ISEN 601
Location Logistics
Dr. Gary M. Gaukler
Fall 2011
Facility Location and SCM
• Goal of supply chain management:
Produce and distribute
• the right quantities
• to the right locations
• at the right time
while minimizing system wide costs and
satisfying customer service level requirements
Facility Location and SCM
• SCM encompasses:
– Financial transactions
– Physical storage & transportation
– Information management
• Supply chain flows:
• We are mostly concerned with the physical flows
in this course
Facility Location and SCM
• Generic sample supply chain:
Facility Location and SCM
• In this course:
Facility location
=
Location of distribution facilities
• e.g.: where to place a new DC in continental
US?
• Hence we will talk about demand at a facility,
and the facility’s distance to the customer etc.
Facility Location and SCM
• Facility Location plays an important role in
designing the supply chain:
– Where to place plants, warehouses, etc.
• Supply chain designs change:
– New markets
– Changes in customer demand
– New technologies
 Facility location is an important and recurring activity!
ProLogis: Industrial Real Estate
Aside: ProLogis
Facility Location
• What metrics do we use? How do we decide
whether one location is better than another?
• Hard
Soft
Facility Location
• In our mathematical analyses, we will disregard the soft
factors
– Use soft factors ahead of time to pare down the candidate set, or
– Use soft factors to decide among multiple solutions
• It’s important to understand that our mathematical
methods are just one tool that should be used to do
facility location
– Our methods do not provide the answer
• Examples:
– Google server farm location
– Toyota truck assembly plant location
Facility Location
• So why bother with quantitative models at all?
Facility Location - Tradeoffs
• Number of facilities vs. response time
Facility Location - Tradeoffs
• Number of facilities vs. inventory cost
Facility Location - Tradeoffs
• Number of facilities vs. transportation cost
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: