Facility Location Decisions: Network Design in a Supply Chain

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Facility Location Decisions Network Design in a
Supply Chain
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Outline

• A strategic framework for facility location and
  capacity allocation
• Facility location models
• Multi-echelon networks
• Solution approaches
• Dynamic location models
• Competitive location models

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Facility Location

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

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Network Design Decisions

• Facility role
• Facility location
• long-term impact, relocation difficult
• Amazon.com single warehouse in Seattle
• Capacity allocation
• utilisation vs. responsiveness
• Market and supply allocation
• impacts production, inventory and transportation
  decisions
• demand dynamic
• expansion or add plant?

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Location Theory - Early History

• Webers 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

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Hoovers (1957) tapered transportation rates

• minimum costs at either production point or
  market point

Material source
Market
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Factors Influencing Network Design Decisions

• Strategic
• Technological
• Macroeconomic
• Political
• Competitive
• Infrastructure
• Logistics and facility costs

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Strategic and Technological Factors

• Strategic dimensions
• cost, quality, responsiveness, variety
• Strategic roles for a facility
• Manufacturing economics/cost driven
• Retail revenue driven
• Service accessibility and availability?
• Outpost regional production to gain local
  skills
• Lead creates new products and processes
• Agglomeration proximity to suppliers/customers,
  skills base
• Economy of scale gt few high-capacity facilities
• Low fixed costs gt many local facilities
• Exchange rate and demand risks reduced if network
  has multiple locations with flexible capacity

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Macroeconomic, Political and Competitive Factors

• Government barriers
• currency controls, trading blocs
• environmental regulations
• Tariffs (import/export duties)
• high tariffs gt local plants for each region
• WTO gt consolidation of global network
• Local content rules
• Government Incentives
• tax breaks
• free trade zones (lower duties if production for
  export)
• Political stability
• currency conversion, independent judicial system
• Environment
• community receptivity, local business climate
• quality of life

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Infrastructural and Resource/Cost-Related
Factors

• Land/Construction costs
• Quality/Availability of labour
• Transportation/Energy infrastructure
• Proximity to suppliers
• Proximity to customers
• Inbound/Outbound distribution costs
• Other (company-owned) facilities
• Competitive Advantage ?

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Service and Number of Facilities Tradeoff
Response time and Local Presence
Response Time
Number of Facilities
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Where inventory needs to be for a one week order
response time - typical results --gt 1 DC
Customer
DC
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Where inventory needs to be for a 5 day order
response time - typical results --gt 2 DCs
Customer
DC
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Where inventory needs to be for a 3 day order
response time - typical results --gt 5 DCs
Customer
DC
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Where inventory needs to be for a next day order
response time - typical results --gt 13 DCs
Customer
DC
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Where inventory needs to be for a same day / next
day order response time - typical results --gt 26
DCs
Customer
DC
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Cost Build-up as a function of facilities

• Transportation
• out-bound usually more expensive than in-bound
• Production process
• weight-reducing (e.g. steel) gt locate close to
  raw material source

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A Framework for Global Site Location
GLOBAL COMPETITION
Competitive STRATEGY
PHASE I Supply Chain Strategy
INTERNAL CONSTRAINTS Capital, growth
strategy, existing network
TARIFFS AND TAX INCENTIVES
PRODUCTION TECHNOLOGIES Cost, Scale/Scope impact,
support required, flexibility
REGIONAL DEMAND Size, growth, homogeneity, local
specifications
PHASE II Regional Facility Configuration
COMPETITIVE ENVIRONMENT
POLITICAL, EXCHANGE RATE AND DEMAND RISK
PHASE III Desirable Sites
AVAILABLE INFRASTRUCTURE
PRODUCTION METHODS Skill needs, response time
PHASE IV Location Choices
FACTOR COSTS Labor, materials, site specific
LOGISTICS COSTS Transport, inventory,
coordination
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Quantitative Tools

• Center of Gravity Method
• Heuristics
• Mixed Integer Programming
• Optimisation-based heuristics
• Other methods
• Supply chain network design
• Single facility location
• Multi-facility location
• Joint location-allocation models
• Dynamic location models
• Competitive location models

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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)21/2

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Centre of Gravity Method

• Grid method
• centroid method
• Locate facility at

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Why is this called the centre-of-gravity method?

• Example
• i Xi Yi Vi
• 1 1 0 3
• 2 0 1 2
• 3 1 1 2
• Centroid is at ( 0.812, 0.541).
• Think of weights of Vi located at positions (Xi,
  Yi).
• Centroid is the point that balances the three
  loads.
• (LOGWARE)

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COG Method
COG
CR (2004) Prentice Hall, Inc.
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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

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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?
• Costs
• transportation, handling, inventory carrying,
  production/purchase
• facility fixed costs

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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 steps until no further
  change.

