FedEx Warehouse Delivery:

“Keep it on the streets”

FedEx Warehouse Delivery:

“Keep it on the streets”

GLOBAL SYSTEMSSpring 2018

The Problem

You are a logistics planner for FedEx. Your goal is to plan a route for a delivery truck in a city. The truck departs from the warehouse, travels to each of a set of stores, and returns to the warehouse.

The objective is to find a delivery route that minimizes the total distance traveled from start to end. We assume that the lowest total distance route is also the lowest-cost route.

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UPS makes no left turns

Q. How have you tried to cut carbon from transportation?

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Bloomberg Business, Sep.20, 2012. “UPS Makes No Left Turns in Quest to Deliver Sustainability.“

Street Map

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Streets run east-west. Avenues run north-south. Addresses are given as 334 2nd St SW, for example.

N

NE

Main St

1st A

ve S

E

2nd St SWC

entra

l Ave

2nd St NW

3rd

Ave

NW

Street Map grid

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Streets are separated by 0.1 miles. Avenues are separated by 0.2 miles.

N 0.1

0.2

Stores labeled: Map 1

6

The warehouse (square) is located at Central Ave and Main St. The stores are noted by circles and located as shown below.

N

NE

1

23

45

6

7

Store locations labeled: Map 1

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The warehouse (square) is located at Central Ave and Main St. The stores are noted by circles and located as shown below.

N

NE

(0,0)

6

7

1

2

5

3

4

(-3,3)

(2,2)

(1,-2)

(-2,-1)

(-1,-3)

(3,-4)

FedEx delivery conditions

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(1) Leave from the warehouse.

(2) Visit each store only once.

(3) Return to the warehouse.

(4) Stay on the streets at all times.

Inter‐store distance data

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(1) Assume all streets can be driven in both directions.

(2) The inter-store distance is the smallest distance on the grid between a pair of stores.

(3) The smallest distances between pairs of stores can be stored in an array. Call it Darr for convenience.

Example Darr array (size 4)

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Store 1 2 3 4

1 0 D(1,2) D (1,3) D(1,4)

2 D(2,1) 0 D(2,3) D(2,4)

3 D(3,1) D(3,2) 0 D(3,4)

4 D(4,1) D(4,2) D(4,3) 0

Read array as:From store i (row) to store j (column).

Find the delivery route with the shortest distance, using Map 1

a. Find the shortest distance between each pair of stores.

b. Generate each possible delivery route.c. Find the total distance for each route.d. Identify the route with the smallest total 

distance. Give its total distance.e. Sketch the route on Map 1.

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Store locations: Map 2

12

Odd streets are one-way West. Even streets are one-way East.Main Street is two-way. All avenues (N-S) are two-way.

N

NE

Stores labeled: Map 2

13

Odd streets are one-way west; even streets are one-way east.Main Street is two-way.

N

NE

671

2

5

3

4

Find the delivery route with the shortest distance, using Map 2

a. Find the shortest distance between each pair of stores.

b. Generate each possible delivery route.c. Find the total distance for each route.d. Identify the route with the smallest total 

distance. Give its total distance.e. Sketch the route on Map 2.

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Any questions for the sys_gu?

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