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
• Focus on “where to put the new facility”
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
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
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
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)
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
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)
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:
Single Facility Minisum
• Define:
– Weight wj = cost of interaction per unit
distance
• So, total cost is:
• Goal:
SFMS with Rectilinear Distances
• Rectilinear distance:
• Total cost:
SFMS with Rectilinear Distances
• Properties of total cost function:
• Graph:
• Consequences:
SFMS with Rectilinear Distances
• Example 4.1:
SFMS with Rectilinear Distances
• Example 4.1:
SFMS with Rectilinear Distances
• Example 4.1:
SFMS with Rectilinear Distances
SFMS with Rectilinear Distances
• Optimality properties:
SFMS with Rectilinear Distances
• Another example:
SFMS with Rectilinear Distances
• Another example: