This article considers a structural equation useful for characterizing the order quantity of several inventory models. A correct interpretation of this equation is provided and it is stressed that the equation should be used in conjunction with another equation for the reorder point. Failure to do so may give rise to improper interpretations and invalid conclusions. A specific case like this is cited for the sake of illustration.
{"title":"On the use of a structural equation for determining inventory order quantities","authors":"C. Das","doi":"10.1002/NAV.3800320415","DOIUrl":"https://doi.org/10.1002/NAV.3800320415","url":null,"abstract":"This article considers a structural equation useful for characterizing the order quantity of several inventory models. A correct interpretation of this equation is provided and it is stressed that the equation should be used in conjunction with another equation for the reorder point. Failure to do so may give rise to improper interpretations and invalid conclusions. A specific case like this is cited for the sake of illustration.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130144267","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}
Control charts are widely used for process surveillance. The design of a control chart refers to the choice of sample size, the width of the control limits, and the interval between samples. Economic designs have been widely investigated and shown to be an effective method of determining control chart parameters. This article describes two different manufacturing process models to which the X¯ control chart is applied: The first model assumes that the process continues in operation while searches for the assignable cause are made, and the second assumes that the process must be shut down during the search. Economic models of the control chart for these two manufacturing process models are developed, and the sensitivity of the control chart parameters to the choice of model is explored. It is shown that the choice of the proper manufacturing process model is critical because selection of an inappropriate process model may result in significant economic penalties.
{"title":"Economic design of X control charts for two manufacturing process models","authors":"M. R. Panagos, Russell Heikes, D. Montgomery","doi":"10.1002/NAV.3800320410","DOIUrl":"https://doi.org/10.1002/NAV.3800320410","url":null,"abstract":"Control charts are widely used for process surveillance. The design of a control chart refers to the choice of sample size, the width of the control limits, and the interval between samples. Economic designs have been widely investigated and shown to be an effective method of determining control chart parameters. This article describes two different manufacturing process models to which the X¯ control chart is applied: The first model assumes that the process continues in operation while searches for the assignable cause are made, and the second assumes that the process must be shut down during the search. Economic models of the control chart for these two manufacturing process models are developed, and the sensitivity of the control chart parameters to the choice of model is explored. It is shown that the choice of the proper manufacturing process model is critical because selection of an inappropriate process model may result in significant economic penalties.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123010690","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 shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment-type constraints along with other constraints. Several unresolved questions of a number-theoretic nature are mentioned at the conclusion of the article.
{"title":"Aggregating assignment constraints","authors":"P. Fishburn, G. Kochenberger","doi":"10.1002/NAV.3800320412","DOIUrl":"https://doi.org/10.1002/NAV.3800320412","url":null,"abstract":"This article shows how simple systems of linear equations with {0,1} variables can be aggregated into a single linear equation whose {0,1} solutions are identical to the solutions of the original system. Structures of the original systems are exploited to keep the aggregator's integer coefficients from becoming unnecessarily large. The results have potential application in integer programming and information theory, especially for problems that contain assignment-type constraints along with other constraints. Several unresolved questions of a number-theoretic nature are mentioned at the conclusion of the article.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116660128","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}
If the probability of “failure” in a multivariate renewal process of the “success run” type is very small, then if certain conditions are imposed on the components of the renewals, the joint distribution of their total durations is approximately exponential with all mass along one line. This result is applied to a 2-i.i.d. unit repairable system of the “1 out of 2:G, Cold Standby” type.
{"title":"Asymptotic distribution of some multivariate “success run” renewal processes, applied to a 2-i.i.d. unit repairable system","authors":"D. Wiens","doi":"10.1002/NAV.3800320405","DOIUrl":"https://doi.org/10.1002/NAV.3800320405","url":null,"abstract":"If the probability of “failure” in a multivariate renewal process of the “success run” type is very small, then if certain conditions are imposed on the components of the renewals, the joint distribution of their total durations is approximately exponential with all mass along one line. This result is applied to a 2-i.i.d. unit repairable system of the “1 out of 2:G, Cold Standby” type.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133062780","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}
Abstract : A promising approach to failure modeling, in particular to developing failure-time distributions, is discussed. Under this approach, system state or wear and tear is modeled by an approximately chosen random process, eg, a diffusion process; and the occurrences of fatal shocks are modeled by a Poisson process whose rate function is state dependent. The system is said to fail when either wear and tear accumulates beyond in acceptable or safe level or a fatal shock occurs. This approach has significant merit. First it provides revealing new insights into most of the famous and frequently used lifetime distributions in reliability theory. Moreover, it suggests intuitively appealing ways for enhancing those standard models. Indeed, this approach provides a means of representing the underlying dynamics inherent in failure processes. Reasonable postulates for the dynamics of failure should lend credence to prediction and estimation of reliability, maintainability, and availability. In other words, accuracy of representation could lead to better, more reliable prediction of failure. (Author)
{"title":"On failure modeling","authors":"A. Lemoine, M. L. Wenocur","doi":"10.1002/NAV.3800320312","DOIUrl":"https://doi.org/10.1002/NAV.3800320312","url":null,"abstract":"Abstract : A promising approach to failure modeling, in particular to developing failure-time distributions, is discussed. Under this approach, system state or wear and tear is modeled by an approximately chosen random process, eg, a diffusion process; and the occurrences of fatal shocks are modeled by a Poisson process whose rate function is state dependent. The system is said to fail when either wear and tear accumulates beyond in acceptable or safe level or a fatal shock occurs. This approach has significant merit. First it provides revealing new insights into most of the famous and frequently used lifetime distributions in reliability theory. Moreover, it suggests intuitively appealing ways for enhancing those standard models. Indeed, this approach provides a means of representing the underlying dynamics inherent in failure processes. Reasonable postulates for the dynamics of failure should lend credence to prediction and estimation of reliability, maintainability, and availability. In other words, accuracy of representation could lead to better, more reliable prediction of failure. (Author)","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123088263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We discuss a time dependent optimal ordering policy for a finite horizon inventory system for which the provision of service is essential and thus no stockout is allowed. It is assumed that the system can place an order at any point in time during the horizon when it cannot meet the customer's demand and that lead time is negligible. The demand is considered to be distributed as a compound Poisson process with known parameters and the functional equation approach of dynamic programming is used to formulate the objective function. An algorithm has been developed to obtain the solution for all the cases. In addition, analytical solutions of the basic equation under two limiting conditions are presented.
