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Operations
             Management
               Module C –
               Transportation Models

                             PowerPoint presentation to accompany
                             Heizer/Render
                             Principles of Operations Management, 7e
                             Operations Management, 9e
© 2008 Prentice Hall, Inc.                                             C–1
Outline
                 Transportation Modeling
                 Developing an Initial Solution
                              The Northwest-Corner Rule
                              The Intuitive Lowest-Cost Method
                 The Stepping-Stone Method
                 Special Issues in Modeling
                              Demand Not Equal to Supply
                              Degeneracy
© 2008 Prentice Hall, Inc.                                        C–2
Learning Objectives
               When you complete this module you
               should be able to:
                       1. Develop an initial solution to a
                          transportation models with the
                          northwest-corner and intuitive
                          lowest-cost methods
                       2. Solve a problem with the stepping-
                          stone method
                       3. Balance a transportation problem
                       4. Solve a problem with degeneracy
© 2008 Prentice Hall, Inc.                                     C–3
Transportation Modeling
             An interactive procedure that finds
              the least costly means of moving
              products from a series of sources
              to a series of destinations
             Can be used to
              help resolve
              distribution
              and location
              decisions
© 2008 Prentice Hall, Inc.                          C–4
Transportation Modeling
                  A special class of linear
                   programming
                  Need to know
                             1. The origin points and the capacity
                                or supply per period at each
                             2. The destination points and the
                                demand per period at each
                             3. The cost of shipping one unit from
                                each origin to each destination
© 2008 Prentice Hall, Inc.                                           C–5
Transportation Problem
                             To
          From                    Albuquerque   Boston   Cleveland
          Des Moines                  $5          $4        $3
          Evansville                  $8          $4        $3
          Fort Lauderdale             $9          $7        $5




          Table C.1


© 2008 Prentice Hall, Inc.                                           C–6
Transportation Problem
                                                                               Boston
                                                               Cleveland     (200 units
                                                               (200 units     required)
                                           Des Moines           required)
                                            (100 units
                                             capacity)

                             Albuquerque
                              (300 units
                               required)                 Evansville
                                                         (300 units
                                                          capacity)


                                                                            Fort Lauderdale
                                                                               (300 units
           Figure C.1                                                           capacity)

© 2008 Prentice Hall, Inc.                                                                C–7
Transportation Matrix
          Figure C.2
                             To                                            Factory      Des Moines
                                  Albuquerque   Boston        Cleveland    capacity     capacity
          From                                                                          constraint
                                           $5            $4           $3
          Des Moines                                                         100
                                                                                        Cell
                                                                                        representing
                                           $8            $4           $3                a possible
          Evansville                                                         300        source-to-
                                                                                        destination
                                                                                        shipping
                                           $9            $7           $5                assignment
          Fort Lauderdale                                                    300
                                                                                        (Evansville
                                                                                        to Cleveland)
          Warehouse
          requirement                300         200            200          700


   Cost of shipping 1 unit from Fort                          Cleveland            Total demand
   Lauderdale factory to Boston warehouse                 warehouse demand         and total supply

© 2008 Prentice Hall, Inc.                                                                       C–8
Northwest-Corner Rule
             Start in the upper left-hand cell (or
              northwest corner) of the table and allocate
              units to shipping routes as follows:
                         1. Exhaust the supply (factory capacity) of each
                            row before moving down to the next row
                         2. Exhaust the (warehouse) requirements of
                            each column before moving to the next
                            column
                         3. Check to ensure that all supplies and
                            demands are met


© 2008 Prentice Hall, Inc.                                              C–9
Northwest-Corner Rule
            1. Assign 100 tubs from Des Moines to Albuquerque
               (exhausting Des Moines’s supply)
            2. Assign 200 tubs from Evansville to Albuquerque
               (exhausting Albuquerque’s demand)
            3. Assign 100 tubs from Evansville to Boston
               (exhausting Evansville’s supply)
            4. Assign 100 tubs from Fort Lauderdale to Boston
               (exhausting Boston’s demand)
            5. Assign 200 tubs from Fort Lauderdale to
               Cleveland (exhausting Cleveland’s demand and
               Fort Lauderdale’s supply)

