OTHER LOCATION METHODS Dr. 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%

Comparison of Results Number of Facilities Demand Covered (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! DEFG A10987 B 1145 C8748

Summary Other methods:  P-Median: minimize average distances  Maximum covering: get as many customers as possible within 100 miles  Break-even analysis Approach of centroid followed by factor rating or break-even