STANFORD UNIV CALIF Dept. of INDUSTRIAL ENGINEERING
Overview
Works:  8 works in 9 publications in 1 language and 12 library holdings 

Classifications:  HD55, 
Publication Timeline
.
Most widely held works by
STANFORD UNIV CALIF Dept. of INDUSTRIAL ENGINEERING
A multiproduct, dynamic, nonstationary inventory problem by
Arthur F Veinott(
Book
)
2 editions published in 1964 in English and held by 3 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)
2 editions published in 1964 in English and held by 3 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)
A dynamic multiproduct multifacility production and inventory model by
Willard I Zangwill(
Book
)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
This paper develops a multiproduct, multifacility economic lot size model. Roughly speaking, economic lot size models deal with production and inventory situations in which the product demand is known in advance and in which the cost functions are concave. The objective of the model is to determine a production schedule, in terms of how much to produce and when, that minimizes overall cost. Another important aspect of the model is that it allows backlogging of unsatisfied demand. The backlogging analysis actually requires consideration of inventory cost functions which are not concave. To treat such situations the piecewise concave function was developed. Basically a piecewise concave function is the maximum of a collection of concave functions. Using the notion of piecewise concavity a small set of production schedules is determined that contains the minimum cost schedule. Dynamic programming algorithms are presented to efficiently calculate the minimum cost schedule for the 'series' and 'parallel' cases. (Author)
1 edition published in 1965 in English and held by 2 WorldCat member libraries worldwide
This paper develops a multiproduct, multifacility economic lot size model. Roughly speaking, economic lot size models deal with production and inventory situations in which the product demand is known in advance and in which the cost functions are concave. The objective of the model is to determine a production schedule, in terms of how much to produce and when, that minimizes overall cost. Another important aspect of the model is that it allows backlogging of unsatisfied demand. The backlogging analysis actually requires consideration of inventory cost functions which are not concave. To treat such situations the piecewise concave function was developed. Basically a piecewise concave function is the maximum of a collection of concave functions. Using the notion of piecewise concavity a small set of production schedules is determined that contains the minimum cost schedule. Dynamic programming algorithms are presented to efficiently calculate the minimum cost schedule for the 'series' and 'parallel' cases. (Author)
On the convergence of some feasible direction algorithms for nonlinear programming(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
Recently Goldstein has considered the problem of determining conditions on the selection of directions in feasible direction algorithms for unconstrained maximization problems which assure the gradient vanishes in the limit. This paper extends his work (when specialized to Euclidian spaces) in various ways, notably by considering constrained maximization problems and by allowing a wider choice in the selection of the step size. For example we allow the ''optimal'' step size among others. We give conditions on the directions which assure convergence to a stationary point in feasible direction algorithms for maximizing a real valued continuous function on a closed set. We also apply this result to establish convergence to a stationary point of several known methods (e.g., Cauchy's method of steepest ascents, the NewtonRaphson method, and ufrank and Wolfe's method), a simple variant of one of Zoutendijk's methods that eliminates the need for his ''antizigzagging'' procedures, and some new second order methods that require quadratic programs to be solved at each stage. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
Recently Goldstein has considered the problem of determining conditions on the selection of directions in feasible direction algorithms for unconstrained maximization problems which assure the gradient vanishes in the limit. This paper extends his work (when specialized to Euclidian spaces) in various ways, notably by considering constrained maximization problems and by allowing a wider choice in the selection of the step size. For example we allow the ''optimal'' step size among others. We give conditions on the directions which assure convergence to a stationary point in feasible direction algorithms for maximizing a real valued continuous function on a closed set. We also apply this result to establish convergence to a stationary point of several known methods (e.g., Cauchy's method of steepest ascents, the NewtonRaphson method, and ufrank and Wolfe's method), a simple variant of one of Zoutendijk's methods that eliminates the need for his ''antizigzagging'' procedures, and some new second order methods that require quadratic programs to be solved at each stage. (Author)
Optimal policy in a dynamic, single product, nonstationary inventory model with several demand classes by
Arthur F Veinott(
Book
)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A multiperiod single product nonstationary inventory problem is studied 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 are several classes of demand for the product in each period. The demands in different periods are independent but not necessarily identically distributed. The cost structure is nonstationary with the ordering cost being proportional to the amount ordered. 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. The results are based on earlier work of the author and on properties of stochastically ordered distributions that are developed in the paper. The case of a linear holding cost and a linear storage cost is studied in detail. (Author)
1 edition published in 1965 in English and held by 1 WorldCat member library worldwide
