Location and Distribution

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Location and Distribution

• Henry C. Co
• Technology and Operations Management,
• California Polytechnic and State University

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Contents

• Location
• Importance of Location
• Systematic Decision Process
• Factor Rating
• Cost-volume Analysis
• Locational Breakeven Analysis
• Single Facility Location
• Multi-Facility Location
• Distribution
• The Transportation Problem
• The Transportation Problem with Lost Sales
• It is not about time!

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Importance of Location
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Location, Location, Location!

• Location decisions for residential homes are
  important because
• They affect travel time to work, to school, to
  recreational centers, and to shopping malls.
• A home in a good school district is particularly
  important for most parents with school-age
  children.
• A home in a bad neighborhood means the
  residents are exposed to higher risk of crimes
  and drugs, while a home is a good neighborhood
  is a source of pride and status.

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• Location decisions are important to business
  organizations because
• They affect the cost of doing business, and the
  flow of goods and services.
• The faster the flow of goods and service in one
  direction, the lower the inventory, and the
  quicker funds () flow back in the reverse
  direction.
• They commit the organization to long lasting
  financial, employment, and distribution patterns.
  
• For retail outlets, location affects the demand
  for their products/services.
• For labor-intensive operations, labor costs may
  force an organization to relocate its operations
  to locations where wages are lower.

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• Location decisions are either demand-pulled,
  supply-pushed, or more frequently, both
  demand-pulled and supply pushed.
• Demand-pulled
• Market-related factors such as the location of
  customers, the location of the competition, the
  need for room for expansion, and the communitys
  attitude towards the organization.

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• Supply-pushed location factors
• Based on the cost of doing business. The cost of
  doing business may be tangible or intangible.
• Tangible costs include the cost of site and
  construction, the availability and costs of
  labor, transportation cost (proximity to
  suppliers and markets), utilities (availability
  and costs), taxes, and real estate (site
  acquisition, preparation and construction) costs.
• Intangible costs include
• Zoning and legal regulations, community
  attitudes, proximity to parent companys
  facilities, expansion potential, labor climate,
  training and employment services, and the quality
  of life (schools and churches, recreation and
  cultural attractions, amount and type of housing
  available) are examples of important location
  factors that are difficult to quantify.

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Technology-Based Firms

• Tend to cluster around these organizations.
• Eventually developed into regional networks of
  expertise.
• Stanford University, which spawned Silicon Valley
• MIT which spawned Route 128 in Boston
• In the United Kingdom, Imperial College and
  Cambridge which spawned Science Parks.
• Large well-established firm also serve as
  incubators.
• Xerox PARC and Bell Laboratories spawned
  Fairchild Semiconductor which in turn led to
  numerous spin-offs including Intel, Advanced
  Memory Systems, Teledyne, and Advanced
  Micro-Devices.
• Engineering Research Associates (ERA) led to more
  than 40 new firms, including Cray, Control Data
  Systems, Sperry and Univac.
• Technology-based firms cluster around their
  incubator organizations to gain financial and
  technical support.

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International Locations

• Trade quotas, language, culture, government
  stability and cooperation, monetary system,
  infrastructure, etc. can sometimes force a
  multinational corporation to divest its interest
  in a country.

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Systematic Decision Process

• Quantitative Approaches
• Qualitative Approaches
• Integrating Qualitative Quantitative Data

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• Define the location objectives and associated
  constraints.
• Identify the relevant decision criteria.
• Quantitative (e.g., cost of doing business)
• Qualitative (i.e., less tangible).
• Relate the objectives to the criteria using
  appropriate models (e.g., economic cost models,
  BEP analysis, LP, factor rating system).
• Do field research to generate relevant data and
  use the models to evaluate the alternative
  locations.
• Select the location that best satisfies the
  criteria.

Monks, J. G., Operations Management Theory and
Problems, 3rd Edition, McGraw-Hill Book Company,
ISBN 0-07-042727-5, p. 106.
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• Qualitative Approaches
• Quantitative Approaches
• Conventional approaches... cost-volume analysis,
  net-present value
• Decision trees
• Transportation (Linear Programming)
• Computer Simulation.
• Integrating Qualitative Quantitative
• Rating scale approach
• Relative-aggregate-scores approach.

