ou are tasked with shipping a number n of goods gi € {1,., n} to a target location t;. In your very rural area, bads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies an use for the transport of any good g;. You have to order one truck for each good, and know the companies' roi ,1, Pi,2 and P3 they would take to all specific locations, where each route consists of a sequence of road segme at it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transp be obstructed, your aim is to pick the paths/companies for the goods in such a way that a single blocked road tercept as few shipments as possible. I.e. choose a path Pij for every good g; such that maxeɛE {l{Pi.j|e E P;, as small as possible, where E is the set of all road segments. ) Formulate the problem as an ILP, and relax to an according LP. ) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees oproximation to the optimal solution, and prove its approximation guarantee.
ou are tasked with shipping a number n of goods gi € {1,., n} to a target location t;. In your very rural area, bads are in bad shape and often blocked by trees and the like, and also, there are only three cargo companies an use for the transport of any good g;. You have to order one truck for each good, and know the companies' roi ,1, Pi,2 and P3 they would take to all specific locations, where each route consists of a sequence of road segme at it uses. Now since you are aware of the frequent road blockages, and you want not too many of your transp be obstructed, your aim is to pick the paths/companies for the goods in such a way that a single blocked road tercept as few shipments as possible. I.e. choose a path Pij for every good g; such that maxeɛE {l{Pi.j|e E P;, as small as possible, where E is the set of all road segments. ) Formulate the problem as an ILP, and relax to an according LP. ) Give a rounding algorithm to compute a feasible solution starting from the LP optimum that guarantees oproximation to the optimal solution, and prove its approximation guarantee.
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
Section: Chapter Questions
Problem 17RP
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