Veinott, Arthur F.
Overview
Works:  52 works in 88 publications in 1 language and 910 library holdings 

Genres:  Conference proceedings 
Roles:  Editor, Author 
Classifications:  QA264, 519.92 
Publication Timeline
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Most widely held works by
Arthur F Veinott
Mathematics of the decision sciences
by
George B Dantzig(
Book
)
19 editions published between 1968 and 1970 in English and Undetermined and held by 473 WorldCat member libraries worldwide
19 editions published between 1968 and 1970 in English and Undetermined and held by 473 WorldCat member libraries worldwide
Mathematical studies in management science
by
Arthur F Veinott(
Book
)
10 editions published in 1965 in English and held by 318 WorldCat member libraries worldwide
10 editions published in 1965 in English and held by 318 WorldCat member libraries worldwide
Mathematics of the decision sciences
(
Book
)
3 editions published between 1968 and 1970 in English and held by 25 WorldCat member libraries worldwide
3 editions published between 1968 and 1970 in English and held by 25 WorldCat member libraries worldwide
A property of sequential control processes
by
Ralph E Strauch(
Book
)
1 edition published in 1966 in English and held by 15 WorldCat member libraries worldwide
1 edition published in 1966 in English and held by 15 WorldCat member libraries worldwide
Mathematics of the decision sciences
by
George B Dantzig(
Book
)
1 edition published in 1968 in English and held by 13 WorldCat member libraries worldwide
1 edition published in 1968 in English and held by 13 WorldCat member libraries worldwide
Mathematics of the decision sciences
(
Book
)
3 editions published between 1968 and 1970 in English and held by 6 WorldCat member libraries worldwide
The volume is Part II of a two volume publication containing the Proceedings of the Fifth Summer Seminar on the Mathematics of the Decision Sciences sponsored by the American Mathematical Society and held at Stanford University from July 10 to August 11, 1967. Part II contains papers resulting from sessions concerned with areas of control theory, mathematical economics, dynamic programming, applied probability and statistics, mathematical psychology and linguistics, and computer science. (Author)
3 editions published between 1968 and 1970 in English and held by 6 WorldCat member libraries worldwide
The volume is Part II of a two volume publication containing the Proceedings of the Fifth Summer Seminar on the Mathematics of the Decision Sciences sponsored by the American Mathematical Society and held at Stanford University from July 10 to August 11, 1967. Part II contains papers resulting from sessions concerned with areas of control theory, mathematical economics, dynamic programming, applied probability and statistics, mathematical psychology and linguistics, and computer science. (Author)
Optimal capacity scheduling
by
Arthur F Veinott(
Book
)
1 edition published in 1962 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1962 in English and held by 5 WorldCat member libraries worldwide
A multiproduct, dynamic, nonstationary inventory problem
by
Arthur F Veinott(
Book
)
3 editions published in 1964 in English and held by 4 WorldCat member libraries worldwide
The paper is concerned with a multiproduct dynamic nonstationary inventory problem in which the system is reviewed at the beginning of each of a sequence of periods of equal length. The model has the following features. There is a general demand process with no stationarity or independence assumptions, partial or complete backlogging of unfilled demand, a fixed nonnegative delivery lag (which may be positive only under complete backlogging), a nonstationary linear ordering cost, a nonstationary holding and shortage cost function, discounting of future costs, and nonstationary restrictions like budget and storage limitations. The objective is to choose an ordering policy that minimizes the expected discounted costs over an infinite time horizon. Conditions are given that ensure that the base stock ordering policy is optimal and that the base stock levels in each period are easy to calculate. (Author)
3 editions published in 1964 in English and held by 4 WorldCat member libraries worldwide
The paper is concerned with a multiproduct dynamic nonstationary inventory problem in which the system is reviewed at the beginning of each of a sequence of periods of equal length. The model has the following features. There is a general demand process with no stationarity or independence assumptions, partial or complete backlogging of unfilled demand, a fixed nonnegative delivery lag (which may be positive only under complete backlogging), a nonstationary linear ordering cost, a nonstationary holding and shortage cost function, discounting of future costs, and nonstationary restrictions like budget and storage limitations. The objective is to choose an ordering policy that minimizes the expected discounted costs over an infinite time horizon. Conditions are given that ensure that the base stock ordering policy is optimal and that the base stock levels in each period are easy to calculate. (Author)
Mathematics of the Decision Sciences Part 1
(
Book
)
2 editions published between 1968 and 1970 in Undetermined and English and held by 3 WorldCat member libraries worldwide
2 editions published between 1968 and 1970 in Undetermined and English and held by 3 WorldCat member libraries worldwide
Mathematics of the decision sciences
(
Book
)
1 edition published in 1970 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1970 in English and held by 3 WorldCat member libraries worldwide
Mathematics of the decision sciences. George B. Dantzig and Arthur F. Veinott ... editors. (Reprinted with corrections.)
