A posynomial geometric programming problem formulated so that the number of objective function terms is equal to the number of primal variables will have a zero degree of difficulty when augmented by multiplying each constraint term by a slack variable and including a surrogate constraint composed of the product of the slack variables, each raised to an undetermined negative exponent or surrogate multiplier. It is assumed that the original problem is canonical. The exponents in the constraint on the product of the slack variables must be estimated so that the associated solution to the augmented problem, obtained immediately, also solves the original problem. An iterative search procedure for finding the required exponents, thus solving the original problem, is described. The search procedure has proven quite efficient, often requiring only two or three iterations per degree of difficulty of the original problem. At each iteration the well‐known procedure for solving a geometric programming problem with a zero degree of difficulty is used and so computations are simple. The solution generated at each iteration is optimal for a problem which differs from the original problem only in the values of some of the constraint coefficients, so intermediate solutions provide useful information.
{"title":"Geometric programming with multiplicative slack variables","authors":"J. McNamara","doi":"10.1002/NAV.3800330314","DOIUrl":"https://doi.org/10.1002/NAV.3800330314","url":null,"abstract":"A posynomial geometric programming problem formulated so that the number of objective function terms is equal to the number of primal variables will have a zero degree of difficulty when augmented by multiplying each constraint term by a slack variable and including a surrogate constraint composed of the product of the slack variables, each raised to an undetermined negative exponent or surrogate multiplier. It is assumed that the original problem is canonical. The exponents in the constraint on the product of the slack variables must be estimated so that the associated solution to the augmented problem, obtained immediately, also solves the original problem. An iterative search procedure for finding the required exponents, thus solving the original problem, is described. The search procedure has proven quite efficient, often requiring only two or three iterations per degree of difficulty of the original problem. At each iteration the well‐known procedure for solving a geometric programming problem with a zero degree of difficulty is used and so computations are simple. The solution generated at each iteration is optimal for a problem which differs from the original problem only in the values of some of the constraint coefficients, so intermediate solutions provide useful information.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"71 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":"127274749","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}
Simple criteria are found for reducing the computational effort in multistage Bayesian acceptance sampling. Regions of optimality are given for both terminal actions accept and reject. Also, criteria are presented for detecting nonoptimality of sets of sample sizes. Finally, nearly optimal (z,c−,c+)‐sampling plans are constructed by restricting attention to a small subset of sample sizes.
{"title":"Computational aspects in multistage Bayesian acceptance sampling","authors":"K. Waldmann","doi":"10.1002/NAV.3800330306","DOIUrl":"https://doi.org/10.1002/NAV.3800330306","url":null,"abstract":"Simple criteria are found for reducing the computational effort in multistage Bayesian acceptance sampling. Regions of optimality are given for both terminal actions accept and reject. Also, criteria are presented for detecting nonoptimality of sets of sample sizes. Finally, nearly optimal (z,c−,c+)‐sampling plans are constructed by restricting attention to a small subset of sample sizes.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"34 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":"114175020","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 scheduling n jobs with random processing times on a single machine in order to minimize the expected variance of the completion times. We prove a number of results, including one to the effect that the optimal schedule must be V shaped when the jobs have identical means or variances or have exponential processing times.
{"title":"A single‐machine scheduling problem with random processing times","authors":"S. Chakravarthy","doi":"10.1002/NAV.3800330305","DOIUrl":"https://doi.org/10.1002/NAV.3800330305","url":null,"abstract":"We consider the problem of scheduling n jobs with random processing times on a single machine in order to minimize the expected variance of the completion times. We prove a number of results, including one to the effect that the optimal schedule must be V shaped when the jobs have identical means or variances or have exponential processing times.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"4 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":"117068024","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 formulates a problem of continuous quality production and maintenance of a machine. Quality is assumed to be a known function of the machine's (Markov diffusion process) degradation states. Applications to a specific quality function are used to obtain analytical solutions to an open-loop and feedback stochastic control maintenance problem.
{"title":"Continuous quality production and machine maintenance","authors":"C. Tapiero","doi":"10.1002/NAV.3800330313","DOIUrl":"https://doi.org/10.1002/NAV.3800330313","url":null,"abstract":"This paper formulates a problem of continuous quality production and maintenance of a machine. Quality is assumed to be a known function of the machine's (Markov diffusion process) degradation states. Applications to a specific quality function are used to obtain analytical solutions to an open-loop and feedback stochastic control maintenance problem.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"39 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":"131342581","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 analyzes the Smith‐heuristic for the single‐machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith‐heuristic is guaranteed to lead to optimal solutions. We also provide a worst‐case analysis of the Smith‐heuristic; the analysis shows that the fractional increase in the objective function value for the Smith‐heuristic from the optimal solution is unbounded in the worst case.
