C
B U S I N E S S A N A L Y T I C S MOD U L E
Transportation Models
DISCUSSION QUESTIONS
1. Three information needs of the model: the origin points and
2. Steps in the intuitive method are:
◼ Step 1: Identify the cell with the lowest cost. Break any
◼ Step 3: Find the cell with the lowest cost from the remaining
(not crossed out) cells.
3. The three steps in the northwest-corner method are:
◼ Step 1: Exhaust the supply of each row before moving
down to the next row.
4. An optimal solution has been reached when all improvement
indices (profits) are non-negative (non-positive).
tion than the northwest-corner solution, but neither suggests an
6. The number of cells used is m + n – 1; the number of possible
routes available is m n. Example: for a 2 3 problem, 4 of
6 routes will be used, for a 5 6 problem, 10 of 30 routes will
7. Nothing prohibits the model from applying over short dis-
tances. The three assumptions do not address issues of scale. An
northwest-corner rule, but it would simply begin in the upper-right
corner instead of the upper-left corner. This initial solution is
AACSB: Reflective thinking
9. Total supply is not equal to total demand in an unbalanced
transportation problem. Such a problem can be balanced by adding
AACSB: Application of knowledge
11. A negative index represents the amount by which total
AACSB: Application of knowledge
BUSINESS ANALYTICS MODULE C TR A N S PO R T A T I O N MO D E L S 311
C.7 Initial solution—Northwest-corner rule
* Indicates an improvement can be made. Therefore, this iteration is
not optimal.
All improvement indices are positive, therefore, an optimal
has been reached.
C.5 (a) The result of the next iteration is:
(b) Total cost if this solution is accepted as final: $1,775.
Evaluation of the unfilled cells reveals the follow-
ing cell indices: A-2, $40; B-1, –$40; B-3, –$15;
C-1, –$30; B-1 should be selected next; 30 units
can be moved.
C.6 Application of the stepping-stone method will yield the following solution. The optimal cost is $2,020.
312 BUSINESS ANALYTICS MODULE C TRA N SP O R T A T I O N MO D E L S
C.8 (a),(b) Initial solution by northwest corner method; solu-
tion using the stepping-stone method:
Improvement indices:
*
improvement can be made by using route YC, which
has an improvement index of –4. A total of 40 units can
be moved along this new route.
Using route YC, we get:
Improvement indices:
most we can move around this route is 10 units.
Using the route YA, we get:
BUSINESS ANALYTICS MODULE C TR A N S PO R T A T I O N MO D E L S 313
Improvement indices:
*
WC 3 6 6 4 1
YB 7 6 4 3 2
ZA 8 4 3 2 5
ZC 5 2 3 4 6 6 2
→ + − + − = −
→ + − + − = +
→ + − + − = +
→ + − + − + − = +
*Indicates that an improvement can be made. Note that the
most we can move around this route is 20 units.
Using the route WC, we get:
Improvement indices:
WA 4 3 6 6 1
YB 7 3 3 6 1
ZA 8 6 6 3 3 2 6
ZC 5 2 3 3 3
→ + − + − = +
→ + − + − = +
→ + − + − + − = +
→ + − + − = +
Because this is a minimization problem and all improvement
indices are positive, this solution is optimal at a cost of $505.
C.9 Solve two separate transportation problems. One will
include Philadelphia and the other will include Seattle. In both
cases, we need a dummy destination.
Philadelphia
Total cost $50(150) $90(225) $40(200) $50(100) $90(25) $0(25)
$7,500 $20,250 $8,000 $5,000 $2,250 $0
$43,000 (A second solution exists; using New Orleans dummy.)
= + + + + +
= + + + + +
=⎯
314 BUSINESS ANALYTICS MODULE C TRA N SP O R T A T I O N MO D E L S
Seattle
Total cost $75(75) $50(50) $0(25) $80(200) $60(25) $30(350)
$5,625 $2,500 $0 $16,000 $1,500 $10,500
$36,125
= + + + + +
= + + + + +
=
Therefore, shipping costs are lower for Seattle.
C.10 Considering East St. Louis, we have:
Optimal solution:
316 BUSINESS ANALYTICS MODULE C TRA N SP O R T A T I O N MO D E L S
C.12*
Improvement indices:
*
DB 4 4 8 5 3
DC 3 5 9 5 2
EC 3 5 9 8 1
FB 7 9 8 4 2
→ + − + − = +
→ + − + − = +
→ + − + − = −
→ + − + − = +
Improvement indices:
DB 4 4 3 5 9 5 2
DC 3 5 9 5 2
EA 8 3 5 9 1
FB 7 4 3 5 1
→ + − + − + − = +
→ + − + − = +
→ + − + − = +
→ + − + − = +
All improvement indices are positive; therefore, an optimal
has been reached.
Total cost = 100 5 + 200 4 + 100 3 + 200 9
+ 100 5 = $3,900
C.13* Table as given in example:
Improvement indices:
C2 9 3 8 5 9
→ + − + − = +
Initial solution—Northwest-corner rule:
Optimal solution:
expensive than St. Louis.