Willard I. Zangwill

Willard I. Zangwill
University of Chicago | UC · Chicago Booth School of Business

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49
Publications
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5,558
Citations

Publications

Publications (49)
Patent
Full-text available
Systems and methods are disclosed that assist in making decisions, valuing a choice or action, promoting creative solutions, and reducing risks. Among other situations, the systems and methods consider situations where the user or users are evaluating a possible single choice or several alternative choices. The criteria to evaluate the decisions ar...
Article
The inability to predict the earnings of growth stocks, such as biotechnology and internet stocks, leads to the high volatility of share prices and difficulty in applying the traditional valuation methods. This paper attempts to demonstrate that the high volatility of share prices can nevertheless be used in building a model that leads to a particu...
Conference Paper
In simplest terms, electronic commerce (EC) is the use of the Internet to help create goods and services and to buy and sell them. Since its start in the 1990s, it has grown at a remarkable rate and has impacted and changed how business is conducted in just about every market category. EC firms and their rapid advent present new challenges for rese...
Conference Paper
Some basic issues of electronic commerce (EC) firms are discussed. A general procedure to model the growth of the EC firms is proposed. A mathematical optimization model to analyze the issues and determine the optimal growth rate is given. Finally, a case model study is presented, and some possible extensions are discussed
Article
Despite the popularity of the “learning” curve, it should be called the “forecasting” curve. Given an industrial process, the traditional learning curve forecasts how costs are expected to decline (or other performance measures improve) in the future. Forecasting is certainly very useful. Nevertheless, the previous literature is notably mute on how...
Article
Full-text available
Continuous improvement (CI) unceasingly strives to improve the performance of production and service firms. The learning curve (LC) provides1988 Department of Industrial Engineering and a means to observe and track that improvement. At present, however, the concepts of CI are abstract and imprecise and the rationale underpinning the LC is obscure....
Article
In this paper we consider the situation where we know the sum of n independent observations from the same probability distribution. We investigate how to empirically determine the marginal probability distributions of the different order statistics conditional upon knowing the sum. This research was motivated by explorations in process improvement...
Article
A cyclic queue has one server and n nodes, where each node has its own distinct type of customers that arrive from the outside. The server visits the nodes cyclically, serving the customers first at node 1, then at node 2, and so on through node n, and then repeating from node 1 again. Setup times are incurred when the server switches nodes. Typica...
Article
The concepts in "Japanese" production theory, also called zero inventory or just-in-time, have often improved productivity dramatically, sometimes by 100 percent or more. The theory's central principle is that inventory reflects underlying waste and that eliminating waste causes inventory to drop and productivity to rise. Costs are reduced, respons...
Article
Utilizing a cyclic queue system, this paper investigates the effect of variance on a multi-item production facility. The variance of setup time, service rate and arrival rate is shown to have a powerful and sometimes paradoxical influence. Reduction in setup time, for example, is usually presumed to reduce inventory. We demonstrate that inventory c...
Article
Full-text available
A conceptualization of production learning is proposed, which resolves costs into groups characterized by the rate at which the costs can be reduced. These groups may correspond to learning in process, materials or technology. This approach suggests a new budget methodology, the Learning Rate Budget (LRB), which combines activities with similar lea...
Article
This paper provides the expected waiting time of a nonsymmetric cyclic server queueing system with Poisson traffic, arbitrary switchover and arbitrary service times. For n the number of queues, the expected waiting time is obtained using n equations which is a significant improvement over the previous best result which requires solution of n<sup>2<...
Article
Gerchak's note further elaborates on an example in my paper "From EOQ Towards ZI" (Zangwill, W. I. 1987. From EOQ towards ZI. Management Sci. 33 1209--1223.). My example is correct. His example is correct also, and I was aware of examples of his type when I wrote the paper as were the referees when they reviewed it. His example makes several additi...
Article
Zero Inventory (ZI) is a new and powerful concept to improve production efficiency. Underpinning ZI is set up reduction and this paper examines what eventuates when set up costs are cut. The folklore is that set up reduction lowers inventory and costs. We obtain results contrary to that. Reducing set up costs need not reduce inventory, for example....
Article
Zero inventory (ZI) and the related concepts of Just in Time and Kanban are innovative and powerful means to improve production efficiency. This paper applies these concepts to a series facility production system and, in particular, identifies which facilities will never hold inventory irrespective of product demand. Pinpointing beforehand that cer...
Article
In a noncongested transportation network where each user chooses the quickest route, the creation of an additional route between some origin-destination pair clearly cannot result in an increase in travel time to users traveling between o-d pair. It seems reasonable to assume the same can be said of congested networks. In 1968, D. Braess presented...
Article
When a mapping is univalent (one-to-one) on a set is a question which has received considerable study. Much of the recent research has focused on the shape of the set on which the mapping is defined. It has been suggested, in fact, that the set must be convex for univalence to hold. This paper presents conditions under which the set need not be con...
Article
A general formulation of equilibrium is introduced which subsumes a large range of equilibrium models in economics, mathematical programming, game theory, networks, organizations, etc. The existence of a solution is proved by path following and without invocation of a fixed point theorem. The path following procedure provides new means for establis...
Article
The authors in a previous paper presented a method for finding all solutions to a system of n nonlinear equations in n unknowns. The explicit calculation of the solutions was based upon a simplicial pivoting algorithm. In this paper we present a different approach for that calculation which is based upon the continuation method and differential equ...
Article
In a previous paper, the authors suggested a procedure for obtaining all solutions to certain systems ofn equations inn complex variables. The idea was to start with a trivial system of equations to which all solutions were easily known. The trivial system was then perturbed into the given system. During the perturbation process, one followed the s...
Article
Spawned by Scarf's pioneering work on the calculation of fixed points, an entire new field in mathematical programming has emerged. A wide array of problems that can be posed as fixed point problems, such as problems involving equilibria, games, systems of equations, global optimization, and structural mechanics, have come into the purview of these...
Article
Suppose F is a differentiable mapping from a rectangle R⊂En into En. Gale and Nikaido proved that if the Jacobian of F is a P-matrix in R, then F is univalent in R. Their paper has served as the basis of numerous results on univalence. Recently H. Scarf conjectured a significant extension: that the Jacobian of F need not be a P-matrix everywhere in...
Article
Only during the past decade has it been discovered how, under fairly reasonable conditions, to calculate a solution of a system of n nonlinear equations in n variables. The technique utilized was the so-called “complementarity” or “fixed point” approach to the Brouwer fixed point theorem. In this paper we extend that approach to calculate for certa...
Article
One of the newest areas of mathematical programming, the calculation of fixed points, permits solution of problems unsolvable by earlier methods. The algorithm of this paper, moreover, details two theoretical improvements over previous fixed point algorithms. First, previous algorithms utilize a homotopy structure in which an additional dimension i...
Article
Conditions which are necessary and sufficient for convergence of a nonlinear programming algorithm are stated. It is also shown that the convergence conditions can be easily applied to most programming algorithms. As examples, algorithms by Arrow, Hurwicz and Uzawa; Cauchy; Frank and Wolfe; and Newton-Raphson are proven to converge by direct applic...
Article
This paper introduces a master cutting plane algorithm for nonlinear programming that isolates the points it generates from one another until a solution is achieved. The master algorithm provides a foundation for the study of cutting plane algorithms and directs the way for development of procedures which permit deletion of old cuts.
Article
Multistage minimum-cost network-flow analysis solves many practical problems in production-inventory-distribution, marketing, personnel, and finance. Unlike previous network papers, which generally restricted themselves to a deterministic situation, this paper investigates the stochastic environment. Starting from the standard multistage network-fl...
Article
Develops a multi-product, multi-facility lot size model to deal with production and inventory problems that have two basic properties: (1) the demand for the product is known, and (2) the cost factor is concave. Thesis (Ph. D.)--Stanford University, 1965. "Literature cited": leaf 100. Microfilm. s
Article
Two dynamic economic lot size production systems are analyzed in this paper, the first being a single product model with backlogging and the second a multi-echelon model. In each model the objective is to find a production schedule that minimizes the total production and inventory costs. A key conceptual difficulty is that the mathematically perple...
Article
The literature is replete with analyses of minimum cost flows in networks for which the cost of shipping from node to node is a linear function. However, the linear cost assumption is often not realistic. Situations in which there is a set-up charge, discounting, or efficiencies of scale give rise to concave functions. Although concave functions ca...
Article
Nonlinear, i.e., pseudo-concave, programming algorithms attempt to maximize an objective function fx subject to x in a feasible set. Large step algorithms seek this maximum by recursively generating both a sequence of points {xk} and a sequence of directions {sk}. Given a point xk and a direction sk the next point xk+1 is the feasible point that gi...
Article
This paper presents a method, called the convex simplex method, for minimizing a convex objective function subject to linear inequality constraints. The method is a true generalization of Dantzig's linear simplex method both in spirit and in the fact that the same tableau and variable selection techniques are used. With a linear objective function...
Article
The Chebyshev problem is to determine a point x<sup>\alpha </sup> which solves max<sub>\alpha </sub> min i - 1,..., N{g<sub>i</sub>(x)}. By exploiting generalized inverses an algorithm is developed for determining x<sup>\alpha </sup>. It is also shown that in a certain sense the Chebyshev problem is equivalent to the concave programming problem. Mo...
Article
An important function which is neither concave nor convex often arises in production and inventory models. This function is herein called piecewise concave and can be considered to be a generalization of the concave function. Essentially it is the maximum of a collection of concave functions. Various properties of piecewise concave functions are ex...
Article
The non-linear programming problem seeks to maximize a function f(x) where the n component vector x must satisfy certain constraints g<sub>i</sub>(x) - 0, i - 1, ..., m<sup>1</sup> and g<sub>i</sub>(z) \geqq 0, i - m<sup>1</sup> + 1, ..., m. The algorithm presented in this paper solves the non-linear programming problem by transforming it into a se...
Article
This paper considers the problem of finding a production schedule, in terms of how much to produce in each period, that minimizes the total cost of supplying known market requirements for a single product. The costs include a concave production cost, a concave inventory cost, and a piecewise concave cost of changing the production level from one pe...
Article
A deterministic multi-period production and inventory model that has concave production costs and piecewise concave [Zangwill, W. I. 1965. A dynamic multi-product, multi-facility production and inventory model. Technical Report 1, Program in Operations Research, Stanford University, Stanford, California, April 29.] inventory costs is analyzed. An e...
Article
A deterministic multiproduct, multifacility, multiperiod production planning model is analyzed. The model considers concave production costs, which can depend upon the production in several different facilities, and piecewise concave inventory costs. Backlogging of unsatisfied demand is permitted. After determining the general form of the minimum c...
Article
This paper develops a multi-product, multi-facility 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 p...

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