© 2008 Prentice Hall, Inc.                                      C – 10
Northwest-Corner Rule
                                   To       (A)          (B)            (C)       Factory
                  From                  Albuquerque     Boston       Cleveland    capacity

                                                  $5            $4           $3
                  (D) Des Moines          100                                      100

                                                  $8            $4           $3
                  (E) Evansville          200           100                        300

                                                  $9            $7           $5
                  (F) Fort Lauderdale                   100          200           300

                  Warehouse
                  requirement              300            200          200         700


                                                 Means that the firm is shipping 100
      Figure C.3                                 bathtubs from Fort Lauderdale to Boston

© 2008 Prentice Hall, Inc.                                                                   C – 11
Northwest-Corner Rule
             Computed Shipping Cost
                        Route
                    From     To   Tubs Shipped   Cost per Unit Total Cost
                      D       A       100             $5          $ 500
                      E       A       200              8           1,600
                      E       B       100              4             400
                      F       B       100              7             700
                      F       C       200              5          $1,000
                                                           Total: $4,200

                                     This is a feasible solution
              Table C.2
                                      but not necessarily the
                                      lowest cost alternative
© 2008 Prentice Hall, Inc.                                                  C – 12
Intuitive Lowest-Cost Method
                 1. Identify the cell with the lowest cost
                 2. Allocate as many units as possible to
                    that cell without exceeding supply or
                    demand; then cross out the row or
                    column (or both) that is exhausted by
                    this assignment
                 3. Find the cell with the lowest cost from
                    the remaining cells
                 4. Repeat steps 2 and 3 until all units
                    have been allocated
© 2008 Prentice Hall, Inc.                                    C – 13
Intuitive Lowest-Cost Method
                                     To       (A)         (B)          (C)       Factory
                    From                  Albuquerque   Boston      Cleveland    capacity

                                                   $5          $4           $3
                    (D) Des Moines                                  100           100

                                                   $8          $4           $3
                    (E) Evansville                                                300

                                                   $9          $7           $5
                    (F) Fort Lauderdale                                           300

                    Warehouse
                    requirement              300         200          200         700

                       First, $3 is the lowest cost cell so ship 100 units from
                       Des Moines to Cleveland and cross off the first row as
                       Des Moines is satisfied
                                                                                   Figure C.4
© 2008 Prentice Hall, Inc.                                                                      C – 14
Intuitive Lowest-Cost Method
                                     To       (A)         (B)          (C)       Factory
                    From                  Albuquerque   Boston      Cleveland    capacity

                                                   $5          $4           $3
                    (D) Des Moines                                  100           100

                                                   $8          $4           $3
                    (E) Evansville                                  100           300

                                                   $9          $7           $5
                    (F) Fort Lauderdale                                           300

                    Warehouse
                    requirement              300         200          200         700

                       Second, $3 is again the lowest cost cell so ship 100 units
                       from Evansville to Cleveland and cross off column C as
                       Cleveland is satisfied
                                                                                   Figure C.4
© 2008 Prentice Hall, Inc.                                                                      C – 15
Intuitive Lowest-Cost Method
                                     To       (A)         (B)          (C)       Factory
                    From                  Albuquerque   Boston      Cleveland    capacity

                                                   $5          $4           $3
                    (D) Des Moines                                  100           100

                                                   $8          $4           $3
                    (E) Evansville                      200         100           300

                                                   $9          $7           $5
                    (F) Fort Lauderdale                                           300

                    Warehouse
                    requirement              300         200          200         700

                       Third, $4 is the lowest cost cell so ship 200 units from
                       Evansville to Boston and cross off column B and row E
                       as Evansville and Boston are satisfied
                                                                                   Figure C.4
© 2008 Prentice Hall, Inc.                                                                      C – 16
Intuitive Lowest-Cost Method
                                     To       (A)         (B)          (C)       Factory
                    From                  Albuquerque   Boston      Cleveland    capacity

                                                   $5          $4           $3
                    (D) Des Moines                                  100           100

                                                   $8          $4           $3
                    (E) Evansville                      200         100           300

                                                   $9          $7           $5
                    (F) Fort Lauderdale    300                                    300

                    Warehouse
                    requirement              300         200          200         700

