Wesley Shi
Problem 10.7 Lingo explanation
This is a transportation problem that seeks to maximize profit, and the product being produced,
transported and stored are refrigerators:
1) It was given that Denver, Atlanta and Chicago’s production capacity as 100,000, 100,000 and
150,000 respectfully
2) It was also given that Boston, Dallas, LA and St.Paul’s storage capacity are 50,000, 70,000,
60,000 and 80,000 respectfully
3) So first, it was important to establish the network representation (as attached).
• I assigned each production facility with a number, Denver as 1, Atlanta as 2 and Chicago as 3
• I Then assigned each storage facility with a number, Boston as 1, Dallas as 2, LA as 3 and St.Paul as 4
• Now with all the facilities assigned with a proper number, we begin the routing as of the following:
Denver to Boston as r11, Denver to Dallas as r12, Denver to LA as r13… so on. (I picked r because it is
refrigerators we are talking about after all)
• Then I specified the capacity as the problem did, and labeled them according on the chart, along with
the cost of each routing
4)
Now that all the variable were all taken care of, I move forward to Lingo in order to find the
optimal solution.
• Constraints #1-3 specified the production capacity in a mathematical language Lingo can understand:
r11+r12+r13+r14 <= 10,000 for example, is everything Denver facility will produce, since that include
every single possible destination for the refrigerator to go. And the same process was done twice
more to show the production capacity for the Atlanta and Chicago Facility
• Constraint #4-6 then sets the boundaries for max storage capacity those destinations possess.
r11+r21+r31 <= 50,000 for example, is all the possible units that will end up in Boston facility. And the
same process was repeated thrice to show the storage capacity for the Dallas, LA and St.Paul facility.
• Lastly, since we want to get the max profit out of this, we have the actual equation to handle this
problem:
Max = 7*r11 + 11*r12 + 8*r13 +13*r14 + 20*r21 + 17*r22 + 12*r23 +10*r24 + 8*r31 + 18*r32 + 13*r33 + 16*r34
(the # multiplying each route being the cost of the shipping fee)
5) After plugging the equation and the constraints above in, I successfully solved the problem
within Lingo; and acquired the optimal solution as:
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Denver to St.Paul (10,000 units)
Atlanta to Boston (50,000 units)
Atlanta to Los Angeles (50,000 units)
Chicago to Dallas (70,000 units)
Chicago to Los Angeles (10,000 units)
Chicago to St.Paul (70,000 units)