by American Mathematical Society(
Book
)
1 edition published in 1970 in Undetermined and held by 2 WorldCat member libraries worldwide
1 edition published in 1970 in Undetermined and held by 2 WorldCat member libraries worldwide
Mathematics of the decision sciences
(
Book
)
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1970 in English and held by 2 WorldCat member libraries worldwide
Optimal policy in a dynamic, single product, nonstationary inventory model with several demand classes
by
Arthur F Veinott(
Book
)
2 editions published in 1965 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1965 in English and held by 2 WorldCat member libraries worldwide
Computing optimal (s,S) inventory policies
by
Arthur F Veinott(
Book
)
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1964 in English and held by 2 WorldCat member libraries worldwide
Polyhedral Sets Having a Least Element
(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
For a fixed m x n matrix A, the authors consider the family of polyhedral sets X(sub b) = (x : Ax> or = b), b belongs to R(sup m), and prove a theorem characterizing in terms of A, the circumstances under which every nonempty X sub b has a least element. In the special case where A contains all the rows of an n x n identity matrix, the conditions are equivalent to A sup T being Leontief. Among the corollaries of the theorem, the authors show the linear complementarity problem always has a unique solution which is at the same time a least element of the corresponding polyhedron if and only if its matrix is square, Leontief, and has positive diagonals. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
For a fixed m x n matrix A, the authors consider the family of polyhedral sets X(sub b) = (x : Ax> or = b), b belongs to R(sup m), and prove a theorem characterizing in terms of A, the circumstances under which every nonempty X sub b has a least element. In the special case where A contains all the rows of an n x n identity matrix, the conditions are equivalent to A sup T being Leontief. Among the corollaries of the theorem, the authors show the linear complementarity problem always has a unique solution which is at the same time a least element of the corresponding polyhedron if and only if its matrix is square, Leontief, and has positive diagonals. (Author)
A solution to a countable system of equations arising in markovian decision processes
(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A countable system of equations arising in Markovian decision processes is studied. Conditions are given ensuring the existence and uniqueness of an explicit solution to the system. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A countable system of equations arising in Markovian decision processes is studied. Conditions are given ensuring the existence and uniqueness of an explicit solution to the system. (Author)
Extreme points of leontief substitution systems
(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A Leontief matrix is a matrix A having exactly one positive element in each column and for which there is a nonnegative (column) vector x such that Ax is positive. Let X(b) be the set of nonnegative solutions to Ax = b where A is Leontief and b> or = 0. The following results are established. An element of X(b) is an extreme point of X(b) if and only if it is determined by a Leontief basis matrix. If A is integral, the extreme points of X(b) are integral for all nonnegative integral b if and only if the determinant of each Leontief basis matrix equals one. The class of Leontief matrices for which X(b) is bounded for all b> or = 0 is characterized. The infimum of a concave function over X(b) is concave in b on the nonnegative orthant. The above results are shown to extend easily to matrices with at most one positive element in each column. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
A Leontief matrix is a matrix A having exactly one positive element in each column and for which there is a nonnegative (column) vector x such that Ax is positive. Let X(b) be the set of nonnegative solutions to Ax = b where A is Leontief and b> or = 0. The following results are established. An element of X(b) is an extreme point of X(b) if and only if it is determined by a Leontief basis matrix. If A is integral, the extreme points of X(b) are integral for all nonnegative integral b if and only if the determinant of each Leontief basis matrix equals one. The class of Leontief matrices for which X(b) is bounded for all b> or = 0 is characterized. The infimum of a concave function over X(b) is concave in b on the nonnegative orthant. The above results are shown to extend easily to matrices with at most one positive element in each column. (Author)
Mathematics of the decision sciences, Part 2 : [Fifth summer Seminar on the mathematics of the decision sciences ; Stanford University, July 10 to August 11, 1967]
by
George B Dantzig(
Book
)
