Maximising a function over a finite set of actions: technical note

Article Abstract:

An algorithm for extending a problem over a finite set of actions is introduced. The original quadratic problem involves maximizing the function denoted by f(x) = x'Px + s'x where P is an n-by-n positive semi-definite matrix, s is an n-dimensional vector and X is a finite set of n-dimensional vectors. With the extension, made with the help of a new function h(x,y) = x'Py where (x,y) belongs to X-by-X, it becomes a problem of maximizing a function over a bi-product set. It also becomes analogous to maximum likelihood estimation and generates a solution set consisting of partial and fixed point solutions for the general case. Its quadratic programming version, in some cases, becomes problems of 'maximizing a bilinear function over polytopes of a special kind.' To solve it, two improvement procedures for generating fixed point solutions are given.

Research, Algorithms, Quadratic programming, Finite groups, Fixed point theory

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Note on Optimal Ordering Quantity to Realize a Pre-Determined Level of Profit

Article Abstract:

A one-period inventory model is studied. It must determine the inventory order quantity that maximizes the probability of realizing a predetermined level of profit. Three cases are presented.

Management science, Manufacturing, Inventory control, Production, Stochastic Model

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Using computers to realize joint gains in negotiations: toward an "electronic bargaining table"

Article Abstract:

The authors explore the use of computers in negotiations. Results indicate negotiation programs can enhance the process for all parties involved.

Software, Negotiation, Negotiations

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