In this paper, I first prove an integral representation theorem: Every quasi-integral on a Stone lattice can be represented by a unique upper-continuous capacity. I then apply this representation theorem to study the topological structure of the space of all upper-continuous capacities on a...

Parallel machine scheduling problems concern the scheduling of "n" jobs on "m" machines to minimize some function of the job completion time. If preemption is not allowed, then most problems are not only NP-hard, but also very hard from a practical point of view. In this paper, we show that...

Given a network, the facility location problem consists of locating a set of sites on the network to serve existing clients so as to minimize its total cost. Special cases include the simple plant location problem (SPLP), bank account location, p-facility location, and p-median problem.

This paper is written as an introduction to epistemic logics and their game theoretic applications. It starts with both semantics and syntax of classical logic, and goes to the Hilbert-style proof-theory and Kripke-style model theory of epistemic logics. In these theories, we discuss individual...

Mathematical economics is compared and contrasted with mathematical engineering. Engineers use mathematics where it is practical and cost-effective, sometimes cutting corners, and leaving theorems and derivations to professional mathematicians. In contrast, papers by mathematical economists are...

Individual decision making is based on predictions about other players' choices as well as on valuations of reactions to predictions. In this sense, a player has a prediction-decision criterion for decision making. We develop a theory of prediction-decision criteria, which enables us to capture...

We consider a two-stage serial supply chain with capacity limits, where each installation is operated by managers attempting to minimize their own costs. A multiple-period model is necessitated by the multiple stages, capacity limits, stochastic demand, and the explicit consideration of...

This paper proposes and studies an optimal placement problem in a limit order book. To gain some analytical insights, a simple correlated random walk model with mean-reversion is proposed for the best ask price. Optimal placement strategies for both single-period and multi-period cases are...