Pub Date : 1988-04-01DOI: 10.1002/1520-6750(198804)35:2<221::AID-NAV3220350207>3.0.CO;2-2
F. Samaniego, Lyn R. Whitaker
Consider an experiment in which only record‐breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X1,K1,X2,K2, …, where X1,X2, … are successive minima and K1,K2, … are the numbers of trials needed to obtain new records. We treat the problem of estimating the mean of an underlying exponential distribution, and we consider both fixed sample size problems and inverse sampling schemes. Under inverse sampling, we demonstrate certain global optimality properties of an estimator based on the “total time on test” statistic. Under random sampling, it is shown than an analogous estimator is consistent, but can be improved for any fixed sample size.
{"title":"On estimating population characteristics from record‐breaking observations. i. parametric results","authors":"F. Samaniego, Lyn R. Whitaker","doi":"10.1002/1520-6750(198804)35:2<221::AID-NAV3220350207>3.0.CO;2-2","DOIUrl":"https://doi.org/10.1002/1520-6750(198804)35:2<221::AID-NAV3220350207>3.0.CO;2-2","url":null,"abstract":"Consider an experiment in which only record‐breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X1,K1,X2,K2, …, where X1,X2, … are successive minima and K1,K2, … are the numbers of trials needed to obtain new records. We treat the problem of estimating the mean of an underlying exponential distribution, and we consider both fixed sample size problems and inverse sampling schemes. Under inverse sampling, we demonstrate certain global optimality properties of an estimator based on the “total time on test” statistic. Under random sampling, it is shown than an analogous estimator is consistent, but can be improved for any fixed sample size.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1988-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130582300","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}
On etudie l'entropie de Renyi et la fonction de divergence associee et on etablit leur nature en termes de concavite (convexite) et pseudoconcavite (pseudoconvexite)
{"title":"Nature of renyi's entropy and associated divergence function","authors":"C. R. Bector, B. L. Bhatia","doi":"10.1002/NAV.3800330416","DOIUrl":"https://doi.org/10.1002/NAV.3800330416","url":null,"abstract":"On etudie l'entropie de Renyi et la fonction de divergence associee et on etablit leur nature en termes de concavite (convexite) et pseudoconcavite (pseudoconvexite)","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121207307","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 consider a variant of the classical transportation problem as well as of the bottleneck transportation problem, which we call the minimax transportation problem. The problem considered is to determine a feasible flow xij from a set of origins I to a set of destinations J for which max(i,j)eIxJ{cijxij} is minimum. In this paper, we develop a parametric algorithm and a primal‐dual algorithm to solve this problem. The parametric algorithm solves a transportation problem with parametric upper bounds and the primal‐dual algorithm solves a sequence of related maximum flow problems. The primal‐dual algorithm is shown to be polynomially bounded. Numerical investigations with both the algorithms are described in detail. The primal‐dual algorithm is found to be computationally superior to the parametric algorithm and it can solve problems up to 1000 origins, 1000 destinations and 10,000 arcs in less than 1 minute on a DEC 10 computer system. The optimum solution of the minimax transportation problem may be noninteger. We also suggest a polynomial algorithm to convert this solution into an integer optimum solution.
{"title":"Algorithms for the minimax transportation problem","authors":"R. Ahuja","doi":"10.1002/NAV.3800330415","DOIUrl":"https://doi.org/10.1002/NAV.3800330415","url":null,"abstract":"In this paper, we consider a variant of the classical transportation problem as well as of the bottleneck transportation problem, which we call the minimax transportation problem. The problem considered is to determine a feasible flow xij from a set of origins I to a set of destinations J for which max(i,j)eIxJ{cijxij} is minimum. In this paper, we develop a parametric algorithm and a primal‐dual algorithm to solve this problem. The parametric algorithm solves a transportation problem with parametric upper bounds and the primal‐dual algorithm solves a sequence of related maximum flow problems. The primal‐dual algorithm is shown to be polynomially bounded. Numerical investigations with both the algorithms are described in detail. The primal‐dual algorithm is found to be computationally superior to the parametric algorithm and it can solve problems up to 1000 origins, 1000 destinations and 10,000 arcs in less than 1 minute on a DEC 10 computer system. The optimum solution of the minimax transportation problem may be noninteger. We also suggest a polynomial algorithm to convert this solution into an integer optimum solution.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115589603","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 consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.
