overview of the combined use of object-oriented programming and simulation, with the objective of analysing and planning the logistic functions of a firm. An object-oriented simulation approach is used to evaluate the reception and distribution function of a courier firm. Both the reception of and operations (sorting) on the parcels in the plant were simulated. The first objective of the firm was to analyse the productivity of the conveyer belts and workers in the sorting plant of the courier firm. The firm's utilisation of most of its resources is fairly good, but it is possible to obtain a more efficient process by restructuring its activities. Results from the simulation study showed an imbalance in the capacities of the workstations. Some of the workers, especially those to the end of the conveyer belts, spent almost all of their time waiting for parcels to reach them, while those at the beginning were working at maximum capacity. This is mainly due to the layout and structure of the system. The biggest bottleneck in the system was the capacity of the coupling between two of the conveyer belts. The conclusion was that the firm should seriously consider redesigning the plant. This is the first computer model of the firm's business activities that can be used as a planning tool, and fills a gap in its current planning function. This simulation can be used to determine where and how workers should be applied in the sorting process. The complete simulation model reaches its potential when used as a strategic operational tool, by forecasting the expected results from changing operations and plant layout. A new plant layout has been proposed to the firm, which the model shows to result in substantial improvements in the productivity of the workers, allowing a reduction in their numbers.
{"title":"Logistiese beplanning met behulp van simulasiemodellering: 'n Gevallestudie","authors":"Loubser Js, S. E. Visagie, W. Pienaar","doi":"10.5784/18-0-182","DOIUrl":"https://doi.org/10.5784/18-0-182","url":null,"abstract":"This article gives an overview of the combined use of object-oriented programming and simulation, with the objective of analysing and planning the logistic functions of a firm. An object-oriented simulation approach is used to evaluate the reception and distribution function of a courier firm. Both the reception of and operations (sorting) on the parcels in the plant were simulated. The first objective of the firm was to analyse the productivity of the conveyer belts and workers in the sorting plant of the courier firm. The firm's utilisation of most of its resources is fairly good, but it is possible to obtain a more efficient process by restructuring its activities. Results from the simulation study showed an imbalance in the capacities of the workstations. Some of the workers, especially those to the end of the conveyer belts, spent almost all of their time waiting for parcels to reach them, while those at the beginning were working at maximum capacity. This is mainly due to the layout and structure of the system. The biggest bottleneck in the system was the capacity of the coupling between two of the conveyer belts. The conclusion was that the firm should seriously consider redesigning the plant. This is the first computer model of the firm's business activities that can be used as a planning tool, and fills a gap in its current planning function. This simulation can be used to determine where and how workers should be applied in the sorting process. The complete simulation model reaches its potential when used as a strategic operational tool, by forecasting the expected results from changing operations and plant layout. A new plant layout has been proposed to the firm, which the model shows to result in substantial improvements in the productivity of the workers, allowing a reduction in their numbers.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89326007","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}
Controlled burning is a necessary and regular activity in Mkuze Game Reserve, South Africa. Predicting the rate and extent of fire spread in controlled burning operations is, therefore, an important management objective. In this paper we evaluate a cellular automaton model for fire spread in terms of this objective using empirical data for two case studies in Mkuze Game Reserve. Incorporating data relating to factors such as temperature reduction in the early evening, subsequent dew formation and increased fuel moisture content, the model was found to closely resemble the observed fire behaviour.
{"title":"Spatial fire modeling in Mkuze Game Reserve: A case study*","authors":"S. G. Berjak, J. Hearne","doi":"10.5784/18-0-184","DOIUrl":"https://doi.org/10.5784/18-0-184","url":null,"abstract":"Controlled burning is a necessary and regular activity in Mkuze Game Reserve, South Africa. Predicting the rate and extent of fire spread in controlled burning operations is, therefore, an important management objective. In this paper we evaluate a cellular automaton model for fire spread in terms of this objective using empirical data for two case studies in Mkuze Game Reserve. Incorporating data relating to factors such as temperature reduction in the early evening, subsequent dew formation and increased fuel moisture content, the model was found to closely resemble the observed fire behaviour.","PeriodicalId":30587,"journal":{"name":"ORiON","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84628935","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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