On presente une solution a la programmation quadratique en presence de la contrainte de la forme Ax≤b en utilisant l'approche du probleme de complementarite lineaire
利用线性互补问题的方法，给出了存在形式Ax≤b约束的二次规划的解
{"title":"A method for quadratic programming","authors":"Shang-Wang Chang","doi":"10.1002/NAV.3800330312","DOIUrl":"https://doi.org/10.1002/NAV.3800330312","url":null,"abstract":"On presente une solution a la programmation quadratique en presence de la contrainte de la forme Ax≤b en utilisant l'approche du probleme de complementarite lineaire","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123892910","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 we examine the one- and two-sided sampling plans for the exponential distribution. Solutions are provided for several situations arising out of the assumptions on the knowledge of the parameters of the distribution. The values of the constants are tabled in the special case of p1 = p2 for the two-sided plans.
{"title":"One- and two-sided sampling plans based on the exponential distribution","authors":"S. Kocherlakota, N. Balakrishnan","doi":"10.1002/NAV.3800330315","DOIUrl":"https://doi.org/10.1002/NAV.3800330315","url":null,"abstract":"In this paper we examine the one- and two-sided sampling plans for the exponential distribution. Solutions are provided for several situations arising out of the assumptions on the knowledge of the parameters of the distribution. The values of the constants are tabled in the special case of p1 = p2 for the two-sided plans.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128206548","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 network model incorporating stochastic features is considered. The model represents a complex sequential process where an object or system moves through a succession of states (nodes) and operating modes (classes) in the course of carrying out its function (fulfilling its purpose). Transitions between states and operating modes occur in a possibly random manner and require (consume) some resource in randomly varying amounts. We discuss the routing behavior and resource requirements of a typical object as it moves through (and eventually out of) the network. We then shift our focus from a single object and its odyssey to the network as a whole, where time is the resource and many objects are entering the network according to a possibly nonhomogeneous Poisson pattern; in this vein, we discuss the evolution of the network over time. Finally, we consider some applications of the formulation, and results.
{"title":"A stochastic network formulation for complex sequential processes","authors":"A. Lemoine","doi":"10.1002/NAV.3800330309","DOIUrl":"https://doi.org/10.1002/NAV.3800330309","url":null,"abstract":"A network model incorporating stochastic features is considered. The model represents a complex sequential process where an object or system moves through a succession of states (nodes) and operating modes (classes) in the course of carrying out its function (fulfilling its purpose). Transitions between states and operating modes occur in a possibly random manner and require (consume) some resource in randomly varying amounts. We discuss the routing behavior and resource requirements of a typical object as it moves through (and eventually out of) the network. We then shift our focus from a single object and its odyssey to the network as a whole, where time is the resource and many objects are entering the network according to a possibly nonhomogeneous Poisson pattern; in this vein, we discuss the evolution of the network over time. Finally, we consider some applications of the formulation, and results.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134518763","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}
Capacity expansion models are typically formulated in the context of some finite horizon. Because the firm lasts longer than the horizon, a bias can enter into the optimal solution from the model horizon chosen. Recently, Grinold [8] has proposed a “dual‐equilibrium method” for ameliorating possible distortions. Although the dual‐equilibrium method has superior analytical properties to other methods, it is conceptually more complex. In this paper it is shown that there are situations where the “primal‐equilibrium” approach of Manne [15] provides equivalent results and that the use of annualized capital costs in the objective function, although somewhat less efficient, results in a similar model.
{"title":"End effects in capacity expansion models with finite horizons","authors":"F. Murphy, A. Soyster","doi":"10.1002/NAV.3800330303","DOIUrl":"https://doi.org/10.1002/NAV.3800330303","url":null,"abstract":"Capacity expansion models are typically formulated in the context of some finite horizon. Because the firm lasts longer than the horizon, a bias can enter into the optimal solution from the model horizon chosen. Recently, Grinold [8] has proposed a “dual‐equilibrium method” for ameliorating possible distortions. Although the dual‐equilibrium method has superior analytical properties to other methods, it is conceptually more complex. In this paper it is shown that there are situations where the “primal‐equilibrium” approach of Manne [15] provides equivalent results and that the use of annualized capital costs in the objective function, although somewhat less efficient, results in a similar model.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130192573","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 system receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. The system fails when the accumulated damage exceeds a fixed threshold. Upon failure the system is replaced by a new one. The damage process is controlled by means of a maintenance policy. There are M possible maintenance actions. Given that a maintenance action m is employed, then the cumulative damage decreases at rate rm. Replacement costs and maintenance costs are considered. The objective is to determine an optimal maintenance policy under the following optimality criteria: (1) long‐run average cost; (2) total expected discounted cost over an infinite horizon. For a diffusion approximation, we show that the optimal maintenance expenditure rate is monotonically increasing in the cumulative damage level.
{"title":"Optimal maintenance policy for stochastically failing equipment: A diffusion approximation","authors":"D. Zuckerman","doi":"10.1002/NAV.3800330311","DOIUrl":"https://doi.org/10.1002/NAV.3800330311","url":null,"abstract":"A system receives shocks at random points of time. Each shock causes a random amount of damage which accumulates over time. The system fails when the accumulated damage exceeds a fixed threshold. Upon failure the system is replaced by a new one. The damage process is controlled by means of a maintenance policy. There are M possible maintenance actions. Given that a maintenance action m is employed, then the cumulative damage decreases at rate rm. Replacement costs and maintenance costs are considered. The objective is to determine an optimal maintenance policy under the following optimality criteria: (1) long‐run average cost; (2) total expected discounted cost over an infinite horizon. For a diffusion approximation, we show that the optimal maintenance expenditure rate is monotonically increasing in the cumulative damage level.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130881587","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 alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r 1,2, …,r, … in sucession. The time spent in state i during any cycle has cumulative distribution function Fi, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], let Ui(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (Ui(T), 1 ≤ i ≤ r) (properly normed and centered) as T → ∞.
