1. Facility Location
Facility location is the determination of the geographical site(s) in which to locate a firm’s operations.
Globalisation
Factors to consider
Quantitative tools for analysis
locating a single facility
locating within a network of facilities
Location decisions must be co-ordinated with production planning and distribution strategies

2. Location Theory - Early History
Weber’s classification of industries (1909)
Weight-losing process
locate close to raw materials
e.g. steel making
Weight-gaining process
incorporate “ubiquitous” raw materials e.g. air, water
locate near markets
Hoover’s (1957) tapered transportation rates
tapered transportation rates
minimum costs at either production point or market point

3. Factors - Location Related
Facility Location
Factors - Location Related
Land/Construction costs
Community receptivity
Local business climate
Quality of life
Government incentives
tax breaks
free trade zone
Government barriers
currency controls
trading blocs
local content
environmental regulations
Political Risks
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4. Factors - Resource/Cost Related
Proximity to suppliers
Quality/Availability of labour
Transportation/Energy infrastructure
Proximity to customers
Inbound/Outbound distribution costs
Other (company-owned) facilities
Competitive Advantage

5. Quantitative Tools Center of Gravity Method Mixed Integer Programming
Simulation
Heuristics
Other methods
Single facility location
Multi-facility location
Supply chain network design
Dynamic location models

6. Single Facility Location
Given a set of demand points, each located at (xi,yi) with a specified volume Vi to be moved to a facility (at transportation rate Ri ),
locate a single facility to minimise total transportation costs.
Find (X,Y) to
Minimise  Vi Ri di
where
di = [(Xi - X)2 + (Yi - Y)2]1/2

7. Centre of Gravity Method
Grid method
centroid method
Locate facility at:

8. Concerns/Assumptions of Centre-of-Gravity Model
continuous
demand concentrated at a point
transportation costs proportional to Euclidean distance
fixed cost of establishing facility ignored
static
simple
useful “first-cut” solution

9. Multi-Facility Location
How many sites?
Where to locate each?
Capacities?
Which customers assigned to each site?
Which products to stock/produce at each site?

10. Multiple Centre-of-Gravity Approach
Pre-assign demand points to each facility (i.e. cluster customers that are closest together).
For each cluster, locate one facility at centre of gravity.
With facility locations fixed, re-assign customers to closest facility.
Find centres of gravity for new clusters.
Repeat cluster-assign until no further change.

11. Linear and Mixed Integer Programming
LP useful in calculating distribution costs
Mixed Integer Programming can `optimize’ site selection and distribution plan simultaneously
Detailed cost estimates needed

12. p-median Problem
Locate p facilities so as to minimise the sum of fixed cost for establishing facilities and transportation costs from demand points to assigned facility.
Ballou (Logware):
demand point co-ordinates given
assume out-and-back along Euclidean distance

13. p-median problem -- MIP formulation

14. Heuristic Methods = Rules of Thumb
Kuehn & Hamburger (1963)
ADD
No facilities open initially
For each facility not currently used: evaluate the savings in total cost if opened (reduced transportation costs less fixed cost)
Add facility that gives maximum (positive) savings
DROP
All (Selected set of) facilities open initially
For each facility currently used: evaluate the savings in total cost if closed (fixed cost less increased transportation costs)
Drop facility that gives maximum savings

15. Multi-Facility Multi-Product Location-Allocation Problem
Find the number and location of the facilities to minimise the total (fixed and variable) costs of moving all products through the logistics network, subject to:
available supply at each plant cannot be exceeded for each product
demand for all products met
throughput of each facility cannot exceed its capacity
minimum throughput of a facility must be achieved before it can be opened
all products from same customers must be met from one facility.