A multiperiod single product nonstationary inventory problem is studied 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 are several classes of demand for the product in each period. The demands in different periods are independent but not necessarily identically distributed. The cost structure is nonstationary with the ordering cost being proportional to the amount ordered. 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. The results are based on earlier work of the author and on properties of stochastically ordered distributions that are developed in the paper. The case of a linear holding cost and a linear storage cost is studied in detail. (Author)
Optimal bound and scan algorithm for integer linear programming by
Frederick S Hillier(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A new algorithm for solving the pure integer linear programming problem is presented and evaluated. Roughly speaking this algorithm proceeds by obtaining tight bounds or conditional bounds on the relevant values of the respective variables, and then identifying a sequence of constantly improving feasible solutions by scanning the relevant solutions. Encouraging computational experience is reported that suggests that this algorithm should compare favorably in efficiency with existing algorithms. Plans for investigating ways of further increasing the efficiency of the algorithm and of extending it to more general problems also are outlined. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A new algorithm for solving the pure integer linear programming problem is presented and evaluated. Roughly speaking this algorithm proceeds by obtaining tight bounds or conditional bounds on the relevant values of the respective variables, and then identifying a sequence of constantly improving feasible solutions by scanning the relevant solutions. Encouraging computational experience is reported that suggests that this algorithm should compare favorably in efficiency with existing algorithms. Plans for investigating ways of further increasing the efficiency of the algorithm and of extending it to more general problems also are outlined. (Author)
Efficient suboptimal algorithms for integer linear programming with an interior by
Frederick S Hillier(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
The paper presents and evaluates some new suboptimal algorithms for the pure integer linear programming problem having only inequality constraints. The computation time required by these algorithms (after obtaining the optimal noninteger solution) has been only a small fraction of that required by the simplex method. Furthermore, the solution obtained by the better algorithms consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these algorithms also are outlines. A companion paper presents an optimal 'boundandscan' algorithm that would be used in conjuection with these suboptimal algorithms. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
The paper presents and evaluates some new suboptimal algorithms for the pure integer linear programming problem having only inequality constraints. The computation time required by these algorithms (after obtaining the optimal noninteger solution) has been only a small fraction of that required by the simplex method. Furthermore, the solution obtained by the better algorithms consistently has been close to optimal and frequently has actually been optimal. Plans for generalizing these algorithms also are outlines. A companion paper presents an optimal 'boundandscan' algorithm that would be used in conjuection with these suboptimal algorithms. (Author)
Optimal policy for a dynamic multiechelon inventory model(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A general multiperiod multiechelon supply system consisting of n facilities each stocking a single product is studied. At the beginning of a period each facility may order stock from an exogenous source with no delivery lag and proportional ordering costs. During the period the (random) demands at the facilities are satisfied according to a given supply policy that determines to what extent stock may be redistributed from facilities with excess stock to those experiencing shortages. There are storage, shortage, and transportation costs. An ordering policy that minimizes expected costs is sought. If the initial stock is sufficiently small and certain other conditions are fulfilled, it is optimal to order up to a certain base stock level at each facility. The special supply policy in which each facility except facility 1 passes its shortages on to a given lower numbered facility called its direct supplier is examined in some detail. Bounds on the base stock levels are obtained. It is also shown that if the demand distribution at facility j is stochastically smaller ('spread' less) than that at another facility k having the same direct supplier and if certain other conditions are fulfilled, then the optimal base stock level ('virtual' stock out probability) at j is less than (greater than) or equal to that at facility k. (Author)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
A general multiperiod multiechelon supply system consisting of n facilities each stocking a single product is studied. At the beginning of a period each facility may order stock from an exogenous source with no delivery lag and proportional ordering costs. During the period the (random) demands at the facilities are satisfied according to a given supply policy that determines to what extent stock may be redistributed from facilities with excess stock to those experiencing shortages. There are storage, shortage, and transportation costs. An ordering policy that minimizes expected costs is sought. If the initial stock is sufficiently small and certain other conditions are fulfilled, it is optimal to order up to a certain base stock level at each facility. The special supply policy in which each facility except facility 1 passes its shortages on to a given lower numbered facility called its direct supplier is examined in some detail. Bounds on the base stock levels are obtained. It is also shown that if the demand distribution at facility j is stochastically smaller ('spread' less) than that at another facility k having the same direct supplier and if certain other conditions are fulfilled, then the optimal base stock level ('virtual' stock out probability) at j is less than (greater than) or equal to that at facility k. (Author)
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)
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