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Qualitative Approach Factor Rating Method
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• Develop a checklist of relevant factors
• Assign weight to each factor to indicate its
  relative importance (total 100)
• Assign a common scale to each factor (e.g., 1-5,
  5best), and designate any minimum
• Score each potential location according to the
  designated scale, and multiply the scores by the
  weights
• Total the points for each location, and choose
  the location with the maximum points

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Factor Rating Template (Illustration)
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Which of these locations is better?
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Locational Breakeven Analysis

• To identify the ranges of demand volume where
  each location is preferable.

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• Determine fixed and variable costs.
• Plot total costs.
• Determine lowest total costs.
• Example

Cell D3 B3C3B1. To determine the total costs
for the other three locations, we copy the
formula for D3 and paste onto cells D4D6.
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• Between of 0 and 5,000 units, the line segment
  associated with location B is the lowest.
• Between annual outputs of 5,000 and approximately
  11,000 units, location C is superior.
• Beyond approximately 11,000 units, location A is
  superior.

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Using Goal Seek to find the breakeven volume

• Between A and C
• D11B11B13C11 and D12 B12B13C12
• Set Cell D13 (the cost difference)
• To value 0 (the two costs must be equal)
• By changing cell B13 (the volume)

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• Between B and C
• D17B17B19C17
• D18B18B19C18
• Set Cell D19 (the cost difference)
• To value 0 (the two costs must be equal)
• By changing cell B19 (the volume)

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• Below 5,000 units, B is the best alternative.
• Beyond 11,111 units, B is the best alternative.
• Between 5,000 and 11,111 units, C is the best
  alternative.
• Alternative D is never a good choice.

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Single Facility Location
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Assumptions

• Demand volumes are frequently assumed to be
  concentrated at one point (demand cluster)
• The basis of variable costs
• Total transportation costs usually are assumed to
  increase proportionately with distance
• Straight-line routes are commonly assumed b/w the
  facility and other network points
• Not dynamic

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Center of Gravity Approach

• Center-of-gravity approach, the grid method,
  centroid method, p-median method
• Transportation cost is the only locational
  factor, static continuous location model
• Illustration

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• E2B2D2 copy an paste onto E3E8
• F2C2D2 copy an paste onto F3F8
• D9SUM(D2D8) copy an paste onto E9F9
• D12E9/D9 D13F9/D9.

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How good is the center of gravity?

• First, consider Euclidean distances.
• Geometrically, the straight line connecting the
  center of gravity and demand center A is the
  hypotenuse of a right triangle.
• The lengths of the two legs of the right triangle
  correspond to the x- and y- coordinate distances
  between the center of gravity and demand center
  A, i.e., (6.669 2.5) along the x-axis, and (4.5
  3.022) along the y-axis.
• From the Pythagorean Theorem, the square of the
  length of the hypotenuse equals the sum of square
  of the length of the two legs (6.669 2.5) 2
  (4.5 3.022)2 19.566.
• The Euclidean distance therefore is 4.423. The
  corresponding Excel formula is F6
  SQRT((B6-C2)2(C6-C3)2).

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Euclidean Distances
Copy and paste the formula for F6 onto
F7F12. The total weighted sum of the distances
is the sumproduct of the forecasted demand and
the Euclidean distances 141,166.
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Use Solver to optimize the location
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Total weighted sum of the distances is reduced to
136,204.
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Rectilinear Distance

• Parallel to the x- and y- axes (east-west,
  north-south, and making 90? turns only.

F6ABS(B6-C2)ABS(C6-C3) copy an paste onto
F7F12 G6D6F6 copy an paste onto
G7G12 G13SUM(G6G12)
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• Use Solver to optimize the location

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Solver was able to reduce the total weighted sum
of the distances based on rectilinear distance
from 180,147 to 161,000 or by about 10.6!
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Multiple Facility Location
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• In many distribution/logistics problems, we are
  concerned with finding the minimum cost way to
  get products from a variety of plants/suppliers
  to their final markets.
• Typically, different suppliers have different
  costs and capacities transportation costs are
  specific to a supplier / market pair and
  different markets have different requirements and
  possibly profitability.
• Realistic problems of this type can involve large
  numbers of suppliers, products, and markets and
  can be difficult to figure out by intuition or
  gut feel.

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Solution Methods

• There are many approaches to the distribution
  system planning problem.
• The usual approach is to develop a first cut
  solution either by making simplifying assumptions
  or using heuristics, and then fine-tuning the
  solution with more advanced methodologies such as
  mathematical programming techniques and computer
  simulation.
• The center of gravity method is an example of a
  first cut solution. The solution was derived by
  taking weighted average of the x- and y-
  coordinates of the demand clusters.
• Solver improved the solution by than 10.
• What we just solved is actually a complex
  non-linear optimization problem. The availability
  of inexpensive high-speed computer has made such
  a complex problem appear so trivial!