                       Finally, ship 300 units from Albuquerque to Fort
                       Lauderdale as this is the only remaining cell to complete
                       the allocations
                                                                                   Figure C.4
© 2008 Prentice Hall, Inc.                                                                      C – 17
Intuitive Lowest-Cost Method
                                     To       (A)         (B)          (C)       Factory
                    From                  Albuquerque   Boston      Cleveland    capacity

                                                   $5          $4           $3
                    (D) Des Moines                                  100           100

                                                   $8          $4           $3
                    (E) Evansville                      200         100           300

                                                   $9          $7           $5
                    (F) Fort Lauderdale    300                                    300

                    Warehouse
                    requirement              300         200          200         700


                 Total Cost = $3(100) + $3(100) + $4(200) + $9(300)
                            = $4,100
                                                                                   Figure C.4
© 2008 Prentice Hall, Inc.                                                                      C – 18
Intuitive Lowest-Cost Method
                                    To        (A)         (B)          (C)       Factory
                    From                  Albuquerque   Boston      Cleveland    capacity

               ThisDes Moines            $5                    $4           $3
                 (D) is a feasible solution,                        100           100
               and an improvement over
               the previous solution, but$8                    $4           $3
               not necessarily the lowest 200
                 (E) Evansville                                     100           300

                       cost alternative $9                     $7           $5
                    (F) Fort Lauderdale    300                                    300

                    Warehouse
                    requirement              300         200          200         700


                 Total Cost = $3(100) + $3(100) + $4(200) + $9(300)
                            = $4,100
                                                                                   Figure C.4
© 2008 Prentice Hall, Inc.                                                                      C – 19
Stepping-Stone Method
                 1. Select any unused square to evaluate
                 2. Beginning at this square, trace a
                    closed path back to the original square
                    via squares that are currently being
                    used
                 3. Beginning with a plus (+) sign at the
                    unused corner, place alternate minus
                    and plus signs at each corner of the
                    path just traced


© 2008 Prentice Hall, Inc.                                    C – 20
Stepping-Stone Method
                 4. Calculate an improvement index by
                    first adding the unit-cost figures found
                    in each square containing a plus sign
                    and subtracting the unit costs in each
                    square containing a minus sign
                 5. Repeat steps 1 though 4 until you have
                    calculated an improvement index for all
                    unused squares. If all indices are ≥ 0,
                    you have reached an optimal solution.


© 2008 Prentice Hall, Inc.                                     C – 21
Stepping-Stone Method
                                To       (A)            (B)             (C)        Factory
              From                   Albuquerque      Boston         Cleveland     capacity

                                                 $5             $4            $3
               (D) Des Moines         100
                                             -        +
                                                                                     100           Des Moines-
              (E) Evansville           200
                                                 $8
                                                      100
                                                                $4            $3
                                                                                     300            Boston index
                                             +        -
              (F) Fort Lauderdale
                                                 $9
                                                      100
                                                                $7
                                                                     200
                                                                              $5
                                                                                     300           = $4 - $5 + $8 - $4
                                                                                                   = +$3
               Warehouse
               requirement              300               200           200          700




                                                                        99                    $5        1          $4
                                                                                   100
                                                                                    -                        +


                                                                       201
                                                                                   +          $8        99
                                                                                                              -    $4
        Figure C.5                                                                 200                       100

© 2008 Prentice Hall, Inc.                                                                                               C – 22
Stepping-Stone Method
                                   To       (A)               (B)           (C)         Factory
                  From                  Albuquerque          Boston      Cleveland      capacity

                                                    $5              $4 Start       $3
                  (D) Des Moines          100                                            100
                                                -                        +
                                                    $8              $4             $3
                  (E) Evansville          200            100                             300
                                                +        -
                                                    $9              $7             $5
                  (F) Fort Lauderdale                    100             200             300
                                                         +               -
                  Warehouse
                  requirement              300                200            200         700


                                         Des Moines-Cleveland index
        Figure C.6                       = $3 - $5 + $8 - $4 + $7 - $5 = +$4
© 2008 Prentice Hall, Inc.                                                                         C – 23
Stepping-Stone Method
                                   To       (A)        (B)          (C)      Factory
                  From                  Albuquerque   Boston     Cleveland   capacity

                                                $5          $4          $3
                  (D) Des Moines          100                                 100

