Chapter 08S – The Transportation Model
From:
To:
RS1
RS2
RS3
RS4
RS5
Supply
.80
.75
.60
.70
.90
Metro
23,000
40,000
17,000
.75
.80
.85
.70
.85
Ridge
16,000
30,000
14,000
.70
.75
.70
.80
.80
Colby
25,000
Demand
24,000
22,000
23,000
16,000
10,000
95,000\95,000
(d) Find the cell (that is not crossed out) in the table above that has the next lowest unit
From:
To:
RS1
RS2
RS3
RS4
RS5
Supply
.80
.75
.60
.70
.90
Metro
23,000
40,000
17,000
.75
.80
.85
.70
.85
Ridge
16,000
30,000
14,000
.70
.75
.70
.80
.80
Colby
24,000
25,000
1,000
Demand
24,000
22,000
23,000
16,000
10,000
95,000\95,000
(e) Find the cell (that is not crossed out) in the table above that has the next lowest unit
transportation cost. Cell Metro-RS2 and Cell Colby-RS2 are tied for the next lowest
Column RS2 total to 5,000. The result is shown below.
Chapter 08S – The Transportation Model
From:
To:
RS1
RS2
RS3
RS4
RS5
Supply
.80
.75
.60
.70
.90
Metro
17,000
23,000
40,000
17,000
.75
.80
.85
.70
.85
Ridge
16,000
30,000
14,000
.70
.75
.70
.80
.80
Colby
24,000
25,000
1,000
Demand
24,000
22,000
5,000
23,000
16,000
10,000
95,000\95,000
(f) Find the cell (that is not crossed out) in the table above that has the next lowest unit
transportation cost. Cell Colby-RS2 has the next lowest cost ($.75). Assign as many
units as possible to Cell Colby-RS2: minimum of 1,000 & 5,000 = 1,000. This
.80
.75
.60
.70
.90
17,000
.75
.80
.85
.70
.85
Ridge
16,000
30,000
14,000
.70
.75
.70
.80
.80
Colby
24,000
25,000
1,000
Chapter 08S – The Transportation Model
From:
To:
RS1
(Index = .70)
RS2
(Index = .75)
RS3
(Index = .60)
RS4
(Index = .65)
RS5
(Index = .80)
Supply
.80
.75
.60
.70
.90
Metro
(Index = 0)
17,000
23,000
40,000
.75
.80
.85
.70
.85
Ridge
(Index = .05)
4,000
16,000
10,000
30,000
.70
.75
.70
.80
.80
Colby
(Index = 0)
24,000
1,000
25,000
Demand
24,000
22,000
23,000
16,000
10,000
95,000\95,000
(1) Row 1 (Metro) Index = 0.
(2) Shift to Cell Metro-RS3:
Row Metro Index + Column RS3 Index = .60
0 + Column RS3 Index = .60
Column RS3 Index = .60 – 0 = .60.
Shift to Cell Metro-RS2:
Row Metro Index + Column RS2 Index = .75
0 + Column RS2 Index = .75
Column RS2 Index = .75 – 0 = .75.
Shift to Cell Ridge-RS4:
Row Ridge Index + Column RS4 Index = .70
.05 + Column RS4 Index = .70
Column RS4 Index = .70 – .05 = .65.
Shift to Cell Ridge-RS5:
Row Colby Index + Column RS2 Index = .75
Row Colby Index + .75 = .75
Row Colby Index = .75 – .75 = 0
Shift to Cell Colby-RS1:
Row Colby Index + Column RS1 Index = .70
Chapter 08S – The Transportation Model
(c) Evaluate the empty cells using the following formula:
Cell Evaluation = Cell Cost – (Row Index + Column Index)
Cell
Evaluation
Metro-RS1
.80 – (0 + .70) = .10
Metro-RS4
.70 – (0 + .65) = .05
Metro-RS5
.90 – (0 + .80) = .10
Ridge-RS1
.75 – (.05 + .70) = 0
Ridge-RS3
.85 – (.05 + .60) = .20
Colby-RS3
.70 – (0 + .60) = .10
Colby-RS4
.80 – (0 + .65) = .15
Colby-RS5
.80 – (0 + .80) = 0
Because no cell evaluations are negative, we have found the optimal solution
(repeated below). Note: The fact that the evaluations for Cells Ridge-RS1 and Colby-
RS5 are all zero indicates that at least one other equivalent alternative exists.
Chapter 08S – The Transportation Model
Enrichment Module: Vogel’s Approximation Method and Supplemental
Problems
In addition to Intuitive Lowest-cost Approach, we can use Vogel’s Approximation to obtain an initial
reasonable solution.
Steps of Vogel’s Approximation
1. Determine the penalty cost for each row and each column. (Penalty cost is obtained by
subtracting the smallest cost from the next smallest cost in a given row or column).
2. Select the row or the column with the highest penalty cost. In that row/column, allocate as
many units as possible to the cell with the smallest cost.
3. Reduce the row supply and column demand by the amount allocated in step 2. If the row
supply is now zero, eliminate the row from further consideration. If the column demand is