2. Exam
• March 4th or May 18th
• Remember to register for the exam at least a
week in advance.
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3. Ex Set 4: Eve and Steven
• Eve does MarkeJng and Dish washing, Steven
does Cooking and Laundry
Em Ec Ed El Sm Sc Sd Sl
1 0 1 0 0 1 0 1
4,5 7,8 3,6 2,9 4,9 7,2 4,3 3,1 18,4
1 1 1 1 2= 2
1 1 1 1 2= 2
1 1 1= 1
1 1 1= 1
1 1 1= 1
1 1 1= 1
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5. Case 2
• Total cost goes down from 11,2 M$ to 9,9 M$
Amount of malt shipped from plant i to brewery j in year 1 (1000 ton)
Istanbul Ankara Total Capacity
Afyon 24,24 24 30,00 30,00
Konya 0 0 18,24 68,00
Import 0 0 0,00 20,00
Total malt 24,24 24
Total beer 202 200 (Million lt)
Amount of beer shipped from brewery j to distribution center k in year 1 (Million liters)
Istanbul Izmir Antalya Bursa Kayseri Export (Izmir) Total Capacity
Istanbul 103 26 0 60 0 13 202 220
Ankara 0 48 50 0 102 0 200,00 200
Total 103 74 50 60 102 13
Demands 103 74 50 60 102 13
Total shipping cost 9,935
(Million dollars)
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6. What next?
• What if more decision makers?
– Different values and priori1es
– Different objec1ves!
• What if no mathemaJcal objecJve funcJon?
– F.e. design of a car
• In real world, many problems are complex.
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7. OpJmizaJon
• Step 1: Need for op-miza-on
• Step 2: Choose decision variables
• Step 3: Formulate constraints
• Step 4: Formulate objec1ve func1ons
• Step 5: Set up variable bounds
• Step 6: Choose an op1miza1on algorithm
• Step 7: Obtain solu1on(s)
• Step 8: If not sa-sfied, move to a suitable step
above.
Deb, 2008
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8. Excel as a decision tool
• In the real world, Excel is probably the most (ab)
used tool for decision making,
– Probably because it’s installed prac1cally everywhere
– There’s nothing wrong in using Excel, but be aware of
the limita1ons
• Many add-‐ins provide more func1onality (f.e.
Crystal Ball)
• Depending on your needs, R, SAS and many other
may give you beZer tools than Excel to analyze and
solve your problems.
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9. Extending Excel
• Macros are not (usually) necessary, but…
• Current versions of Excel support Visual Basic
for ApplicaJons (VBA), but more powerful
VB.NET is also an opJon
– If you want to do serious Excel-‐programming, learn
VB.NET (or C#.NET) instead
– If interested, as a student you can get Microso^’s
development tools for free at
hZps://downloads.channel8.msdn.com/
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