{"title":"Rescheduling to minimize makespan on a changing number of identical processors","authors":"C. Tovey","doi":"10.1002/NAV.3800330414","DOIUrl":"https://doi.org/10.1002/NAV.3800330414","url":null,"abstract":"We consider the problem of rescheduling n jobs to minimize the makespan on m parallel identical processors when m changes value. We show this problem to be NP-hard in general. Call a list schedule totally optimal if it is optimal for all m = 1, …,n. When n is less than 6, there always exists a totally optimal schedule, but for n ≥ 6 this can fail. We show that an exact solution is less robust than the largest processing time first (LPT) heuristic and discuss implications for polynomial approximation schemes and hierarchical planning models.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121905401","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}
P. Korhonen, H. Moskowitz, J. Wallenius, Stanley Zionts
In this article we propose a formal man-machine interactive approach to multiple criteria optimization with multiple decision makers. The approach is based on some of our earlier research findings in multiple criteria decision making. A discrete decision space is assumed. The same framework may readily be used for multiple criteria mathematical programming problems. To test the approach two experiments were conducted using undergraduate Business School students as subjects in Finland and in the United States. The context was, respectively, a high-level Finnish labor-management problem and the management-union collective bargaining game developed at the Krannert Graduate School of Management, Purdue University. The results of the experiments indicate that our approach is a potentially useful decision aid for group decision-making and bargaining problems.
{"title":"An interactive approach to multiple criteria optimization with multiple decision‐makers","authors":"P. Korhonen, H. Moskowitz, J. Wallenius, Stanley Zionts","doi":"10.1002/NAV.3800330405","DOIUrl":"https://doi.org/10.1002/NAV.3800330405","url":null,"abstract":"In this article we propose a formal man-machine interactive approach to multiple criteria optimization with multiple decision makers. The approach is based on some of our earlier research findings in multiple criteria decision making. A discrete decision space is assumed. The same framework may readily be used for multiple criteria mathematical programming problems. To test the approach two experiments were conducted using undergraduate Business School students as subjects in Finland and in the United States. The context was, respectively, a high-level Finnish labor-management problem and the management-union collective bargaining game developed at the Krannert Graduate School of Management, Purdue University. The results of the experiments indicate that our approach is a potentially useful decision aid for group decision-making and bargaining problems.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125843199","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}
Product quality is emerging as a major strategic instrument for competition. The purpose of this article is to assess the effects of quality control on sales, and, vice versa, the effects of the sales process on quality control. A model relating quality control and the sales process (advertising, repeat purchase, and word‐of‐mouth effects) is developed to evaluate the above relationships. Two special cases, with degenerate and beta distribution for defect items in the production lot, are analyzed in detail. In the former case, analytical results for the optimal quality control schemes are obtained, whereas in the latter, efficient bounds are derived to search for the optimal scheme. It is shown, analytically and numerically, that the sales parameters have significant impact on whether more “stringent” or “tighter” quality control is warranted. Future research directions are also discussed.
{"title":"Quality control and the sales process","authors":"Hau L. Lee, C. Tapiero","doi":"10.1002/NAV.3800330404","DOIUrl":"https://doi.org/10.1002/NAV.3800330404","url":null,"abstract":"Product quality is emerging as a major strategic instrument for competition. The purpose of this article is to assess the effects of quality control on sales, and, vice versa, the effects of the sales process on quality control. A model relating quality control and the sales process (advertising, repeat purchase, and word‐of‐mouth effects) is developed to evaluate the above relationships. Two special cases, with degenerate and beta distribution for defect items in the production lot, are analyzed in detail. In the former case, analytical results for the optimal quality control schemes are obtained, whereas in the latter, efficient bounds are derived to search for the optimal scheme. It is shown, analytically and numerically, that the sales parameters have significant impact on whether more “stringent” or “tighter” quality control is warranted. Future research directions are also discussed.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"29 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125785056","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 shows that one of the fundamental results of inventory theory is valid under conditions much broader than those treated previously. The result characterizes the distributions of inventory level and inventory position in the standard, continuous‐time model with backorders, and leads to the relatively easy calculation of key performance measures. We treat both fixed and random leadtimes, and we examine both stationary and limiting distributions under different assumptions. We consider demand processes described by several general classes of compound‐counting processes and a variety of order policies. For the stochastic‐leadtime case we provide the first explicit proof of the result, assuming the leadtimes are generated according to a specific, but plausible, scenario.
{"title":"Stochastic leadtimes in continuous‐time inventory models","authors":"Paul H. Zipkin","doi":"10.1002/NAV.3800330419","DOIUrl":"https://doi.org/10.1002/NAV.3800330419","url":null,"abstract":"This paper shows that one of the fundamental results of inventory theory is valid under conditions much broader than those treated previously. The result characterizes the distributions of inventory level and inventory position in the standard, continuous‐time model with backorders, and leads to the relatively easy calculation of key performance measures. We treat both fixed and random leadtimes, and we examine both stationary and limiting distributions under different assumptions. We consider demand processes described by several general classes of compound‐counting processes and a variety of order policies. For the stochastic‐leadtime case we provide the first explicit proof of the result, assuming the leadtimes are generated according to a specific, but plausible, scenario.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130664061","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}
Single- and multi-facility location problems are often solved with iterative computational procedures. Although these procedures have proven to converage, in practice it is desirable to be able to compute a lower bound on the objective function at each iteration. This enables the user to stop the iterative process when the objective function is within a prespecified tolerance of the optimum value. In this article we generalize a new bounding method to include multi-facility problems with lp distances. A proof is given that for Euclidean distance problems the new bounding procedure is superior to two other known methods. Numerical results are given for the three methods.
{"title":"Bounding methods for facilities location algorithms","authors":"P. D. Dowling, R. Love","doi":"10.1002/NAV.3800330420","DOIUrl":"https://doi.org/10.1002/NAV.3800330420","url":null,"abstract":"Single- and multi-facility location problems are often solved with iterative computational procedures. Although these procedures have proven to converage, in practice it is desirable to be able to compute a lower bound on the objective function at each iteration. This enables the user to stop the iterative process when the objective function is within a prespecified tolerance of the optimum value. In this article we generalize a new bounding method to include multi-facility problems with lp distances. A proof is given that for Euclidean distance problems the new bounding procedure is superior to two other known methods. Numerical results are given for the three methods.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"63 27","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134195350","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}
Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β1 in one tail and no more than β2 in the other tail with probability γ may be computed for any size sample. They are computed from X ‐ k1S and X ‐ k2S, where X and S are the usual sample mean and standard deviation and k1 and k2 are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X – k1S) and (X + k2S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.
对于任何大小的样本，都可以计算出控制正态分布两端的容差极限，使一条尾巴的比例不超过β1，另一条尾巴的比例不超过β2，其概率为γ。它们由X‐k1S和X‐k2S计算得出，其中X和S是通常的样本平均值和标准差，k1和k2是先前在Odeh和Owen[3]中列出的常数。要解决的问题是，“对于不同大小的样本，这些区间(- Infin;， X - k1S)和(X + k2S，∞)的覆盖率到底有多准确?”这个问题的答案是，在给定置信度γ′下，每个尾区间的覆盖范围与相应所需内容的差异有多大。
{"title":"Estimating the accuracy of the coverages of outer β‐content tolerance intervals, which control both tails of the normal distribution","authors":"Y. Chou, D. Owen","doi":"10.1002/NAV.3800330421","DOIUrl":"https://doi.org/10.1002/NAV.3800330421","url":null,"abstract":"Tolerance limits which control both tails of the normal distribution so that there is no more than a proportion β1 in one tail and no more than β2 in the other tail with probability γ may be computed for any size sample. They are computed from X ‐ k1S and X ‐ k2S, where X and S are the usual sample mean and standard deviation and k1 and k2 are constants previously tabulated in Odeh and Owen [3]. The question addressed is, “Just how accurate are the coverages of these intervals (– Infin;, X – k1S) and (X + k2S, ∞) for various size samples?” The question is answered in terms of how widely the coverage of each tail interval differs from the corresponding required content with a given confidence γ′.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123340599","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 many-against-many battle, which is a variant of the Friedman's one-against-many battle, is formulated as a two-person constant-sum game. It is shown that the matrix which expresses this game has a saddle point. Some cases are presented in which the payoff matrix of the game can be reduced. Finally, some parametrically special cases are analyzed.
{"title":"The matrix game derived from the many‐against‐many battle","authors":"K. Kikuta","doi":"10.1002/NAV.3800330406","DOIUrl":"https://doi.org/10.1002/NAV.3800330406","url":null,"abstract":"The many-against-many battle, which is a variant of the Friedman's one-against-many battle, is formulated as a two-person constant-sum game. It is shown that the matrix which expresses this game has a saddle point. Some cases are presented in which the payoff matrix of the game can be reduced. Finally, some parametrically special cases are analyzed.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"5 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123459298","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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