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ISEN 601 Location Logistics

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

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ISEN 601 Location Logistics

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  1. ISEN 601Location 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 Pj = (aj, bj) • X location of NF, X = (x,y)

  9. Single Facility Minisum • Notation: • tj = number trips per month between j and NF • vj = avg velocity between j and NF • cj = cost of transportation per unit time • d(X,Pj) = distance between j and NF • So, monthly cost of moving material between j and NF is:

  10. Single Facility Minisum • Define: • Weight wj = 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. SFMS with Rectilinear Distances • Optimality properties:

  18. SFMS with Rectilinear Distances • Another example:

  19. SFMS with Rectilinear Distances • Another example:

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