Question

International Paper Company has four warehouses at different cities: Buffalo, Detroit, Pittsburgh and Raleigh. They provide paper to five book publishers in Boston, New York, Chicago, Indianapolis and Memphis.


The costs of shipping one box of paper, the amount of paper (in boxes) available at each warehouse, and the amount of paper ordered (in boxes) by each publisher are found in the table below:

From / To	Boston	New York	Chicago	Indianapolis	Memphis	Supply
Buffalo	9	7	11	12	13	1100
Detroit	12	11	10	10	8	1400
Pittsburgh	11	9	9	10	10	900
Raleigh	6	5	9	8	7	600
Demand	1300	600	600	800	700

Amount Shipped from
Buffalo to Boston =

Buffalo to New York =

Detroit to Indianapolis =

Detroit to Memphis=

Pittsburgh to Chicago=

Pittsburgh to Indianapolis=

Raleigh to Boston=

Raleigh to Indianapolis =

The Total Shipping Costs =

(Leave off $ Sign and Commas )
Hint: The Cost is between 33200 and 33800

Answer 1

Demand = Supply =4000 (Balanced assignment problem)

Please find below the answer:

Buffalo to Boston = 500
Buffalo to New York = 600
Detroit to Indianapolis = 700
Detroit to Memphis= 700
Pittsburgh to Chicago= 600
Pittsburgh to Indianapolis= 100
Raleigh to Boston= 600
Raleigh to Indianapolis = 0

In red are the units transported from to a location.

Notes to Solution:

• The lowest shipping cost is $5 and then $6 from Raleigh to NY and Boston respectively. If we assign supply from Raleigh to NY, the cost at Boston will be up by min $3 per shipping unit (9-6 = 3). Hence, we assign all supply from Raleigh to Boston. This exhausts supply at Raleigh.
• Next lowest shipping cost is $7. We supply 600 units from Buffalo to NY. The next is $8 and we supply 700 units from Detroit to Memphis. The next lowest cost is $9 and we supply 500 units from Buffalo to Boston. This exhausts supply at Buffalo. Similarly, at $9 , 600 units are supplied from Pittsburg to Chicago.
• Next lowest shipping cost is $10 at which 700 units from Detroit are moved to Indianapolis and 100 are moved from Pittsburg to Indianapolis. This exhausts supply at Detroit.
• Balance 200 is moved from Boston to Pittsburg.

Total cost = 9*500+11*200+6*600+7*600+9*600+10*700+10*100+8*700 = $33500