Curse of dimensionality reduction in max-plus based approximation methods: theoretical estimates and improved pruning algorithms

Max-plus based methods have been recently developed to approximate the value function of possibly high dimensional optimal control problems. A critical step of these methods consists in approximating a function by a supremum of a small number of functions (max-plus "basis functions") taken from a prescribed dictionary. We study several variants of this approximation problem, which we show to be continuous versions of the facility location and $k$-center combinatorial optimization problems, in which the connection costs arise from a Bregman distance. We give theoretical error estimates, quantifying the number of basis functions needed to reach a prescribed accuracy. We derive from our approach a refinement of the curse of dimensionality free method introduced previously by McEneaney, with a higher accuracy for a comparable computational cost.Comment: 8pages 5 figure

Layout Optimization of a repair facility using discrete event simulation

Technological advancements in the field of simulation have enabled production managers to model and simulate their facilities under various scenarios, in order to optimize system performance. In particular the reconfiguration of factory layouts can be time consuming and expensive; Discrete Event Simulation (DES) can be used to model and assess various scenarios to assist production managers with layout planning. Significant benefits can be achieved through the use of DES for factory layout optimization including: decreased lead times, reduced manufacturing costs, efficient materials handling and increased profit. This paper presents the development of a DES model in WITNESS for the analysis and factory layout optimization of a repair facility. The aim of the model is to allow decision makers to assess various layouts and configurations with a view to optimize production. The model has been built with a link to an Excel spreadsheet to enable data input and the visualization of Key Performance Indicators (KPIs). Specific functions have been built into the simulation model to set and save new layouts within Excel to facilitate layout optimization. The model will be used to optimize the factory configuration

A taxonomy for emergency service station location problem

The emergency service station (ESS) location problem has been widely studied in the literature since 1970s. There has been a growing interest in the subject especially after 1990s. Various models with different objective functions and constraints have been proposed in the academic literature and efficient solution techniques have been developed to provide good solutions in reasonable times. However, there is not any study that systematically classifies different problem types and methodologies to address them. This paper presents a taxonomic framework for the ESS location problem using an operations research perspective. In this framework, we basically consider the type of the emergency, the objective function, constraints, model assumptions, modeling, and solution techniques. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions