problemset8_soln(1)

problemset8_soln(1) - ORIE 3300/5300 Optimization I...

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ORIE 3300/5300 Optimization I Homework #8 Solutions Fall 2011 3.(a) The percentages invested in each bond is the same for any of the diﬀerent amounts of available cash: A = 21 . 8%, B = 0%, C = 73 . 6%, D = 0%, and E = 4 . 54%. 3.(b) Revised model ﬁle: set BONDS ; # possible bonds for investment set GOVTANDAGENCY_BONDS; # subset of government and agency bonds param quality_rating {BONDS} >=0; # 3rd column in table param years_to_maturity {BONDS} >=0; # 4th column in table param yield {BONDS} >=0; # 6th column in table param cash_avail >=0; # amount of money to invest param avg_quality_max >=0; # threshold (3) in problem param avg_maturity_max >=0; # threshold (2) in problem param govtandagency_bonds_min >=0 ; # threshold (1) in problem param cash_borrowed >= 0; param borrowrate >= 0; var INVEST{BONDS} >= 0; # decision variable of how much to invest in each bond var BORROWED >=0; maximize total_earnings: sum {j in BONDS} yield[j] * INVEST[j] - borrowrate* BORROWED; 1

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# maximum profit after tax subject to cash: sum {j in BONDS} INVEST[j] <= cash_avail + BORROWED ; # cannot spend more than cash subject to govtandagency_requirement: sum {j in GOVTANDAGENCY_BONDS} INVEST[j] >= govtandagency_bonds_min; # minimum investment in government and agency bonds subject to avg_quality: sum {j in BONDS} (quality_rating[j] - avg_quality_max) * INVEST[j] <= 0; # maximum quality requirement (linearization of proportion constraint) subject to avg_maturity: sum {j in BONDS} (years_to_maturity[j] - avg_maturity_max) * INVEST[j] <= 0; # maximum time to maturity requirement # (linearization of proportion constraint) subject to borrowconstraint: BORROWED <= cash_borrowed ; Revised data ﬁle: set BONDS := A B C D E; set GOVTANDAGENCY_BONDS := B C D; param : quality_rating years_to_maturity yield := A 2 9 .043 B 2 15 .027 C 1 4 .025 D 1 3 .022 E 5 2 .045;
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problemset8_soln(1) - ORIE 3300/5300 Optimization I...

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