ISEN 601Location Logistics

Dr. Gary M. GauklerFall 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: