Multicriteria optimization : a general characterization of efficient solutions

Efficient decisions -- Constructive characterizations of XE

A probabilistic model of vehicle speeds on public transit routes

The models -- The model of whitehead and yagar -- A refined model -- Analysis of the refined model -- Result

An Algorithm for Separable Nonconvex Programming Problems II: Nonconvex Constraints

We extend a previous algorithm in order to solve mathematical programming problems of the form: Find x = (x 1, ..., x n) to minimize \sum \varphi i0 (x i) subject to x \in G, l \leqq x \leqq L and \sum \varphi ij (x i) \leqq 0, j = 1, ..., m. Each \varphi ij is assumed to be lower semicontinuous, possibly nonconvex, and G is assumed to be closed. The algorithm is of the branch and bound type and solves a sequence of problems in each of which the objective function is convex. In case G is convex each problem in the sequence is a convex programming problem. The problems correspond to successive partitions of the set C = { x | l \leqq x \leqq L}. Two different rules for refining the partitions are considered; these lead to convergence of the algorithm under different requirements on the problem functions. An example is given, and computational considerations are discussed.

Optimal Operation of Public Lotteries

Public lotteries form an important source of revenue for many national and state governments, but little quantitative effort has been applied to their efficient operation. We here formulate a model in which the net revenue per unit time from the operation of a lottery depends upon the prizes offered, the price charged per ticket, and the time interval between successive drawings. The model is solved for the optimal values of these decision variables, and some illustrative numerical results are presented.