Statistical Process Control

Document Sample
Statistical Process Control Powered By Docstoc
					Facility Location

Operations Management
Dr. Ron Tibben-Lembke
Location Decisions
 Long-term decisions
 Difficult to reverse
 Affect fixed & variable costs
     Transportation costs (25% of price)
     Other costs: taxes, wages, rent

   Objective: maximize benefit of location to
    firm
What factors should we consider?

 Skilled workforce
 Environmental laws / cost of compliance
 Cost of utilities, labor, taxes
 Suppliers close by – fast & cheap access
 Customers close by
 Competitors close by? Skilled labor pool
 International - control issues?
Service Facilities – Traffic focus
   Revenue changes a huge amount, depending
    on the location.
     Old Navy in Stead because of cheap land?
     Location, location, location: you need traffic
     Make it convenient!
     vitamins: need enough, but it has to be the right kind
     people who would want to buy your products when
      they are there.
   Cost probably doesn’t change nearly as much,
    by location
     All   malls have high rent
Northtowne Center




   Wal-Mart   Office           Toys
              Max      WinCo   Party
A Tale of Two Stores



      W




          K
Kmart Access



               “I-80 & McCarran” sounds great.

               Kmart Sins:
               Can’t see from anywhere
               - see where we’re going
               Very circuitous entry
               - feels inconvenient, no matter
                how long it actually takes
Wal-Mart Access
Cost Focus
   Revenue does not vary much, depending
    on the location.
     Customers  don’t care if your warehouse is in
      Sparks or Sacramento
   Location is a major cost driver
     Impacts shipping, labor, production costs
     Varies greatly by location
Cost Minimization
Identify the costs that will vary most with the
  location you choose.
   Transportation,  taxes, labor,
   Facility construction cost, utilities
Other considerations
   Proximity  of services, suppliers
   Quality of life
   Government incentives
Cost Focus Process Overview
1.   Identify general region to locate in
        Usually based on mostly on transp. costs
2.   Identify a list of candidate cities
        Choose cities with good transp. Access
        Estimate labor cost & availability, facilities costs
3.   Select metro area, identify candidate
     properties.
        Find cost of building or leasing individual properties
Case Study:
Importing from China to E. Coast
Customer Location
     China to U.S. Container Rates
                                       NY / NJ $3,600
                                       36 days

                                      Wilmington DE $3,950
                                      36 days (door)


                                      Norfolk $3,600
                                      34 days




                                      Charleston $3,600
                                      35 days



                     Atlanta
New Orleans $3,200   $3,200
36 days              37 days (door)
                             Allentown
                                                        Elizabeth, NJ

Drayage   Harrisburg



Rates                                    Philadelphia


                                    Wilmington

              Baltimore




Roanoke



                          Norfolk
China to Long Beach
Landbridge Data

             Columbus $3000, 21days

           Cincinnati $2925, 21d


               Louisville $3050, 20d

         Murray $3350, 22d

                                         Nashville
         Memphis $2900, 18.5d
                                         $3300, 22d


                          Atlanta $3300, 23d
Distribution Center Location
 Minimize demand-weighted distance:
  distance to each customer times the
  volume of shipments to the customer
 How many to build?
 Where to build?
Case Study: Retailer
 Location of a 5th returns processing facility
 Addresses of 2125 Continental U.S. stores
 Location of 4 Return Goods Processing
  Centers
 List of all return shipments from each
  store, including pounds and # pallets
 Calculated actual highway distances from
  every store to its DC
Local Streets
Transportation Cost Approx.
 Current Pallets:               205,254
 Current Pallet Miles:          77.9m
 Cost / pallet-mile             11.68 cents
 Pallet-Mile = 1 pallet traveling 1 mile
 Minimize average distance traveled
Current RCs
Dallas Realignment
Close 1 Existing RC
Location Methods
   Minimize demand-weighted distance
     Center of Gravity – minimizing demand-weighted
      distances of one facility
     Ardalan – minimize transportation of multiple facilities,
      but must locate by customers
     (P-Median Problem, Maximum Covering)

