Outline u Whitt Window Company u Hotdogs and

Outline u Whitt Window Company u Hotdogs and Buns u Portfolio Optimization u u u Production Planning 1 -period u u u No debt With debt Forward: Setting Formulation Backward: Formulation Setting Production Planning Metalco Blends Alloys Fagersta Steelworks u Backward: Incomplete Setting, Formulation Complete Setting utdallas Page 1 Formulation Problems /~metin . edu

utdallas Page 2 Whitt Window Company - Setting /~metin . edu

utdallas Page 3 Whitt Window Company - Formulation /~metin . edu

utdallas Page 4 Hotdogs and Buns - Setting /~metin . edu

utdallas Page 5 Hotdogs and Buns - Formulation /~metin . edu

utdallas Page 6 Portfolio Optimization - Setting Linear Programming formulations can be used to select a desirable bond portfolio. u u Pro. Max has raised $8, 000 to invest into four bonds. The average annual return, the worst-case annual return and the duration of each bond is below: Average Return Worst-case Return Duration Bond 1 14% 5% 2 Bond 2 9% 8% 1 Bond 3 12% 10% 3 Bond 4 15% 12% 3 /~metin . edu

utdallas Page 7 Portfolio Optimization - Formulation /~metin . edu

utdallas Page 8 Portfolio Optimization with Debt - Setting Financial institutions use debt to increase their investment capital. u Pro. Max has raised $8, 000 from a private equity fund to invest into four bonds. u The average annual return, the worst-case annual return and the duration of each bond is below: Average Return u Duration Bond 1 7% 3% 1 Bond 2 5% 4% 1 Bond 3 10% 1% 1 Bond 4 12% -2% 1 Pro. Max wants to maximize the expected return from its bond investments – – – u Worst-case Return The worst-case return of bond portfolio must be at least 2%. To achieve diversification, at most 35% can be invested in a single bond. Pro. Max can borrow extra money to invest into bonds 1 & 2 and bonds 3 & 4 » High leverage: Bonds 1 & 2 have relatively high worst-case return. Pro. Max leverages its high worstcase return investments by a factor of 4. At least 20% (=1/(1+4)) of investments in high return investments must come from Pro. Max raised funds. The rest, at most 80%, can come from debt. » Low leverage: Bonds 3 & 4 have relatively low worst-case return. Pro. Max leverages its low worstcase return investments by a factor of 1. At least 50% (=1/(1+1)) of investments in high return investments must come from Pro. Max raised funds. The rest, at most 50%, can come from debt. » Borrowed money must be returned in a year with 1% interest Formulate a linear program to maximize the average annual return of a portfolio over a year. /~metin . edu

utdallas Page 9 Portfolio Optimization with Debt - Formulation /~metin . edu

u u u A company produces products A, B, C Products A, B, C are sold at prices $15, $60 and $100 in unlimited numbers Products require the following – – – A: Input material and 1 labor hour B: 2 product As and 2 labor hours C: 1 product B and 3 labor hours Input and 1 hr: A Sell A at $15 Sell B at $60 2 As and 2 hrs: B 1 B and 3 hrs: C u u A total of 60 labor hours are available Formulate a linear program to maximize profit Sell C at $100 utdallas Page 10 Production Planning 1 -period - Setting /~metin . edu

utdallas Page 11 Production Planning 1 -period - Formulation /~metin . edu

Input and ? hr: Product 1 Sell Product 1 at $? ? Product 1 and ? hrs: Product 2 Sell Product 2 at $? ? Product 2 and ? hrs: Product 3 Sell Product 3 at $? u A total of ? labor hours are available Page 12 utdallas . edu /~metin Production Planning 1 -period – Formulation Setting

utdallas Page 13 Production Planning - Setting /~metin . edu

utdallas Page 14 Production Planning - Formulation /~metin . edu

utdallas Page 15 Metalco Blends Alloys - Setting /~metin . edu

utdallas Page 16 Metalco Blends Alloys - Formulation /~metin . edu

A friend of yours is given a formulation problem and a diagram. The problem is as follows: Your friend provides the formulation on the next page but loses the diagram. Using the information on the next page re-generate the diagram. utdallas Page 17 Incomplete Setting, Formulation Complete Setting . edu /~metin Fagersta Steelworks

utdallas Page 18 Formulation . edu /~metin Fagersta Steelworks

Complete Setting: Diagram Capacity M 1 S 1 Demand P Capacity M 2 S 2 Page 19 utdallas . edu /~metin Fagersta Steelworks

u u u Whitt Window Company Hotdogs and Buns Portfolio Optimization u u u Production Planning 1 -period u u u No debt With debt Forward: Setting Formulation Backward: Formulation Setting Production Planning Metalco Blends Alloys Fagersta Steelworks u Backward: Incomplete Setting, Formulation Complete Setting utdallas Page 20 Summary /~metin . edu