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Multiple Centre-of-Gravity Approach - Example
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Multiple Centre-of-Gravity Approach - Example

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Multiple Centre-of-Gravity Approach - Example

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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.
• Fixed costs of facility considered
• Candidate locations given (pre-selected)

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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 (or 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

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Kuehn Hamburger - Example

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Kuehn Hamburger - Example
First iteration Find the initial facility to
open by minimizing the total costs
Cost of point i supplied by candidate j
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Kuehn Hamburger - Example
Second iteration Find a facility to add (if any)
with maximum positive saving
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10
9
7
8
5
6
4
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2
1
3
Saving at point i if candidate j is added
reduced transportation cost if point i is
supplied by candidate j
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p-median Problem

• Ballou (Logware)
• demand point co-ordinates given
• assume out-and-back along Euclidean distance
• Candidate locations given

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P-Median
13-31
CR (2004) Prentice Hall, Inc.
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P-Median (Contd)
Repeating the analysis for a different number of
incinerators can find the optimal number of
incinerators as well.
13-33
CR (2004) Prentice Hall, Inc.
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Linear and Mixed Integer Programming

• LP useful in evaluating distribution costs
• Mixed Integer Programming can optimize site
  selection and distribution plan simultaneously
• Detailed cost estimates needed

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Network Optimization Models

• Allocating demand to production facilities
• Locating facilities and allocating capacity

• Key Costs
• Fixed facility cost
• Transportation cost
• Production cost
• Inventory cost
• Coordination cost

Which plants to establish? How to configure the
network?
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Demand Allocation TelecomOne and HighOptic
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Demand Allocation Model

• Which market is served by which plant?
• Which plants are used as supply sources?
• xij Quantity shipped from plant site i to
  customer/market j

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TelecomOne and High Optic - Production and
Transportation Costs (per 1000 units)
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Location-allocation models

• How many sites?
• Where to locate each?
• Capacities?
• Which customers assigned to each site?
• Which products to stock/produce at each site?

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Plant Location with (Multiple) Sourcing

• yi 1 if plant is located at site i, 0
  otherwise
• xij Quantity shipped from plant site i to
  customer j

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Plant Location with Single Sourcing

• yi 1 if plant is located at site i, 0 otherwise
• xij 1 if market j is supplied from plant site
  i, 0 otherwise

p-median problem !!
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Multi-echelon NetworksLocation-Allocation
Decisions
Which plants to establish? Which warehouses to
establish? How to configure the network?
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Locating Plants and Warehouses Simultaneously

• yi 1 if plant is located at site i, 0
  otherwise,
• ze 1 if warehouse is located at site e, 0
  otherwise
• xie amount shipped from factory i to warehouse
  e per year,
• wej amount shipped from warehouse e to market j
  per year,
• vhi amount shipped from supplier h to factory i
  per year.

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Supply Chain Network Design

• How many of each type of facilities?
• Where to locate each?
• Capacities?
• Fixed Costs?
• Which customers to be supplied from where?
• Which products to stock/produce at each site?
• Inventory Costs?

Non-linear
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Relevant Costs for Supply Network Design

• 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?

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Location Costs Tradeoffs
(Figure 13-8, Ballou)

Total cost
Warehouse fix cost
Inventory holding cost
Production/purchasing and order processing
Cost
Transportation cost
Number of warehouses
Generalized cost of trade-offs in facility
location problem
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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.

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The situation
MIP
A Multiple Product Network Design Problem
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MIP formulation
Handling rate
Fixed costs
Inbound and outbound transport rates
Sum of demand for customer l across all products
Plant capacity
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Non-linear CostsGuided Linear Programming
(Optimisation-based Heuristic)

• Relevant costs include both fixed and variable
  costs
• Accurate model requires a mixed-integer program,
  or worse, a non-linear 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.

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Guided LP (Single product, fixed costs,
inventory costs)
The situation
CR (2004) Prentice Hall, Inc.
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Example - Exact Formulation

• Let xpj amt. shipped from plant p to warehouse j
• wjk amt. shipped from warehouse j to customer k

non-linear
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Example - Computations

• Iteration 1
• Fixed cost assume all throughput (200000) flow
  through warehouse
• Warehouse 1 per-unit cost 100000/200000
  0.50/cwt
• Warehouse 2 per-unit cost 400000/200000
  2.00/cwt
• Inventory cost assume throughput equally divided
• Warehouse 1 2 per-unit cost
  100(100000)0.7/100000 3.2/cwt
• x1160000, x22140000, w1260000,
  w2150000,w2240000,w2350000
• Iteration 2
• Fixed cost
• Warehouse 1 per-unit cost 100000/60000
  1.67/cwt
• Warehouse 2 per-unit cost 400000/140000
  2.86/cwt
• Inventory cost
• Warehouse 1 per-unit cost 100(60000)0.7/60000
  3.69/cwt
• Warehouse 2 per-unit cost 100(140000)0.7/14000
  0 2.86/cwt
• x22200000, w2150000, w2240000, w2350000
• Iteration 3 . No change in
  solution!
• Re-compute true cost using non-linear functions!

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Conventional Network
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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 DCs
• assignment of DCs to production sites
• choice of transportation modes
• inventory policies
• frequency of replenishment
• order size

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Tailored Network Multi - Echelon Finished Goods
Network
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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

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Location and Network Design 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

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Integrated Decisions

• Location
• Transportation (Allocation)
• Inventory
• Iterative approach
• Solve approximations of each problem in sequence
• Update approximations and iterate