   Factor Weighting – consider qualitative factors
   Break-even – Consider fixed & variable costs
Center of Gravity
   Compute X and Y
    coordinates separately
                                           d W    ix       i
                                    CX    i
   dix is the X coordinate of
    location i.
                                           W  i
                                                        i




    diy is the Y coordinate of i.
    Wi is the X demand at i.
                                           d W    iy       i
                                    CY    i
   CX and CY are the
    coordinates of the DC.
                                           W  i
                                                        i
Center of Gravity Example 1
 You need to decide where to build a new
  DC for Motorola.
 It needs to serve wholesalers in Reno,
  Dallas, and Chicago.
 Locate these cities on an unscientific,
  rectangular grid.
 Grid must maintain relative distances, but
  X and Y grids could be different.
  Center of Gravity – Ex 1
100


 80


 60


 40


 20


 0
      0   20   40   60   80   100   120   140   160
Center of Gravity Method
City              Location    Demand
 Reno is at           17, 55   100
 Dallas is at         78, 20    90
 Chicago is at      110, 65. 120

   Demand is TL/month
Center of Gravity
           d W        ix       i
                                      17 *100  78 * 90  110 *120
    CX    i
                                    
           W      i
                            i               100  90  120

         1,700  7,020  13,200 21,920
    CX                                  70.7
                   310             310
          diyWi 55 *100  20 * 90  65 *120
    CY  i        
          Wi  i
                          100  90  120

         5,500  1,800  7,800 15,100
    CY                               48.7
                  310           310
100       Center of Gravity – Ex 1, Map 2
 80


 60


 40


 20


 0
      0    20   40   60   80   100   120   140   160
                  North
                  Platte



Sharon
Springs

          Salina KS


                           Ctr Grav. Ex
                           1 - Detail
Compromise Solution
   Closest town is Sharon Springs, KN
     Population  872
     30 miles from I-70.
     Probably not a good choice

 Salina, KN puts us at I-70 and I-35
 North Platte NE is at I-80 and 83.
     Access   to Dallas less convenient
100
                              Ardalan Map 2

 80


 60


 40


 20


 0
      0   20   40   60   80   100   120   140   160
Finalizing City
   Go where other warehouses are
     More  choice in pre-built buildings
     Cheaper, easier to build a new one
     More trucks to and from town, means more carriers
      there, means cheaper rates.
     Backhaul situation

   Get estimates of inbound, outbound trucking
    costs.
     Provide lists of # loads per year to each destination,
      from each source
Center of Gravity Example 2
 You need to decide where to locate a DC
  in South Dakota
                 X    Y    Demand
 Pierre        78 47           50
 Watertown    150 65            8
 Sioux Falls  160 25           90
 Rapid         12 42           60
100                  Ardalan Map 2 - Detail

80


60


40


20



 0
  0   20   40   60   80   100   120   140   160
Center of Gravity
            d W        ix              i
                                                78 * 50  150 * 8  160 * 90  12 * 60
     CX       i
                                            
            W     i
                                i                          50  8  90  60

          3,900  1,200  14,400  720 20,220
     CX                                      97.2
                      208               208

           d W        iy           i
                                              47 * 50  65 * 8  25 * 90  42 * 60
    CY    i
                                            
           W  i
                            i                          50  8  90  60

         2,350  520  2,250  2,520 7,640
    CY                                    36.7
                    208               310
100                       Final Location?
80


60


40


20



 0
  0   20   40   60   80   100   120   140   160
Ardalan Heuristic
   Need a matrix of distances or costs from each
    customer location to every other location
   Demand at each location
   Weight – give higher weight to more important
    customers – their pain of traveling a longer
    distance is worth more.
   Only consider locating where customers are
   Identify the one best place to locate at, then the
    second one to add, then the third, etc.
Ardalan Heuristic
        weighted distance traveled
Minimize
        From               The distance from A
                           to A is shown as 0,
To A B C D Dem.            but there is no
                           reason we couldn’t
A 0 11 8 12 10             put the actual
                           mileage in.
B 11  0 10 7        8
                            Carriers might
C 8 10 0       9 20         charge more on
                            popular routes, so
D 9.5 7   9    0 12         costs may not be
                                symmetrical.
Ardalan Method
 Compute cost of satisfying each demand
  from each possible distribution center
  location.
 Step 1: Multiply distances * demand
 A to B: 11 * 10 = 110
Ardalan Heuristic
   Multiply distances times demand, and sum

