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Other location methods

Dr. Ron Lembke. Other location methods. 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.

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Other location methods

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  1. Dr. Ron Lembke Other location methods

  2. 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.

  3. 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.

  4. Max Covering 10 = 82%

  5. Max Covering 20 = 97%

  6. Comparison of Results (Using Distances of 150, 200, 250,250) Demand Covered Number of Facilities

  7. Solving large problems

  8. 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!

  9. 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

  10. 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.

  11. 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)

  12. 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.

  13. Transportation Method You have 3 DCs, and need to deliver product to 4 customers. Find cheapest way to satisfy all demand D 2 A 10 E 4 B 10 F 12 C 10 G 11

  14. Solving Transportation Problems • Trial and Error • Linear Programming – ooh, what’s that?! • Tell me more!

  15. 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

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