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Basic Planning Question

• Warehouses
• How many warehouses should there be in the
  logistics network?
• How large should they be, and where should they
  be located?
• Customers
• Which customers should be assigned to which
  warehouses?
• Which warehouses should be assigned to which
  plants, vendors, and ports?
• Distribution
• Which products should be stocked in which
  warehouses?
• Which products should be shipped directly from
  plants/vendors/ports to customers?

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Distribution
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The Transportation Problem

• How to satisfy demands at a given number of
  destinations with supplies from given set of
  origins.
• Structure of the system is known
• Location and characteristics of facilities
• Location and profile/demand of customers
• Transportation means and costs
• Distribution strategy to satisfy demand at least
  cost.

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Illustration

• The Hottest Mexican Restaurant has restaurants in
  5 Midwestern cities. They order their tortillas
  from the Laredo Tortilla Factory, which has
  warehouses in 6 cities. The shipping costs (in
  dollars per dozen tortillas) are given below

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• The demand for each restaurant and the tortillas
  available at each warehouse are

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Excel Spreadsheet

• Step 1 Set up the EXCEL spreadsheet as shown
  below

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• Notice that there are two sections. The first
  section shows the unit shipping costs. The cells
  have been formatted as currency with 2 decimal
  places (Select by highlighting the cells, then
  click on Format- Cell- Currency ).
• The second section shows the allocation and
  shipping costs. The optimal allocations have been
  assigned to cells B20F25. (at this time, these
  cells are all blanks). These are the decision
  variables.
• The demand and supply have been entered in cells
  B27F27 and cells H20H25, respectively. Also,
  row 28 has been formatted as currency with 2
  decimal places, and all other cells formatted as
  number with 2 decimal places.

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Sums of Cells

• Step 2 Enter the formulae for the sum of demand
  (cells B26F26) and the sum of supply (cells
  G20G25), respectively.
• For example, B26SUM(B20B25) copy and paste the
  formula from C26F26 .
• G20SUM(B20F20) copy and paste the formula from
  G21G25 .
• To find out if supply is sufficient, enter the
  formulae of the total system demand and the total
  system supply.
• Total system supply H26SUM(H20H25)
• Total system demand G27SUM(B27F27)
• The sum of supply is H26423. Similarly, compute
  the sum of demand. The sum is G27370. In this
  case, there will be excess supply.

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Shipments from ... Shipments to

• Step 3 Enter the formula for cell
  G20SUM(B20F20), the total shipment from Tulsa,
  as shown. Note that cells B20F20 the
  allocations from Tulsa to Minneapolis, Salina,
  Kansas, Lincoln, and Wichita, respectively. Copy
  this formula and paste it onto cells G21G25.
• Step 4 Likewise, enter the formula for cell
  B26SUM(B20B25), the shipments to Minneapolis
  copy and paste the formula onto cells C26F26.

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Shipping Costs

• Step 5 Enter the formula for cell
  B28SUMPRODUCT(B3B8,B20B25), the total shipping
  cost to Minneapolis. Copy and paste the formula
  onto cells C28F28.
• Step 6 Enter the formula for cell
  G28SUM(B28F28), the total system cost.

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• What we have just modeled is a linear programming
  problem.
• The objective function is the total
  transportation cost (to be minimized),
• subject to the demand-supply constraints.
• We are now ready to solve the problem using an
  Excel tool called Solver.

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The Northwest Corner Solution

• Starting from cell B20 (the northwest corner),
  let us find out how many units we can allocate
  from Tulsa to Minneapolis.
• Tulsa has 77 units available and Minneapolis
  needs 52 units. Suppose we allocated 52 from
  Tulsa, to satisfy the demand of Minneapolis.
• The leaves Tulsa with a remaining capacity of
  77-5225 units. Allocate the remaining 25 units
  from Tulsa to Salina (cell C20).
• Salina has a demand of 99 units. With 25 units
  from Tulsa, Salina still needs 74 units. Allocate
  45 units from the next origin Oklahoma. This will
  exhaust the supply of Oklahoma. The remaining 29
  units will come from Denver.
• Etc., etc.

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Solver

• Step 8 In the Tool-Solver menu, enter the
  following (the Set Target Cell is G28, the
  grand total cost)
• By changing cells B20F25 (the cells highlighted
  in light green is our allocation table).
• Select the Min button to minimize the grand total
  cost.

• Step 7 Click on Tool, and choose Solver in
  the pull-down menu. You should see this

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Adding Constraints

• Step 9 Add the following constraints (one at a
  time)
• Since total capacity exceeds demand, the shipment
  from each source should be less than or equal to
  its capacity G20G25 ? H20H25, i.e.
• Since total demand is less than total capacity,
  the total shipment to each destination should be
  equal to its demand, B26F26 B27F27

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Options Linear, Non-negative, Auto-Scale

• Step 10After entering all constraints, set the
  option as shown

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• Step 11 Click the Solve button!

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The Transportation Problem with Lost Sales
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• Suppose, the warehouse in Omaha becomes
  unavailable.
• Originally, the sum of supply was 423.
• With Omaha gone, the total supply is now 351
  units.
• Since total demand is 370 units, 19 (370-351)
  units of demand will not be satisfied.
• Replace Omaha by Lost Sales, with capacity
  equal to the demand not satisfied, i.e., 19
  units.
• Suppose the unit cost of unsatisfied demand is
  30 for the restaurants in Salina and Kansas, and
  20 for the other locations.

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The Northwest Corner Solution

• Row 8 has been changed to Lost Sales.
• Cell H25 and cell B16 equals the demand not
  satisfied 19 units.

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• Solver reduced total cost by 40 (from 2,277
  down to 1,369).
• Lincoln Wichita will have shortages (4 15
  units, respectively).

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It is not about time!

• Based in part from
• http//www.business.auburn.edu/gibsobj/SCM20-20
  012920-20Location20Location.doc.
• Journal of Commerce Inc. Feb 26, 2001

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How many warehouses?

• About every five years, large companies undertake
  a network design project to determine if their
  warehouses are properly positioned.
• Many companies hire consultants for this and use
  software to perform the analysis.
• They address the positioning of warehouses but
  not all the elements of the supply chain.
• Most important of these elements is how warehouse
  design affect customer service.

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Customer's Lead-time

• Lead-time is based on two components - inventory
  availability and product acquisition time.
• Acquisition time is only relevant when the
  inventory is unavailable.
• When inventory is available, the time to get
  product from the warehouse to the customer is
  almost always fixed. It consists of the time to
  process the order plus the time it takes to
  transport it to the customer. These times don't
  vary much. Moreover, customers generally are
  aware of and accustomed to them.
• When inventory is unavailable. Acquisition time
  becomes important.
• Customer's lead time includes the added time to
  get the product back in stock or the time to
  process and ship the product from some other
  location such as another warehouse, a
  manufacturing plant or a supplier.

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Example

• Suppose a warehouse processes all the orders for
  which it has inventory in one day and that the
  average transit time is an additional day.
• If inventory is available, customer's lead time
  2 days.
• Suppose the product is available 90 of the time
  and the average time to acquire out-of-stock
  product is 10 days.
• The expected customer's lead time 2 days
  (100-90)10 days 3 days.

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Components of Customer Lead-time

• Components of Customer Lead-time
• Transit time (one day, on average, in our
  example)
• Order processing time (also one day)
• Probability that inventory is available (90
  percent)
• The acquisition time (10 days).
• Which of these is dependent on the location of
  the warehouses?

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• The location impacts only one of these elements
  the transit time from the warehouse to the
  customer.
• This transit time generally depends on the
  distance from the warehouse to the customer.
• In most supply chains the average distance
  decreases as warehouses are added to the network.
  
• In our example, the location only impacts one day
  of the three-day average customer lead time.
  That's only a third of the total!

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Adding more warehouses

• Think about the capability of the network to
  decrease transit times by adding more warehouses.
  In most markets, customers are distributed
  approximately like the U.S. population and adding
  more warehouses impacts the average distance only
  slightly.
• In a 4-warehouse network, for example, the most
  the transit time can be reduced by adding a 5th
  warehouse is 15.9.
• Moreover the transit time is only part of the
  customer's lead time - a third in this case.
• The added warehouse reduces overall customer lead
  time by 1/315.9 ? 5!

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Conclusion

• Importance of warehouse location is overrated.
• Warehouse network may have some effect on these
  components. However, that effect is small.
• May have contrary effect. As the number of
  warehouses increases, inventory availability goes
  down, causing lead times and costs to increase.
• More effective levers include
• Order processing times
• Inventory availability
• Acquisition time

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• Warehouse network designers must consider more
  than just where warehouses are located. They
  should account for all the elements of the
  customer's lead time.