To   A B      C    D * Dem =     A   B     CD
  A 0 11      8    12 * 10       0 110    80 1
  20
  B 11 0      10   7   *   8    88    0   80 5
  6
  C 8 10      0    9   *   20   160 200    01
  80
Ardalan Heuristic
   Choose smallest total as first location

          A     B     C     D     If we only build one facility,
                                  we should build it in C, and
   A      0    110    80   120    the total transportation costs
                                  will be 268 truckload miles.
   B      88    0     80   56
   C     160   200    0    180    Notice that even if we built a
                                  facility in B or D, it will
                                  continue to be cheaper to
   D     114   84    108    0     serve A from C.
                                  In the next step, we will
Total    362   394   268   356    make use of that.
Ardalan Heuristic
Compare each cost in row to the cost in
 the chosen cost, and switch is lower
                           Why do we do that?
       A B C D             Before, the first row said
                           “0, 110, 80, 120.”
   A   0 80 80 80          We’ve decided to build in C
                           If we build in A, B, or D, how
   B 80 0 80 56            much will we spend to haul to
                           A? No matter what, we’ll
   C   0    0    0   0     spend 80.

   D 108 84 108 0          If we locate in D, we’ll serve B
                           from D, but otherwise, we’ll
Total 188 164 268 136 serve B from C, because it’s
                                    cheaper.
Ardalan Heuristic
 Don’t need first chosen city any more.
 Choose second cheapest city
         A B D           This means that if we locate #2
                         in D (and we already decided to
   A     0 80 80         locate one in C), total costs will
                         be $136. How?
   B 80 0 56
                         A served at cost of $80 by C.
   C     0   0     0     B served at cost of $56 by D.
                         C served at cost of $0 by C.
   D 108 84 0            D served at cost of $0 by D.

                         This is why we needed to change
Total 188 164 136        the costs above.
Ardalan Heuristic
 Compare non-chosen cities’ costs to cost
  of chosen, and choose the lower cost
From A B D
    A   0 80 80
    B 56 0 56
    C   0    0    0
    D   0    0    0
Total 56 80 136
Ardalan Heuristic
 Compare non-chosen cities’ costs to cost
  of chosen, and choose the lower cost
From A B
    A   0 80         If we locate the third facility in A, we will have
                     facilities in C, D, and A. B is the only city
                     without a DC, and it will be served at a cost
    B 56 0           of $56.
    C   0    0       What happens if we do the method one more
                     time?
    D   0    0
Total 56 80
Ardalan Heuristic
 Compare non-chosen cities’ costs to cost
  of chosen, and choose the lower cost
From A B           After we get rid of the now-unnecessary
    A   0    0     column A, there is only column B, with total
                   costs of 0.
                   Does that make sense? Well, yes: every city
    B 56 0         gets served by the DC located in that city, so
                   if the cost of serving a city from that city is 0,
    C   0    0     then yes, it makes sense.

    D   0    0
Total 56 0
Ardalan Summary
    Total            Transp   Transp
   # DCs   Locations Total   Savings
      1     C         268
      2     C,D       136      152
      3     C,D,A      56       80
      4     C,D,A,B     0       56
Ardalan Summary
   Assumes that we have to locate in the same city as one
    of our customers, which is not always the case.
   However, it can be used to find more than one location.
   Center of Gravity does not try to locate in the same city
    as one of the customers, but can only set one site.
   If we choose the same sites as customers A and X, we
    obviously don’t really have to put the warehouses in
    those exact cities.
P-Median Problem
 Minimize average weighted distance to
  customers, when locating P facilities,
  where P>=1.
 Can consider 100s of locations.
 Complex to solve – there is software for
  this.
Maximum Covering Problem
 A facility can “cover” a customer if the
  customer is within X miles of the facility.
 Try to find the best location, and minimum
  number of facilities to cover all demands.
 Cover a table with plates.
 Math also very hard.
Max Covering
Max Covering 2
                 Comparison of Results
                                              (Using Distances of 150, 200, 250,250)
           100.00%
Demand Covered