                                                $8          $4          $3
                  (E) Evansville        Evansville-Cleveland index
                                          200      100                        300

                                        = $3 - $4 + $7 - $5 = +$1
                                                 $9       $7            $5
                  (F) Fort Lauderdale                 100        200          300
                                        (Closed path = EC - EB + FB - FC)
                  Warehouse
                  requirement           Fort Lauderdale-Albuquerque index
                                           300      200     200    700
                                        = $9 - $7 + $4 - $8 = -$1
                                        (Closed path = FA - FB + EB - EA)

© 2008 Prentice Hall, Inc.                                                              C – 24
Stepping-Stone Method
                 1. If an improvement is possible, choose
                    the route (unused square) with the
                    largest negative improvement index
                 2. On the closed path for that route,
                    select the smallest number found in the
                    squares containing minus signs
                 3. Add this number to all squares on the
                    closed path with plus signs and
                    subtract it from all squares with a
                    minus sign
© 2008 Prentice Hall, Inc.                                    C – 25
Stepping-Stone Method
                                     To       (A)             (B)           (C)       Factory
                    From                  Albuquerque        Boston      Cleveland    capacity

                                                    $5              $4           $3
                    (D) Des Moines          100                                        100

                                                    $8              $4           $3
                    (E) Evansville          200          100                           300
                                              -          +
                                                    $9              $7           $5
                    (F) Fort Lauderdale                  100             200           300
                                              +          -
                    Warehouse
                    requirement              300              200          200         700
                                             1.    Add 100 units on route FA
                                             2.    Subtract 100 from routes FB
                                             3.    Add 100 to route EB
        Figure C.7                           4.    Subtract 100 from route EA
© 2008 Prentice Hall, Inc.                                                                       C – 26
Stepping-Stone Method
                                     To       (A)        (B)           (C)       Factory
                    From                  Albuquerque   Boston      Cleveland    capacity

                                                   $5          $4           $3
                    (D) Des Moines          100                                    100

                                                   $8          $4           $3
                    (E) Evansville          100         200                        300

                                                   $9          $7           $5
                    (F) Fort Lauderdale     100                     200            300

                    Warehouse
                    requirement              300         200          200          700

                 Total Cost = $5(100) + $8(100) + $4(200) + $9(100) + $5(200)
                            = $4,000
                                                                                 Figure C.8
© 2008 Prentice Hall, Inc.                                                                    C – 27
Special Issues in Modeling

                  Demand not equal to supply
                              Called an unbalanced problem
                              Common situation in the real world
                              Resolved by introducing dummy
                               sources or dummy destinations as
                               necessary with cost coefficients of
                               zero


© 2008 Prentice Hall, Inc.                                           C – 28
Special Issues in 50($3) + 150($5) + 150(0)
          Total Cost = 250($5) + 50($8) + 200($4) +
                                                    Modeling
                             = $3,350
                                To       (A)         (B)           (C)                  Factory
                                                                             Dummy      capacity
               From                  Albuquerque    Boston      Cleveland

                                               $5          $4           $3          0
               (D) Des Moines           250                                              250

                                               $8          $4           $3          0
               (E) Evansville           50          200          50                      300

                                               $9          $7           $5          0
               (F) Fort Lauderdale                              150          150         300

               Warehouse
               requirement               300         200          200         150        850


                                                                             New
               Figure C.9                                                    Des Moines
                                                                             capacity
© 2008 Prentice Hall, Inc.                                                                         C – 29
Special Issues in Modeling

                  Degeneracy
                              To use the stepping-stone
                               methodology, the number of
                               occupied squares in any solution
                               must be equal to the number of
                               rows in the table plus the number
                               of columns minus 1
                              If a solution does not satisfy this
                               rule it is called degenerate

© 2008 Prentice Hall, Inc.                                           C – 30
Special Issues in Modeling
                                    To   Customer      Customer     Customer     Warehouse
                    From                     1             2            3         supply

                                                 $8            $2           $6
                    Warehouse 1          100                                        100

                                                 $10           $9           $9
                    Warehouse 2           0            100           20             120

                                                 $7          $10            $7
                    Warehouse 3                                      80              80

                    Customer
                    demand                 100           100          100           300

