**Travelling Salesman Problem (TSP):** Given the following distance matrix, use the nearest neighbor (NN) heuristic to find a route that starts from the warehouse (W), visits each customer only once, and finishes at the warehouse to minimize the distance traveled. What is the route and the corresponding distance?**Distances in miles:**\[\begin{array}{c|ccccc} & W & 1 & 2 & 3 & 4 \\ \hlineW & 0 & 18 & 57 & 27 & 50 \\1 & 18 & 0 & 65 & 29 & 61 \\2 & 57 & 65 & 0 & 36 & 99 \\3 & 27 & 29 & 36 & 0 & 76 \\4 & 50 & 61 & 99 & 76 & 0 \\\end{array}\]**Route Options:**- Route=W-1-3-2-4, Distance=182 miles- Route=W-3-1-2-4-W, Distance=270 miles- Route=W-3-1-2-4, Distance=220 miles- Route=W-1-3-2-4-W, Distance=232 miles- Route=W-1-3-4-2, Distance=272 miles

Given data is, Distance in miles w 1 2 3 4 w 0 18 57 27 50 1 18 0 65 29 61 2 57 65 0 36 99…

Travelling Salesman Problem (TSP): Given the following distance matrix, use the nearest neighbor (NN) heuristic to find a route that starts from the warehouse (W), visits each customer only once, and finishes at the warehouse to minimize the distance traveled. What is the route and the corresponding distance? Distances W 1 2 3 4 in miles w 18 57 27 50 18 0 65 29 61 57 65 36 99 3 27 29 36 0 76 4 50 61 99 76 0 Route=W-1-3-2-4, Distance=182 miles Route=W-3-1-2-4-W, Distance=270 miles Route = W-3-1-2-4, Distance=220 miles Route=W-1-3-2-4-W, Distance=232 miles Route=W-1-3-4-2, Distance=272 miles 1, 2.

Travelling Salesman Problem (TSP): Given the following distance matrix, use the nearest neighbor (NN) heuristic to find a route that starts from the warehouse (W), visits each customer only once, and finishes at the warehouse to minimize the distance traveled. What is the route and the corresponding distance? Distances W 1 2 3 4 in miles w 18 57 27 50 18 0 65 29 61 57 65 36 99 3 27 29 36 0 76 4 50 61 99 76 0 Route=W-1-3-2-4, Distance=182 miles Route=W-3-1-2-4-W, Distance=270 miles Route = W-3-1-2-4, Distance=220 miles Route=W-1-3-2-4-W, Distance=232 miles Route=W-1-3-4-2, Distance=272 miles 1, 2.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Concept explainers

Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.

Question

**Travelling Salesman Problem (TSP):** Given the following distance matrix, use the nearest neighbor (NN) heuristic to find a route that starts from the warehouse (W), visits each customer only once, and finishes at the warehouse to minimize the distance traveled. What is the route and the corresponding distance?

**Distances in miles:**

\[
\begin{array}{c|ccccc}
& W & 1 & 2 & 3 & 4 \\ \hline
W & 0 & 18 & 57 & 27 & 50 \\
1 & 18 & 0 & 65 & 29 & 61 \\
2 & 57 & 65 & 0 & 36 & 99 \\
3 & 27 & 29 & 36 & 0 & 76 \\
4 & 50 & 61 & 99 & 76 & 0 \\
\end{array}
\]

**Route Options:**

- Route=W-1-3-2-4, Distance=182 miles
- Route=W-3-1-2-4-W, Distance=270 miles
- Route=W-3-1-2-4, Distance=220 miles
- Route=W-1-3-2-4-W, Distance=232 miles
- Route=W-1-3-4-2, Distance=272 miles

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