Let G be a finite connected graph of order at least two. Two players (a cop and a robber) are allowed to play a game on G according to the following rule: The cop chooses a vertex to stay then the robber chooses a vertex afterwards. After that they move alternately along edges of G, where the robber may opt to stay put when his turn to move comes. The cop wins if he succeeds in putting himself ...

We consider a two echelon supply chain with a single retailer and a single manufacturer. Inventory replenishment policies at the retailer level transmit customer demand variability to the manufacturer, sometimes even in an amplified form (known as the bullwhip effect). When production is inflexible at the manufacturing level, significant costs may be incurred by ramping up and down production l...

291 THE RECENT CONTENTIONS that a government scientist was responsible for the 2001 anthrax letter attacks represent a challenge to this country’s resolve to remain a global leader. Our future is inextricably bound with our ability to maintain a pre-eminent role in science, and so it is imperative that our leadership and citizenry have the confidence in American science that it well warrants. N...

We investigate the role of the information available to the players on the outcome of the cops and robbers game. This game takes place on a graph and players move along the edges in turns. The cops win the game if they can move onto the robber’s vertex. In the standard formulation, it is assumed that the players can “see” each other at all times. A graph G is called cop-win if a single cop can ...