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
1 edition published in 1968 in English and held by 1 WorldCat member library worldwide
On the optimality of (s, s) inventory policies: new conditions and a new proof
(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
Scarf has shown that the (s, S) policy is optimal for a class of discrete review dynamic nonstationary inventory models. In this paper a new proof of this result is found under new conditions which do not imply and are not implied by Scarf's hypotheses. We replace Scarf's hypothesis that the one period expected costs are convex by the weaker assumption that the negative of these expected costs are unimodal. In addition, the bounds on the optimal parameter values given by Veinott and Wagner are established for the present case. The bounds in a period are easily computed, and depend only upon the expected costs for that period. Moreover, simple conditions are given which ensure that the optimal parameter values in a given period equal their lower bounds. This result is exploited to derive a planning horizon theorem. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
Scarf has shown that the (s, S) policy is optimal for a class of discrete review dynamic nonstationary inventory models. In this paper a new proof of this result is found under new conditions which do not imply and are not implied by Scarf's hypotheses. We replace Scarf's hypothesis that the one period expected costs are convex by the weaker assumption that the negative of these expected costs are unimodal. In addition, the bounds on the optimal parameter values given by Veinott and Wagner are established for the present case. The bounds in a period are easily computed, and depend only upon the expected costs for that period. Moreover, simple conditions are given which ensure that the optimal parameter values in a given period equal their lower bounds. This result is exploited to derive a planning horizon theorem. (Author)
Minimum concave cost solution of leontief substitution models of multifacility inventory systems
(
Book
)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The paper shows that a broad class of problems can be formulated in terms of minimizing a concave function over the solution set of a Leontief substitution system. The class includes deterministic single and multifacility economic lot size, lot size smoothing, warehousing, product assortment, batch queueing, capacity expansion, investmentconsumption, and reservoir control problems in which all cost functions are concave. For such problems the optimum occurs at an extreme point of the solution set. The extreme points are characterized in each case by using the characterization of the extreme points of the solution set of a Leontief substitution system given in a companion paper. This approach enables most existing qualitative characterizations of optimal policies for inventory models with concave costs to be obtained in a unified manner. Dynamic programming recursions for searching the extreme points to find one that is optimal are given for a number of cases. The only algorithms given are those for which the computational effort increases algebraically (instead of exponentially) with the size of the problem. (Author)
1 edition published in 1967 in English and held by 1 WorldCat member library worldwide
The paper shows that a broad class of problems can be formulated in terms of minimizing a concave function over the solution set of a Leontief substitution system. The class includes deterministic single and multifacility economic lot size, lot size smoothing, warehousing, product assortment, batch queueing, capacity expansion, investmentconsumption, and reservoir control problems in which all cost functions are concave. For such problems the optimum occurs at an extreme point of the solution set. The extreme points are characterized in each case by using the characterization of the extreme points of the solution set of a Leontief substitution system given in a companion paper. This approach enables most existing qualitative characterizations of optimal policies for inventory models with concave costs to be obtained in a unified manner. Dynamic programming recursions for searching the extreme points to find one that is optimal are given for a number of cases. The only algorithms given are those for which the computational effort increases algebraically (instead of exponentially) with the size of the problem. (Author)
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Related Identities
 Dantzig, George B. (George Bernard) 19142005 Author Editor
 American Mathematical Society
 Stanford University
 American mathematical society Publisher
 Strauch, Ralph E. Author
 Institute of Management Sciences
 STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
 Stanford University Department of Operations Research
 STANFORD UNIV CALIF DEPT OF INDUSTRIAL ENGINEERING
 National Science Foundation (U.S.)