16. MIP formulation FIGURE 13.5 A small Multiproduct Warehouse Location
Customer C1
50,000 cwt.
$4/cwt.
Plant P1
Production = $4/cwt.
Capacity = 60,000 cwt.
$0/cwt.
Handling = $2/cwt.
Warehouse W1
$2/cwt.
$5/cwt.
$3/cwt.
Customer C2
100,000 cwt.
$1/cwt.
$4/cwt.
Handling = $1/cwt.
Warehouse W2
Plant P2
Production = $4/cwt.
Capacity = unrestricted
$2/cwt.
$2/cwt.
$5/cwt.
Customer C3
50,000 cwt.
Fixed = $100,000
Capacity = 110,000 cwt.
Fixed = $500,000
Capacity = unrestricted
Product 2
Customer C1
20,000 cwt.
$3/cwt.
Plant P1
Production = $3/cwt.
Capacity = 50,000 cwt.
$0/cwt.
Handling = $2/cwt.
Warehouse W1
$3/cwt.
$5/cwt.
$2/cwt.
Customer C2
30,000 cwt.
$2/cwt.
$4/cwt.
Handling = $1/cwt.
Warehouse W2
Plant P2
Production = $2/cwt.
Capacity = unrestricted
$2/cwt.
$3/cwt.
$4/cwt.
Customer C3
60,000 cwt.
FIGURE 13.5 A small Multiproduct Warehouse Location
Problem for Mixed Integer Linear Programming

17. Sum of demand for customer l
Technical Supplement
Fixed costs
Handling rate
Inbound and outbound
transport rates
Sum of demand for customer l
across all products
Plant capacity

18. Minimum warehouse throughput
Customer demand
Minimum warehouse throughput
Warehouse capacity

20. Relevant Costs for Location Decision
production/purchase costs
warehouse storage and handling
warehouse fixed costs
cost for carrying inventory
stock order and customer ordering costs
warehouse inbound and outbound transportation costs
Tradeoffs? (Figure 13-8, Ballou)

21. Facility Location
Selective Evaluation
Modified multiple centre-of-gravity to include inventory and fixed costs
form clusters of `markets’
find centres of gravity
re-assign `markets’
evaluate total costs (including transportation, inventory and fixed costs)
Can be used to determine the number of warehouses that best tradeoffs transportation, inventory and fixed costs
(See Ballou, p )
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22. Guided Linear Programming
Relevant costs include both fixed and variable costs
Accurate model requires a mixed-integer program
Computationally intensive
Approximation: distribute the fixed cost over the throughput (unknown until problem solved)
Problem then becomes a linear programming which is much easier to solve
Allocate fixed costs according to approximate throughput, solve LP, re-adjust fixed cost allocation, re-solve LP, etc.
(See Ballou, p )

23. Simulation Methods
Optimisation models are often “approximation” of “real-world” problems
accurate problem description
incorporate time-related aspects
integrate inventory and geographical concerns
only evaluative
candidate solutions must be provided
no optimality guarantee
Sub-optimal solution to accurately described problem

24. Appraisal of Multi-Location Methods
Mathematical Programming based methods gaining popularity
inexpensive and robust decision support tool
Extensions:
non-linear cost structure
discontinuous cost structure
integrated inventory and transportation issues
revenue effects

25. Other methods Regression analysis Factor rating system
Analytic Hierarchy Process (AHP)
Covering models
Game theory
Location-allocation models
goal programming
mixed integer programming

26. Logistics Network (Supply Chain) Planning
(Multi) product flow from source to demand points
number, size and location of production facilities
number, size and location of distribution centres
assignment of products and customers to DC’s
assignment of DC’s to production sites
choice of transportation modes
inventory policies:
frequency of replenishment
order size

27. Complexities Spatial and temporal aspects
Data collection and aggregation
Costs allocation and approximation
fixed
storage (related to inventory levels)
handling (related to throughput)
transportation cost non-linear
inventory-throughput relationship non-linear

28. Integrated Decisions Iterative approach Location
Transportation (Allocation)
Inventory
Iterative approach
Solve approximations of each problem in sequence
Update approximations and iterate