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Location and Distribution

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Title: Location and Distribution


1
Location and Distribution
  • Henry C. Co
  • Technology and Operations Management,
  • California Polytechnic and State University

2
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!

3
Importance of Location
4
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.

5
  • 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.

6
  • 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.

7
  • 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.

8
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.

9
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.

10
Systematic Decision Process
  • Quantitative Approaches
  • Qualitative Approaches
  • Integrating Qualitative Quantitative Data

11
  • 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.
12
  • 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.

13
Qualitative Approach Factor Rating Method
14
  • 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

15
Factor Rating Template (Illustration)
16
Which of these locations is better?
17
Locational Breakeven Analysis
  • To identify the ranges of demand volume where
    each location is preferable.

18
  • 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.
19
  • 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.

20
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)

21
  • 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)

22
  • 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.

23
Single Facility Location
24
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

25
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

26
  • E2B2D2 copy an paste onto E3E8
  • F2C2D2 copy an paste onto F3F8
  • D9SUM(D2D8) copy an paste onto E9F9
  • D12E9/D9 D13F9/D9.

27
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).

28
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.
29
Use Solver to optimize the location
30
Total weighted sum of the distances is reduced to
136,204.
31
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)
32
  • Use Solver to optimize the location

33
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!
34
Multiple Facility Location
35
  • 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.

36
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!

37
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?

38
Distribution
39
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.

40
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

41
  • The demand for each restaurant and the tortillas
    available at each warehouse are

42
Excel Spreadsheet
  • Step 1 Set up the EXCEL spreadsheet as shown
    below

43
  • 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.

44
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.

45
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.

46
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.

47
(No Transcript)
48
  • 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.

49
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.

50
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

51
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

52
Options Linear, Non-negative, Auto-Scale
  • Step 10After entering all constraints, set the
    option as shown

53
  • Step 11 Click the Solve button!

54
The Transportation Problem with Lost Sales
55
  • 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.

56
The Northwest Corner Solution
  • Row 8 has been changed to Lost Sales.
  • Cell H25 and cell B16 equals the demand not
    satisfied 19 units.

57
  • Solver reduced total cost by 40 (from 2,277
    down to 1,369).
  • Lincoln Wichita will have shortages (4 15
    units, respectively).

58
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

59
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.

60
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.

61
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.

62
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?

63
  • 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!

64
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!

65
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

66
  • 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.
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