OTHER LOCATION METHODSDr. Ron Lembke

P-Median Problem

Minimize average weighted distance to customers, when locating P facilities, where P>=1.

Can consider 100s of locations. Complex to solve – there is software for

this.

Maximum Covering Problem

A facility can “cover” a customer if the customer is within X miles of the facility.

Try to find the best location, and minimum number of facilities to cover all demands.

Cover a table with plates to cover coins sprinkled across it

Math also very hard.

Max Covering 10 = 82%

Max Covering 20 = 97%

90.00%

91.00%

92.00%

93.00%

94.00%

95.00%

96.00%

97.00%

98.00%

99.00%

100.00%

15 16 17 18 19 20 21 22 23 24 25 26

Lower Bound

Greedy Solution

Upper Bound

Comparison of Results

Number of Facilities

Dem

and

Cov

ered

(Using Distances of 150, 200, 250,250)

Solving large problems

Break-Even Analysis

Determine fixed and variable costs for each location

Fixed cost: how much it would cost to open a facility there

Variable cost: how much total costs would increase as production increases: Transportation costs Labor costs Taxes Increased construction costs

Hey – this sounds familiar!

Locating Service Facilities with Multiple Linear Regression Collect data about your current facilities

Median income, # homes sold, education level, population,

Use regression to determine which variables have a significant impact on profits

Choose new facilities which have these characteristics

Incremental or clean-slate approach Take into account existing facilities What is the best location to add, given the

existing facilities? What is the best to add, if we were to

close down one of the current facilities? Unfortunately, only P-Median or Maximum

Covering can deal with these.

Possible Approach Use Centroid (Center of Gravity) to find

out which general regions to locate in (state / county).

Choose city:Factor weighting (services, or revenue focus)Break-even (cost focus)

Method Comparison Center of gravity minimizes average

distance for one facility only. Breakeven: fixed & variable costs. Factor weighting considers many other

important aspects of location, but does not minimize distance.

Transportation Method

You have 3 DCs, and need to deliver product to 4 customers.

Find cheapest way to satisfy all demand

A 10

B 10

C 10

D 2

E 4

F 12

G 11

Solving Transportation Problems

Trial and Error Linear Programming

– ooh, what’s that?! Tell me more!

D E F G

A 10 9 8 7

B 10 11 4 5

C 8 7 4 8

Summary

Other methods:P-Median: minimize average distancesMaximum covering: get as many customers

as possible within 100 milesBreak-even analysis

Approach of centroid followed by factor rating or break-even