SUPPLEMENT TO CHAPTER 8:
THE TRANSPORTATION MODEL
Teaching Notes
The transportation method seems to be middleoftheroad in terms of students’ abilities to develop an
intuitive feel for what is happening during the process. Although in practice much of the actual
computations are done by computers using the simplex algorithm, I feel that students gain a certain
amount of insight and intuitive understanding by going through the calculations.
Cell evaluations are illustrated using the steppingstone method and the MODI method. While it may be
more efficient to use the MODI method, note that for the size of the problems students will encounter, the
two methods are probably fairly similar in terms of efficiency. Consequently, I think it is more a
matter
of personal preference which method is used.
Solutions to Problems
1.
Ship 15 units from source 1 to destination 2
Ship 75 units from source 1 to destination 3
Ship 105 units from source 2 to destination 1
Ship 45 units from source 3 to destination 1
Ship 60 units from source 3 to destination 2
Total cost of this transportation schedule is =
$1,050.
2.
If
N1 is opened, then the shipment schedule is as follows:
Ship 500 units from warehouse 1 to store B at a cost of $1,500
Ship 400 units from warehouse 2 to store A at a cost of $2,000
Ship 100 units from warehouse N1 to store B at a cost of $800
Ship 350 units from warehouse N1 to store C at a cost of $2,450
Excess supply at warehouse N1 is 50 units
Total cost of the transportation schedule if N1 is opened is $6,750.
If N2 is opened, then the shipment schedule is as follows:
Ship 500 units from warehouse 1 to store B at a cost of $1,500
Ship 400 units from warehouse 2 to store A at a cost of $2,000
Ship 100 units from warehouse N2 to store B at a cost of $600
Ship 350 units from warehouse N2 to store C at a cost of $ 1,400
Instructor’s Manual, Chapter 8 Supplement
227
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View Full DocumentExcess supply at warehouse N2 is 50 units
Total cost of the transportation schedule if N2 is opened is $5,500.
Since 5,500 < 6,750, open the warehouse in location N2.
3.
If the plant is located in Toledo, the shipment schedule is as follows:
Ship 210 units from Plant 1 to Destination C at a cost of $2,100
Ship 140 units from plant 2 to destination A at a cost of $1,680
Ship 80 units from plant 3 to destination A at a cost of
$880
Ship 60 units from plant 3 to destination B at a cost of $660
Ship 10 units from plant 3 to destination C at a cost of $120
Ship 160 units from Toledo to destination B at a cost of $1,280
Total cost of the shipment schedule if the plant is constructed in Toledo is $6,720.
If the plant is located in Cincinnati, the shipment schedule is as follows:
Ship 210 units from plant 1 to destination C at a cost of $2,100
Ship 60 units from plant 2 to destination A at a cost of $720
Ship 80 units from plant 2 to destination B at a cost of $1,360
Ship 140 units from plant 3 to destination B at a cost of $1540
Ship 10 units from plant 3 to destination C at a cost of $120
Ship 160 units from Cincinnati to destination A at a cost of $1,120
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 Spring '11
 GAD
 Harshad number

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