                 99.00%
                 98.00%
                 97.00%
                 96.00%                                                                  Lower Bound
                 95.00%                                                                  Greedy Solution

                 94.00%                                                                  Upper Bound

                 93.00%
                 92.00%
                 91.00%
                 90.00%
                                                                                      Number of
                          15   16   17   18   19   20   21   22   23   24   25   26   Facilities
Solving large problems
Incremental or clean-slate apprach

 Take into account existing facilities
 What is the best location to add, given the
  existing facilities?
 What is the best to add, if we were to
  close down one of the current facilities?
 Unfortunately, only P-Median or Maximum
  Covering can deal with these.
Factor Rating Method
   Most widely used method?
   Useful for service or industrial facilities: can
    include intangible, qualitative factors
   List relevant factors, assign a weight
   Develop a scale for each factor
   Score each factor using the scale
   Multiply scores by weights, add up
   Choose location with highest total score
   Kind of like “Miss America”
Factor Rating Example
   We need to decide where to build a new coffee
    roasting plant. There are two possible locations:
    Dallas, and Denver.
   We consider the following factors
     Transp:  annual trucking costs in $k
     Lease: annual costs in $k
     Labor availability: scale 1-10, unemployment, related
      industries
     Quality of life: scale 1-10: outdoor activities, cultural,
      sports, education
Factor Rating Example
 Using a scoring system we developed, we
  have the following.
Factor          Weight      TX    CO
Transportation       0.5   900 1023
Plant Lease Cost 0.3         45    39
Labor availability   0.2     10     8
Quality of Life      0.1      7     9.5
Normalizing Scores
 All factors must be scored on the same
  scale, like 1-10, or 0-1.0, etc.
 Costs need to be re-scaled
     Lowest cost site gets a 10.
     More expensive site gets
        Plant Lease: 39/45 * 10 = 8.7
        Transportation: 900/1,023 * 10 = 8.8

   Multiply these raw scores by the weights
    for weighted scores
 Factor Rating Example
                 TX            CO
Factor Wt      Raw Wtd        Raw Wtd
Transp. 0.4      10     4.00     8.80 3.52
Plant    0.3      8.7 2.61      10    3.00
Labor    0.2     10     2.00     8    1.60
Q Life   0.1      7     0.70     9.5 0.95
TOTAL                   9.31          9.07
TX is best, but not by a huge amount
Possible Approach
 Use Ardalan to find out which general
  regions to locate in (state / county).
 Use factor weighting to choose city.
 Ardalan has disadvantage of choosing
  weights -- difficult to set levels.
Break-Even Analysis
   Determine fixed and variable costs for each
    location
   Fixed cost: how much it would cost to open a
    facility there
   Variable cost: how much total costs would
    increase as production increases:
     Transportation   costs
     Labor costs
     Taxes
     Increased   construction costs
   Hey – this sounds familiar!
Locating Service Facilities
Using Linear Regression
 Collect data about your current facilities
 Use regression to determine which
  variables have a significant impact on
  profits
 Choose new facilities which have these
  characteristics
Method Comparison
 Center of gravity minimizes average
  distance for one facility only.
 Ardalan Minimizes weighted distances for
  more than one facility.
 Breakeven: fixed & variable costs.
 Factor weighting considers many other
  important aspects of location, but does not
  minimize distance.
Transportation Method
You have 3 DCs, and need to deliver
 product to 4 customers.         D2

   A 10
                                 E4
   B 10
                                 F 12
   C 10

                                 G 11

Find cheapest way to satisfy all demand
Solving Transportation Problems

   Trial and Error            D    E    F   G
   Linear Programming
    – ooh, what’s that?!   A   10   9    8   7
   Tell me more!
                           B   10   11   4   5

                           C   8    7    4   8

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:3
posted:9/4/2011
language:English
pages:69