                                  Initial solution is degenerate
                                  Place a zero quantity in an unused square
         Figure C.10              and proceed computing improvement indices
© 2008 Prentice Hall, Inc.                                                                   C – 31

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Heizer mod c

  • 1. Operations Management Module C – Transportation Models PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 7e Operations Management, 9e © 2008 Prentice Hall, Inc. C–1
  • 2. Outline  Transportation Modeling  Developing an Initial Solution  The Northwest-Corner Rule  The Intuitive Lowest-Cost Method  The Stepping-Stone Method  Special Issues in Modeling  Demand Not Equal to Supply  Degeneracy © 2008 Prentice Hall, Inc. C–2
  • 3. Learning Objectives When you complete this module you should be able to: 1. Develop an initial solution to a transportation models with the northwest-corner and intuitive lowest-cost methods 2. Solve a problem with the stepping- stone method 3. Balance a transportation problem 4. Solve a problem with degeneracy © 2008 Prentice Hall, Inc. C–3
  • 4. Transportation Modeling  An interactive procedure that finds the least costly means of moving products from a series of sources to a series of destinations  Can be used to help resolve distribution and location decisions © 2008 Prentice Hall, Inc. C–4
  • 5. Transportation Modeling  A special class of linear programming  Need to know 1. The origin points and the capacity or supply per period at each 2. The destination points and the demand per period at each 3. The cost of shipping one unit from each origin to each destination © 2008 Prentice Hall, Inc. C–5
  • 6. Transportation Problem To From Albuquerque Boston Cleveland Des Moines $5 $4 $3 Evansville $8 $4 $3 Fort Lauderdale $9 $7 $5 Table C.1 © 2008 Prentice Hall, Inc. C–6
  • 7. Transportation Problem Boston Cleveland (200 units (200 units required) Des Moines required) (100 units capacity) Albuquerque (300 units required) Evansville (300 units capacity) Fort Lauderdale (300 units Figure C.1 capacity) © 2008 Prentice Hall, Inc. C–7
  • 8. Transportation Matrix Figure C.2 To Factory Des Moines Albuquerque Boston Cleveland capacity capacity From constraint $5 $4 $3 Des Moines 100 Cell representing $8 $4 $3 a possible Evansville 300 source-to- destination shipping $9 $7 $5 assignment Fort Lauderdale 300 (Evansville to Cleveland) Warehouse requirement 300 200 200 700 Cost of shipping 1 unit from Fort Cleveland Total demand Lauderdale factory to Boston warehouse warehouse demand and total supply © 2008 Prentice Hall, Inc. C–8
  • 9. Northwest-Corner Rule  Start in the upper left-hand cell (or northwest corner) of the table and allocate units to shipping routes as follows: 1. Exhaust the supply (factory capacity) of each row before moving down to the next row 2. Exhaust the (warehouse) requirements of each column before moving to the next column 3. Check to ensure that all supplies and demands are met © 2008 Prentice Hall, Inc. C–9
  • 10. Northwest-Corner Rule 1. Assign 100 tubs from Des Moines to Albuquerque (exhausting Des Moines’s supply) 2. Assign 200 tubs from Evansville to Albuquerque (exhausting Albuquerque’s demand) 3. Assign 100 tubs from Evansville to Boston (exhausting Evansville’s supply) 4. Assign 100 tubs from Fort Lauderdale to Boston (exhausting Boston’s demand) 5. Assign 200 tubs from Fort Lauderdale to Cleveland (exhausting Cleveland’s demand and Fort Lauderdale’s supply) © 2008 Prentice Hall, Inc. C – 10
  • 11. Northwest-Corner Rule To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 200 100 300 $9 $7 $5 (F) Fort Lauderdale 100 200 300 Warehouse requirement 300 200 200 700 Means that the firm is shipping 100 Figure C.3 bathtubs from Fort Lauderdale to Boston © 2008 Prentice Hall, Inc. C – 11
  • 12. Northwest-Corner Rule Computed Shipping Cost Route From To Tubs Shipped Cost per Unit Total Cost D A 100 $5 $ 500 E A 200 8 1,600 E B 100 4 400 F B 100 7 700 F C 200 5 $1,000 Total: $4,200 This is a feasible solution Table C.2 but not necessarily the lowest cost alternative © 2008 Prentice Hall, Inc. C – 12