{"title":"A note on the single-machine scheduling problem with minimum weighted completion time and maximum allowable tardiness","authors":"S. Chand, H. Schneeberger","doi":"10.1002/NAV.3800330319","DOIUrl":"https://doi.org/10.1002/NAV.3800330319","url":null,"abstract":"This paper analyzes the Smith‐heuristic for the single‐machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith‐heuristic is guaranteed to lead to optimal solutions. We also provide a worst‐case analysis of the Smith‐heuristic; the analysis shows that the fractional increase in the objective function value for the Smith‐heuristic from the optimal solution is unbounded in the worst case.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"122 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":"130362460","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 large sample test based on normal approximation for the traffic intensity parameter ρ in the cases of single and multiple-server queues has been proposed. The test procedure is developed without imposing steady-state assumptions and is applicable to queueing systems with general interarrival and service-time distributions.
{"title":"On a large sample test for the traffic intensity in GI|G|s queue","authors":"S. S. Rao, K. Harishchandra","doi":"10.1002/NAV.3800330318","DOIUrl":"https://doi.org/10.1002/NAV.3800330318","url":null,"abstract":"A large sample test based on normal approximation for the traffic intensity parameter ρ in the cases of single and multiple-server queues has been proposed. The test procedure is developed without imposing steady-state assumptions and is applicable to queueing systems with general interarrival and service-time distributions.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"3 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":"131304001","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 the single-facility and multifacility problems of the minisum type of locating facilities on the plane. Both demand locations and the facilities to be located are assumed to have circular shapes, and demand and service is assumed to have a uniform probability density inside each shape. The expected distance between two facilities is calculated. Euclidean and squared-Euclidean distances are discussed.
{"title":"Location of regional facilities","authors":"Z. Drezner","doi":"10.1002/NAV.3800330316","DOIUrl":"https://doi.org/10.1002/NAV.3800330316","url":null,"abstract":"In this paper we consider the single-facility and multifacility problems of the minisum type of locating facilities on the plane. Both demand locations and the facilities to be located are assumed to have circular shapes, and demand and service is assumed to have a uniform probability density inside each shape. The expected distance between two facilities is calculated. Euclidean and squared-Euclidean distances are discussed.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"461 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":"132970493","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 decision-making situations, each activity that can be undertaken may have associated with it both a fixed and a variable cost. Recently, we have encountered serveral practical problems in which the fixed cost of undertaking an activity depends upon which other activities are also undertaken. To our knowledge, no existing optimization model can accomodate such a fixed cost structure. To do so, we have therefore developed a new model called the interactive fixed charge linear programming problem (IFCLP). In this paper we present and motivate problem (IFCLP), study some of its characteristics, and present a finite branch and bound algorithm for solving it. We also discuss the main properties of this algorithm.
{"title":"The interactive fixed charge linear programming problem","authors":"S. Erenguc, H. Benson","doi":"10.1002/NAV.3800330202","DOIUrl":"https://doi.org/10.1002/NAV.3800330202","url":null,"abstract":"In many decision-making situations, each activity that can be undertaken may have associated with it both a fixed and a variable cost. Recently, we have encountered serveral practical problems in which the fixed cost of undertaking an activity depends upon which other activities are also undertaken. To our knowledge, no existing optimization model can accomodate such a fixed cost structure. To do so, we have therefore developed a new model called the interactive fixed charge linear programming problem (IFCLP). In this paper we present and motivate problem (IFCLP), study some of its characteristics, and present a finite branch and bound algorithm for solving it. We also discuss the main properties of this algorithm.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"48 11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115352273","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}
Minimum cardinality set covering problems (MCSCP) tend to be more difficult to solve than weighted set covering problems because the cost or weight associated with each variable is the same. Since MCSCP is NP-complete, large problem instances are commonly solved using some form of a greedy heuristic. In this paper hybrid algorithms are developed and tested against two common forms of the greedy heuristic. Although all the algorithms tested have the same worst case bounds provided by Ho [7], empirical results for 60 large randomly generated problems indicate that one algorithm performed better than the others.
{"title":"Hybrid heuristics for minimum cardinality set covering problems","authors":"Francis J. Vasko, G. Wilson","doi":"10.1002/NAV.3800330207","DOIUrl":"https://doi.org/10.1002/NAV.3800330207","url":null,"abstract":"Minimum cardinality set covering problems (MCSCP) tend to be more difficult to solve than weighted set covering problems because the cost or weight associated with each variable is the same. Since MCSCP is NP-complete, large problem instances are commonly solved using some form of a greedy heuristic. In this paper hybrid algorithms are developed and tested against two common forms of the greedy heuristic. Although all the algorithms tested have the same worst case bounds provided by Ho [7], empirical results for 60 large randomly generated problems indicate that one algorithm performed better than the others.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116932605","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 a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.
{"title":"MINIMIZING MEAN ABSOLUTE DEVIATION OF COMPLETION TIMES ABOUT A COMMON DUE DATE.","authors":"U. Bagchi, R. S. Sullivan, Yih-Long Chang","doi":"10.1002/NAV.3800330206","DOIUrl":"https://doi.org/10.1002/NAV.3800330206","url":null,"abstract":"We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.","PeriodicalId":431817,"journal":{"name":"Naval Research Logistics Quarterly","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1986-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117044811","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：