E (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands. Using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between th...

In this paper the classical Vehicle Routing Problem (VRP) is extended to cover the more realistic case of uncertainty about customer demands. This case is modelled as a VRP with stochastic demands and tackled with a heuristic solution approach based on Ant Colony Optimization (ACO). The main issues studied in this paper are the modelling of the uncertainty (i) in terms of its influence on the p...

The periodic demands of a single product are forecasted and given by a distribution function for each period. The product can be manufactured in n plants with heterogeneous characters. Each plant has its specific stochastic production capability. The expected capability and the standard deviation of each plant can be increased by allocation of additional budgets. The problem is to determine the...

We study a unidirectional hyperbolic transport equation, with a homogeneous stochastic transport velocity, solved by Monte Carlo simulation. Several finite difference schemes are applied to the deterministic problem in each Monte Carlo iteration, and the numerical solution of the stochastic problem is compared to analytical solutions derived in the paper. We present both a theoretical analysis ...

Nanofabrication has allowed the development of new concepts such as magnetic logic and race-track memory, both of which are based on the displacement of magnetic domain walls on magnetic nanostripes. One of the issues that has to be solved before devices can meet the market demands is the stochastic behaviour of the domain wall movement in magnetic nanostripes. Here we show that the stochastic ...

The stochastic nature of emergency service requests and the unavailability of emergency vehicles when requested to serve demands are critical issues in constructing valid models representing real life emergency medical service (EMS) systems. We consider an EMS system design problem with stochastic demand and locate the emergency response facilities and vehicles in order to ensure target levels ...

In this paper, we address a surgery capacity sharing problem with multiple hospitals, and formulate a model where hospitals who have their own capacity (the Operating Room) locally. Each hospital has several surgery teams facing random demands and seeks appropriate capacities to accommodate the demands, so that its total profit is maximized. We first study the allocation of available surgery ca...

A queue is a waiting line (like customers waiting at a supermarket checkout counter); queueing theory is the mathematical theory of waiting lines. More generally, queueing theory is concerned with the mathematical modeling and analysis of systems that provide service to random demands. A queueing model is an abstract description of such a system. Typically, a queueing model represents (1) the s...

We consider a stochastic version of a dynamic resource allocation problem. In this setting, reusable resources must be assigned to demands that arise randomly over time. Both resources and demands are heterogeneous, and satisfying a demand generally will change the attributes of a resource. These problems arise in eet management, personnel training and assignment, and the remnant inventory prob...

We consider the problem of assigning objects probabilistically among a group of agents who may have multi-unit demands. Each agent has linear preferences over the (set of) objects. The most commonly used extension of preferences to compare probabilistic assignments is by means of stochastic dominance, which leads to corresponding notions of envy-freeness, efficiency, and strategy-proofness. We ...