{"title":"The asymptotic joint distribution of the state occupancy times in an alternating renewal process","authors":"J. Angus","doi":"10.1002/NAV.3800330304","DOIUrl":"https://doi.org/10.1002/NAV.3800330304","url":null,"abstract":"An alternating renewal process starts at time zero and visits states 1,2,…,r, 1,2, …,r 1,2, …,r, … in sucession. The time spent in state i during any cycle has cumulative distribution function Fi, and the sojourn times in each state are mutually independent, positive and nondegenerate random variables. In the fixed time interval [0,T], let Ui(T) denote the total amount of time spent in state i. In this note, a central limit theorem is proved for the random vector (Ui(T), 1 ≤ i ≤ r) (properly normed and centered) as T → ∞.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134074254","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}
Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A2 statistic calculated from a set zi of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A2 is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.
{"title":"Tests for the Extreme Value and Weibull Distributions Based on Normalized Spacings.","authors":"R. Lockhart, F. O'Reilly, M. Stephens","doi":"10.1002/NAV.3800330307","DOIUrl":"https://doi.org/10.1002/NAV.3800330307","url":null,"abstract":"Discussed in this article are tests for the extreme-value distribution, or, equivalently, for the two-parameter Weibull distribution when parameters are unknown and the sample may be censored. The three tests investigated are based on the median, the mean, and the Anderson-Darling A2 statistic calculated from a set zi of values derived from the spacings of the sample. The median and the mean have previously been discussed by Mann, Scheuer, and Fertig [10] and by Tiku and Singh [14]. Asymptotic distributions and points are given for the test statistics, based on recently developed theory, and power studies are conducted to compare them with each other and with two other statistics suitable for the test. Of the normalized spacings tests, A2 is recommended overall; the mean also gives good power in many situations, but can be nonconsistent.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122572563","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 approximation for P(X2 + Y2 ≤ K2σ21) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ21 and σ22 and σ1 ≥ σ2. Also, we provide asymptotic expressions for the probabilities for large values of β = K2(1 - c2)/4c2 where c = σ2/σ1. These are illustrated by comparing with values tabulated by Harter [6]. Solution of K for specified P and c is also considered. The main point of this note is that simple and easily calculable approximations for P and K can be developed and there is no need for numerical evaluation of integrals.
{"title":"A note on circular error probabilities","authors":"Z. Govindarajulu","doi":"10.1002/NAV.3800330308","DOIUrl":"https://doi.org/10.1002/NAV.3800330308","url":null,"abstract":"An approximation for P(X2 + Y2 ≤ K2σ21) based on an unpublished result of Kleinecke is derived, where X and Y are independent normal variables having zero means and variances σ21 and σ22 and σ1 ≥ σ2. Also, we provide asymptotic expressions for the probabilities for large values of β = K2(1 - c2)/4c2 where c = σ2/σ1. These are illustrated by comparing with values tabulated by Harter [6]. Solution of K for specified P and c is also considered. The main point of this note is that simple and easily calculable approximations for P and K can be developed and there is no need for numerical evaluation of integrals.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126696127","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 optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.
{"title":"A forward network simplex algorithm for solving multiperiod network flow problems","authors":"J. Aronson, B. Chen","doi":"10.1002/NAV.3800330310","DOIUrl":"https://doi.org/10.1002/NAV.3800330310","url":null,"abstract":"An optimization model which is frequently used to assist decision makers in the areas of resource scheduling, planning, and distribution is the minimum cost multiperiod network flow problem. This model describes network structure decision-making problems over time. Such problems arise in the areas of production/distribution systems, economic planning, communication systems, material handling systems, traffic systems, railway systems, building evacuation systems, energy systems, as well as in many others. Although existing network solution techniques are efficient, there are still limitations to the size of problems that can be solved. To date, only a few researchers have taken the multiperiod structure into consideration in devising efficient solution methods. Standard network codes are usually used because of their availability and perceived efficiency. In this paper we discuss the development, implementation, and computational testing of a new technique, the forward network simplex method, for solving linear, minimum cost, multiperiod network flow problems. The forward network simplex method is a forward algorithm which exploits the natural decomposition of multiperiod network problems by limiting its pivoting activity. A forward algorithm is an approach to solving dynamic problems by solving successively longer finite subproblems, terminating when a stopping rule can be invoked or a decision horizon found. Such procedures are available for a large number of special structure models. Here we describe the specialization of the forward simplex method of Aronson, Morton, and Thompson to solving multiperiod network network flow problems. Computational results indicate that both the solution time and pivot count are linear in the number of periods. For standard network optimization codes, which do not exploit the multiperiod structure, the pivot count is linear in the number of periods; however, the solution time is quadratic.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129452463","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}
Estimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, say t, of the renewal function. However, in warranty analusis, typically t is small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.
{"title":"Warranty analysis and renewal function estimation","authors":"E. Frees","doi":"10.1002/NAV.3800330302","DOIUrl":"https://doi.org/10.1002/NAV.3800330302","url":null,"abstract":"Estimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, say t, of the renewal function. However, in warranty analusis, typically t is small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":" 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120828788","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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