  • 13. Intuitive Lowest-Cost Method 1. Identify the cell with the lowest cost 2. Allocate as many units as possible to that cell without exceeding supply or demand; then cross out the row or column (or both) that is exhausted by this assignment 3. Find the cell with the lowest cost from the remaining cells 4. Repeat steps 2 and 3 until all units have been allocated © 2008 Prentice Hall, Inc. C – 13
  • 14. Intuitive Lowest-Cost Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 300 $9 $7 $5 (F) Fort Lauderdale 300 Warehouse requirement 300 200 200 700 First, $3 is the lowest cost cell so ship 100 units from Des Moines to Cleveland and cross off the first row as Des Moines is satisfied Figure C.4 © 2008 Prentice Hall, Inc. C – 14
  • 15. Intuitive Lowest-Cost Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 100 300 $9 $7 $5 (F) Fort Lauderdale 300 Warehouse requirement 300 200 200 700 Second, $3 is again the lowest cost cell so ship 100 units from Evansville to Cleveland and cross off column C as Cleveland is satisfied Figure C.4 © 2008 Prentice Hall, Inc. C – 15
  • 16. Intuitive Lowest-Cost Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 200 100 300 $9 $7 $5 (F) Fort Lauderdale 300 Warehouse requirement 300 200 200 700 Third, $4 is the lowest cost cell so ship 200 units from Evansville to Boston and cross off column B and row E as Evansville and Boston are satisfied Figure C.4 © 2008 Prentice Hall, Inc. C – 16
  • 17. Intuitive Lowest-Cost Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 200 100 300 $9 $7 $5 (F) Fort Lauderdale 300 300 Warehouse requirement 300 200 200 700 Finally, ship 300 units from Albuquerque to Fort Lauderdale as this is the only remaining cell to complete the allocations Figure C.4 © 2008 Prentice Hall, Inc. C – 17
  • 18. Intuitive Lowest-Cost Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 200 100 300 $9 $7 $5 (F) Fort Lauderdale 300 300 Warehouse requirement 300 200 200 700 Total Cost = $3(100) + $3(100) + $4(200) + $9(300) = $4,100 Figure C.4 © 2008 Prentice Hall, Inc. C – 18
  • 19. Intuitive Lowest-Cost Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity ThisDes Moines $5 $4 $3 (D) is a feasible solution, 100 100 and an improvement over the previous solution, but$8 $4 $3 not necessarily the lowest 200 (E) Evansville 100 300 cost alternative $9 $7 $5 (F) Fort Lauderdale 300 300 Warehouse requirement 300 200 200 700 Total Cost = $3(100) + $3(100) + $4(200) + $9(300) = $4,100 Figure C.4 © 2008 Prentice Hall, Inc. C – 19
  • 20. Stepping-Stone Method 1. Select any unused square to evaluate 2. Beginning at this square, trace a closed path back to the original square via squares that are currently being used 3. Beginning with a plus (+) sign at the unused corner, place alternate minus and plus signs at each corner of the path just traced © 2008 Prentice Hall, Inc. C – 20
  • 21. Stepping-Stone Method 4. Calculate an improvement index by first adding the unit-cost figures found in each square containing a plus sign and subtracting the unit costs in each square containing a minus sign 5. Repeat steps 1 though 4 until you have calculated an improvement index for all unused squares. If all indices are ≥ 0, you have reached an optimal solution. © 2008 Prentice Hall, Inc. C – 21
  • 22. Stepping-Stone Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 - + 100 Des Moines- (E) Evansville 200 $8 100 $4 $3 300 Boston index + - (F) Fort Lauderdale $9 100 $7 200 $5 300 = $4 - $5 + $8 - $4 = +$3 Warehouse requirement 300 200 200 700 99 $5 1 $4 100 - + 201 + $8 99 - $4 Figure C.5 200 100 © 2008 Prentice Hall, Inc. C – 22
  • 23. Stepping-Stone Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 Start $3 (D) Des Moines 100 100 - + $8 $4 $3 (E) Evansville 200 100 300 + - $9 $7 $5 (F) Fort Lauderdale 100 200 300 + - Warehouse requirement 300 200 200 700 Des Moines-Cleveland index Figure C.6 = $3 - $5 + $8 - $4 + $7 - $5 = +$4 © 2008 Prentice Hall, Inc. C – 23
  • 24. Stepping-Stone Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville Evansville-Cleveland index 200 100 300 = $3 - $4 + $7 - $5 = +$1 $9 $7 $5 (F) Fort Lauderdale 100 200 300 (Closed path = EC - EB + FB - FC) Warehouse requirement Fort Lauderdale-Albuquerque index 300 200 200 700 = $9 - $7 + $4 - $8 = -$1 (Closed path = FA - FB + EB - EA) © 2008 Prentice Hall, Inc. C – 24
