1. ISEN 601 Location Logistics Dr. Gary M. Gaukler Fall 2011

2. Setup of a Facility Location Problem Locate new facilities Considering: –Interaction with existing facilities –Customer demands –Customer locations –Potential locations of new facilities –Capacity considerations Focus on “where to put the new facility”

3. Classes of Facility Location Problems Continuous Location Models –Customers anywhere on plane –New facilities anywhere on plane –Demand point = aggregated area demand –Distance calculations important Euclidean distance Rectilinear distance –In general, “quick and dirty” models

4. Classes of Facility Location Problems Continuous Location Models –Single Facility Minisum Minimize sum of weighted distances from NF to customers –Single Facility Minimax Minimize maximum weighted distance from NF to customers

5. Classes of Facility Location Problems Continuous Location Models –Multi-facility Minisum Like SFMS, but place more than one NF –Location-Allocation Like MFMS, but also determine optimal interaction between NFs

6. Classes of Facility Location Problems Network Location Models –Customers are on network nodes –NFs located on network nodes –Distances implicitly given by network –Network = tree or general network –Types of models: Covering (“each customer is within 2 hours of a warehouse”) Center (~ minimax principle) Median (~ minisum principle)

7. Classes of Facility Location Problems Discrete Location Models –Uncapacitated / capacitated warehouse location models –Candidate NF locations –Facilities can split demand –Cost of opening warehouse vs. service coverage

8. Single Facility Minisum Ex: locating a machine in a shop, locating a warehouse in a sales region Objective: minimize total cost –Total cost depends on location of NF Notation: –m existing facilities, with facility j located at P j = (a j, b j ) –X location of NF, X = (x,y)

9. Single Facility Minisum Notation: –t j = number trips per month between j and NF –v j = avg velocity between j and NF –c j = cost of transportation per unit time –d(X,P j ) = distance between j and NF So, monthly cost of moving material between j and NF is:

10. Single Facility Minisum Define: –Weight w j = cost of interaction per unit distance So, total cost is: Goal:

11. SFMS with Rectilinear Distances Rectilinear distance: Total cost:

12. SFMS with Rectilinear Distances Properties of total cost function: Graph: Consequences:

13. SFMS with Rectilinear Distances Example 4.1:

14. SFMS with Rectilinear Distances Example 4.1:

15. SFMS with Rectilinear Distances Example 4.1:

16. SFMS with Rectilinear Distances

17. Optimality properties:

18. SFMS with Rectilinear Distances Another example:

19. SFMS with Rectilinear Distances Another example: