https://ceprofs.civil.tamu.edu/ezechman/CVEN665/winston_ch9_Part2.pdf
INSY 3410-Midterm Exam 2
November 13, 2002
3-hours and total 127 points: Q1-20, Q2-20, Q3-10, Q4-10, Q5-25, Q6-20, Q7-12, Q8-10
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) A company is considering opening warehouses in four cities: New York, Los Angles, Chicago, and Atlanta.
Each warehouse can ship 100 units per week.
The weekly fixed cost of keeping each warehouse open is $400
for New York, $500 for Los Angles, $300 for Chicago, and $150 for Atlanta.
Region 1 of the country requires
80 units per week, region 2 requires 70 units per week, and region 3 requires 40 units per week. The costs of
sending one unit from a plant to a region are shown in the following table.
To
From
Region 1
Region 2
Region 3
New York (NY)
$20
$40
$50
Los Angles (LA)
$48
$15
$26
Chicago (CH)
$26
$35
$18
Atlanta (AT)
$24
$50
$35
We want to meet weekly demands at minimum cost, subject to following restrictions
If the New York warehouse is opened, the Los Angeles warehouse must be opened.
At most two warehouses can be opened.
Either the Atlanta or the Los Angles warehouses must be opened.
Formulate a MIP model for the problem. Briefly define decision variables and constraints.
Solution:
Xij= units shipped from city i to region j, i=1,2,3,4 and j=1,2,3.
Yi= 1 if a warehouse is opened in city i, 0 otherwise.
Min z= 20X11+40X12+50X13+…+35X43+400Y1+500Y2+300Y3+150Y4
st.
CAPACITY AND FIXED CHARGE CONSTRAINTS
X11+X12+X13 <= 100Y1
X21+X22+X23<=100Y2
X31+X32+X33 <=100Y3
X41+X42+X43<=100Y4
DEMAND CONSTRAINTS
X11+X21+X31+X41 >=80
X12+X22+32+X42 >=70
X13+X23+X33+X43>=40
Y1 <= Y2 (if NY is opened, then LA must be opened)
Y1+Y2+Y3+Y4<=2 (at most two warehouses can be opened)
Y2+Y4 >=1 (either AT or LA must be opened. Both are ok)
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