science

Stacker crane problem

Stacker crane problem is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Stacker crane problem rather than just read about it. In short: 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.

Key takeaways

Stacker crane problem belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Stacker crane problem to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Stacker crane problem from memory before moving on to harder problems.

Reference excerpt

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 Frederickson, Hecht & Kim (1978), 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 ( p , p ) {\displaystyle (p,p)} 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.

References

Worked examples

Example 1 — a first encounter with Stacker crane problem

Start with the simplest possible case. Write down what Stacker crane problem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Stacker crane problem before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Stacker crane problem ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Stacker crane problem

In research: Stacker crane problem appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Stacker crane problem in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Stacker crane problem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Travelling salesman problem, so understanding it makes those chapters shorter.
In everyday life: Look for Stacker crane problem outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Stacker crane problem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Stacker crane problem means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Stacker crane problem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Stacker crane problem in simple terms?

Why does Stacker crane problem matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Stacker crane problem?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Stacker crane problem.