  • 25. Stepping-Stone Method 1. If an improvement is possible, choose the route (unused square) with the largest negative improvement index 2. On the closed path for that route, select the smallest number found in the squares containing minus signs 3. Add this number to all squares on the closed path with plus signs and subtract it from all squares with a minus sign © 2008 Prentice Hall, Inc. C – 25
  • 26. Stepping-Stone Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 200 100 300 - + $9 $7 $5 (F) Fort Lauderdale 100 200 300 + - Warehouse requirement 300 200 200 700 1. Add 100 units on route FA 2. Subtract 100 from routes FB 3. Add 100 to route EB Figure C.7 4. Subtract 100 from route EA © 2008 Prentice Hall, Inc. C – 26
  • 27. Stepping-Stone Method To (A) (B) (C) Factory From Albuquerque Boston Cleveland capacity $5 $4 $3 (D) Des Moines 100 100 $8 $4 $3 (E) Evansville 100 200 300 $9 $7 $5 (F) Fort Lauderdale 100 200 300 Warehouse requirement 300 200 200 700 Total Cost = $5(100) + $8(100) + $4(200) + $9(100) + $5(200) = $4,000 Figure C.8 © 2008 Prentice Hall, Inc. C – 27
  • 28. Special Issues in Modeling  Demand not equal to supply  Called an unbalanced problem  Common situation in the real world  Resolved by introducing dummy sources or dummy destinations as necessary with cost coefficients of zero © 2008 Prentice Hall, Inc. C – 28
  • 29. Special Issues in 50($3) + 150($5) + 150(0) Total Cost = 250($5) + 50($8) + 200($4) + Modeling = $3,350 To (A) (B) (C) Factory Dummy capacity From Albuquerque Boston Cleveland $5 $4 $3 0 (D) Des Moines 250 250 $8 $4 $3 0 (E) Evansville 50 200 50 300 $9 $7 $5 0 (F) Fort Lauderdale 150 150 300 Warehouse requirement 300 200 200 150 850 New Figure C.9 Des Moines capacity © 2008 Prentice Hall, Inc. C – 29
  • 30. Special Issues in Modeling  Degeneracy  To use the stepping-stone methodology, the number of occupied squares in any solution must be equal to the number of rows in the table plus the number of columns minus 1  If a solution does not satisfy this rule it is called degenerate © 2008 Prentice Hall, Inc. C – 30
  • 31. Special Issues in Modeling To Customer Customer Customer Warehouse From 1 2 3 supply $8 $2 $6 Warehouse 1 100 100 $10 $9 $9 Warehouse 2 0 100 20 120 $7 $10 $7 Warehouse 3 80 80 Customer demand 100 100 100 300 Initial solution is degenerate Place a zero quantity in an unused square Figure C.10 and proceed computing improvement indices © 2008 Prentice Hall, Inc. C – 31

Hinweis der Redaktion

  1. This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.
  2. This slide provides some reasons that capacity is an issue. The following slides guide a discussion of capacity.
  3. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  4. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  5. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  6. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  7. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  8. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  9. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  10. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  11. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  12. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  13. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  14. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  15. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  16. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  17. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  18. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  19. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  20. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  21. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  22. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  23. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  24. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  25. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  26. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  27. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.
  28. This slide can be used to frame a discussion of capacity. Points to be made might include: - capacity definition and measurement is necessary if we are to develop a production schedule - while a process may have “maximum” capacity, many factors prevent us from achieving that capacity on a continuous basis. Students should be asked to suggest factors which might prevent one from achieving maximum capacity.