{"title":"A time dependent continuous review inventory model with compound poisson demand","authors":"P. Banerjee, A. Hamidi-Noori, W. Knight","doi":"10.1002/NAV.3800320307","DOIUrl":"https://doi.org/10.1002/NAV.3800320307","url":null,"abstract":"We discuss a time dependent optimal ordering policy for a finite horizon inventory system for which the provision of service is essential and thus no stockout is allowed. It is assumed that the system can place an order at any point in time during the horizon when it cannot meet the customer's demand and that lead time is negligible. The demand is considered to be distributed as a compound Poisson process with known parameters and the functional equation approach of dynamic programming is used to formulate the objective function. An algorithm has been developed to obtain the solution for all the cases. In addition, analytical solutions of the basic equation under two limiting conditions are presented.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129933343","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 bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.
Mitchell和Paulson[17]在b = c = 0情况下的二元负二项分布与Edwards和Gurland[4]和Subrahmaniam[19,20]的事故倾向模型等效。然后导出了其联合概率函数的对角级数展开式。还考虑了该分布的另外两种表述:(i)作为混合模型，表明它是如何作为Wicksell-Kibble二元伽马分布的离散模拟而产生的，以及(ii)作为移民线性出生和死亡过程的结果。
{"title":"On the bivariate negative binomial distribution of Mitchell and Paulson","authors":"S. Ong, P. A. Lee","doi":"10.1002/NAV.3800320309","DOIUrl":"https://doi.org/10.1002/NAV.3800320309","url":null,"abstract":"The bivariate negative binomial distribution of Mitchell and Paulson [17] for the case b = c = 0 is shown to be equivalent to the accident proneness model of Edwards and Gurland [4] and Subrahmaniam [19,20]. The diagonal series expansion of its joint probability function is then derived. Two other formulations of this distribution are also considered: (i) as a mixture model, which showed how it arises as the discrete analogue to the Wicksell-Kibble bivariate gamma distribution, and (ii) as a consequence of the linear birth-and-death process with immigration.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124594215","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}
Least absolute value (LAV) regression has become a widely accepted alternative to least squares regression. This has come about as the result of advancements in statistical theory and computational procedures to obtain LAV estimates. Computer codes are currently available to solve a wide range of LAV problems including the best subset regression. The purpose of this article is to study the use of penalty calculations and other branching rules in developing the solution tree for the best subset LAV regression.
{"title":"Penalty calculations and branching rules in a LAV best subset procedure","authors":"R. Armstrong, P. Beck","doi":"10.1002/NAV.3800320305","DOIUrl":"https://doi.org/10.1002/NAV.3800320305","url":null,"abstract":"Least absolute value (LAV) regression has become a widely accepted alternative to least squares regression. This has come about as the result of advancements in statistical theory and computational procedures to obtain LAV estimates. Computer codes are currently available to solve a wide range of LAV problems including the best subset regression. The purpose of this article is to study the use of penalty calculations and other branching rules in developing the solution tree for the best subset LAV regression.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124168168","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 concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.
{"title":"One‐facility location with rectilinear tour distances","authors":"Z. Drezner, G. Steiner, G. O. Wesolowsky","doi":"10.1002/NAV.3800320304","DOIUrl":"https://doi.org/10.1002/NAV.3800320304","url":null,"abstract":"This article concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131399262","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 considers the problem of locating multiple new facilities to minimize the cost function consisting of the sum of weighted distances among new facilities and between new and existing facilities. The hyperboloid approximate procedure (HAP) is probably the most widely used approach for solving this problem. In this article, an optimality condition for this problem is derived and a method to accelerate the convergence rate of the HAP for the case of Euclidean distances is presented. From the numerical results presented in this article, it can be concluded that the performance of the new algorithm is superior to the performance of the original HAP.
{"title":"Acceleration of the HAP approach for the multifacility location problem","authors":"C. Charalambous","doi":"10.1002/NAV.3800320303","DOIUrl":"https://doi.org/10.1002/NAV.3800320303","url":null,"abstract":"This article considers the problem of locating multiple new facilities to minimize the cost function consisting of the sum of weighted distances among new facilities and between new and existing facilities. The hyperboloid approximate procedure (HAP) is probably the most widely used approach for solving this problem. In this article, an optimality condition for this problem is derived and a method to accelerate the convergence rate of the HAP for the case of Euclidean distances is presented. From the numerical results presented in this article, it can be concluded that the performance of the new algorithm is superior to the performance of the original HAP.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126251651","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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