Stacker crane problem

Travelling salesman problem

In combinatorial optimization, the stacker crane problem is an optimization problem closely related to the traveling salesperson problem. Its input consists of a collection of ordered pairs of points in a metric space, and the goal is to connect these points into a cycle of minimum total length that includes all of the pairs, oriented consistently with each other. It models problems of scheduling the pickup and delivery of individual loads of cargo, by a stacker crane, construction crane or (in drayage) a truck, in a simplified form without constraints on the timing of these deliveries. It was introduced by , with an equivalent formulation in terms of mixed graphs with directed edges modeling the input pairs and undirected edges modeling their distances. Frederickson et al. credit its formulation to a personal communication of Daniel J. Rosenkrantz. The stacker crane problem can be viewed as a generalization of the traveling salesperson problem in metric spaces: any instance of the traveling salesperson problem can be transformed into an instance of the stacker crane problem, having a pair for each point in the travelling salesman instance. In the other direction, the stacker crane problem can be viewed as a special case of the asymmetric traveling salesperson problem, where the points of the asymmetric traveling salesperson problem are the pairs of a stacker crane instance and the distance from one pair to another is taken as the distance from the delivery point of the first pair, through its pickup point, to the delivery point of the second pair. Because it generalizes the traveling salesperson problem, it inherits the same computational complexity: it is NP-hard, and at least as hard to approximate. An approximation algorithm based on the Christofides algorithm for the traveling salesperson problem can approximate the solution of the stacker crane problem to within an approximation ratio of 9/5. The problem of designing the back side of an embroidery pattern to minimize the total amount of thread used is closely related to the stacker crane problem, but it allows each of its pairs of points (the ends of the visible stitches on the front side of the pattern) to be traversed in either direction, rather than requiring the traversal to go through all pairs in a consistent direction. It is NP-hard by the same transformation from the traveling salesperson problem, and can be approximated to within an approximation ratio of 2. Another variation of the stacker crane problem, called the dial-a-ride problem, asks for the minimum route for a vehicle to perform a collection of pickups and deliveries while allowing it to hold some number k > 1 of loads at any point along its route. (Wikipedia).

How tower cranes are built

You’re walking down the street and see a colossal tower crane. This giant structure seems as if it has always been there; however, it wasn’t when you passed the same road just a few days ago. It is quite surprising to see that happen in such little time. It might make you wonder about how

From playlist Engineering Wonders

The Crane Problem (Physics)

#physics #science #shorts

From playlist General Mechanics

Shopping Cart Truck Mishap

I guess this is what happens when you don't put anything up to keep the shopping carts from falling out of the truck.

From playlist Inertia

How to drive and operate a crane. ✔

More details visit: http://www.techtrixinfo.com/ This video gives you an outlook on how to operate a crane. Cranes are widely been used these days for construction works, wood handling etc. This product is a result of Construction equipment revolution worldwide. In earlier days in India,

From playlist How To Drive

Engineering Behind Australia's Gigantic Coal Industry | Mega Mechanics | Spark

On today’s episode of Mega Mechanics: the dangers on a high wind, deconstruction project. One misstep could bring the mighty coal service conveyer belt to a standstill, and it’s up to the mechanical fitters to keep it moving. A sticky situation at the Rocky Point Sugar Mill calls from a qu

From playlist Mega Mechanics

Building a Fly Cutter - Addendum

Some Q&A; a follow-up of sorts, for the fly cutter build. Hope this answers some questions!

From playlist All Uploads

Resurrecting the Beast | Gold Rush

For the first time in nearly three decades, the tailings conveyor will be brought back to life. | For more, visit http://www.discovery.com/tv-shows/gold-rush/#mkcpgn=ytdsc1 Subscribe to Discovery: http://www.youtube.com/subscription_center?add_user=discoverynetworks Watch full episodes:

From playlist Gold Rush

Why Things Fall Off Cranes

Things can and still go wrong with heavy lifts even when the crane is perfectly safe and sound. The bundle deal with Curiosity Stream has ended, but you can still get a great discount on Nebula and support Practical Engineering here: https://go.nebula.tv/practical-engineering “Rigging” is

From playlist Civil Engineering

How to check hydraulic pressure. ✔

More details visit: http://www.techtrixinfo.com/ Hydraulic pressure checking of a back hoe loader machine is shown and explained in this video. Please rate us and drop your comments. Hydraulic pressure is the most critical parameter which determines the efficiency of hydraulic machinery

From playlist Hydraulics and related stuff.

Offsite Manufacturing Explained: Special Report

In our special report, Fred Mills explores the rise of "offsite manufacturing" and its impact on the construction industry. For more by The B1M subscribe now - http://ow.ly/GxW7y Read the full story on this video, including images and useful links, here - https://www.theb1m.com/video/man

From playlist Offsite Construction - The B1M

Serious Issue! The Super Stacker Is Leaking Fluid | Gold Rush

Stream Gold Rush on discovery+: https://www.discoveryplus.com/show/gold-rush #GoldRush #Discovery #discoveryplus Subscribe to Discovery: http://bit.ly/SubscribeDiscovery Follow Us on TikTok: https://www.tiktok.com/@Discovery We're on Instagram! https://instagram.com/Discovery Join Us

From playlist Adventure & Exploration

Watch the explosive demise of a weather balloon

What happens when a weather balloon climbs too high? Learn more: http://www.sciencemag.org/news/2017/03/watch-explosive-demise-weather-balloon

From playlist Materials and technology

The Computer Chronicles - File Compression (1991)

Special thanks to archive.org for hosting these episodes. Downloads of all these episodes and more can be found at: http://archive.org/details/computerchronicles

From playlist Computer Chronicles Episodes on Software

A Rare Look Inside Shanghai Tower

Get a glimpse of the sky gardens, which set Shanghai Tower apart from any high-rise ever built. http://bit.ly/1aNxP18

From playlist Shanghai Tower | The B1M Mail Feature

Electrical Gremlins Plague Parker’s Equipment! | Gold Rush

Stream Gold Rush on discovery+: https://www.discoveryplus.com/show/gold-rush Subscribe to Discovery: http://bit.ly/SubscribeDiscovery Follow Us on TikTok: https://www.tiktok.com/@Discovery We're on Instagram! https://instagram.com/Discovery Join Us on Facebook: https://www.facebook.co

From playlist Adventure & Exploration

Country Farming: Innovations of the Modern Tractor (1955-1959) | British Pathé

In this Pathé documentary from the '50s, labour practices in country farming are examined with the helping hoe of a tractor. For Archive Licensing Enquiries Visit: https://goo.gl/W4hZBv Explore Our Online Channel For FULL Documentaries, Fascinating Interviews & Classic Movies: https://go

From playlist British Pathé | Explore the Archive

Computer History: IBM 1401 Product Announcement 1959, Data Processing Mainframe (& 7070)

Computer History: Rare original IBM 1401 Product Announcement film of October 5, 1959, for IBM’s historic 1401 Transistorized, General Purpose Mainframe Computer. Titled “Balanced Data Processing.” Features IBM 1401 Data Processing Machine. Opening narrator, Mr. Gilbert E. Jones, Man

From playlist IBM 1401 Computer Family (1959-1960's)

Mitch Fixes Parker's Super Stacker | Gold Rush

From playlist Adventure & Exploration

CHW10.12 Beakers (buoyant force)

From playlist Problems | Fluid Mechanics

Parker’s Crew Sets Up a Massive Radial Stacker | Gold Rush

From playlist Adventure & Exploration

Stacker crane problem

Related pages