We consider a distribution system consisting of a single warehouse and many geographically dispersed retailers. Each retailer faces demands for a single item which arise at a deterministic, retailer specific rate. The retailers’ stock is replenished by a fleet of vehicles of limited capacity, departing and returning to the warehouse and combining deliveries into efficient routes. The cost of an...

For problems of data compression, gambling, and prediction of individual sequences 1 the following questions arise. Given a target family of probability mass functions ( 1 ), how do we choose a probability mass function ( 1 ) so that it approximately minimizes the maximum regret /belowdisplayskip10ptminus6pt max (log 1 ( 1 ) log 1 ( 1 )̂) and so that it achieves the best constant in the asymptot...

We study the average case complexity of a linear multivariate problem (LMP) defined on functions of d variables. We consider two classes of information. The first Λ std consists of function values and the second Λ all of all continuous linear functionals. Tractability of LMP means that the average case complexity is O((1/ε) p) with p independent of d. We prove that tractability of an LMP in Λ s...

This paper presents a new technique for generating linear fractional transformation based uncertainty models for use in the robustness analysis of flight control systems using the structured singular value . The proposed approach does not require closedform linear expressions for the aircraft dynamics – only a non-linear software model of the closed loop aircraft, which can be efficiently trimm...

A k-hitting set in a hypergraph is a set of at most k vertices that intersects all hyperedges. We study the union of all inclusion-minimal khitting sets in hypergraphs of rank r (where the rank is the maximum size of hyperedges). We show that this union is relevant for certain combinatorial inference problems and give worst-case bounds on its size, depending on r and k. For r = 2 our result is ...

We consider continuous-time models in which the agent is paid at the end of the time horizon by the principal, who does not know the agent’s type. The agent dynamically affects either the drift of the underlying output process, or its volatility. The principal’s problem reduces to a calculus of variation problem for the agent’s level of utility. The optimal ratio of marginal utilities is random...