We have four types of refined oils and we need to blend (some of) them into...

 

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We have four types of refined oils and we need to blend (some of) them into three types of gasoline to maximize profit. Type of oil available quantity barrel 5000 2400 Brent Blend(BB) MediumOils (MO) WestTexas (WT) LightOils (LO) Type of gasoline price $/barrel 12 A B C 18 10 4000 1500 min oil type ΜΟ WT price $/barrel 97 12 6 max % oil type % 20 MO 30 40 ΜΟ 50 # Blending data #set OILTYPE := BB MO WT LO; #set GASOLINES: A B C; param: OILTYPE: BB MO WT LO param a :- BB 5000 MO 2400 WT 4000 LO 1500 ; param: GASOLINES: A B C param Q - WT A 0.3 MO C 0.5 ; param q = MO A 0.2 WT B 0.4 ; US7 с 9 12 6; P :- 12 18 10; param p[GASOLINES} >=0; #unit selling price of gasolines param Q{OILTYPE, GASOLINES} >-0, <1, default 1; #Q[i,j] is the maximum fraction of type i oil #that can be used when making gasoline j param qfi in OILTYPE, j in GASOLINES} >=0, <= Q[i, j], default 0; #q[i,j] is the minimum fraction of type i oil #that must be used when making gasoline j # VARS var x {OILTYPE, GASOLINES} >= 0; var y {GASOLINES}; var z{i in OILTYPE}, <= a[i]; # OBJECTIVE FUNCTION maximize totalprofit: #x[i,j] is the amount of type i oil used to make gasoline j #amounts of gasolins produced #amounts of oils used in the process sum{j in GASOLINES} p[j] *y[j] # CONSTRAINTS subject to usedoil{i in OILTYPE}: sum{j in GASOLINES} x[i,j] = z[i]; sum {i in OILTYPE} c[i] * z[i]; #subject to availabilityfi in OILTYPE}: #z[i]<= a[i]; subject to conservation{j in GASOLINES}: sum{i in OILTYPE} x[i,j] = y[j]; subject to maxlimit{i in OILTYPE, j in GASOLINES}: x[i, j] <= Q[i,j] * y[j]; subject to minrequirement {i in OILTYPE, j in GASOLINES}: q[i, j]y[j]; x[i, j] # execution option solver cplex; data blending.dat; solve; display {i in OILTYPE, j in GASOLINES: x[i,j]>0} x[i,j]; display{j in GASOLINES: y[j]>0} y[j]; display {i in OILTYPE: z[i]>0} z[i]; 1) Modify the blending model and data file. Assume that you also have $2000 to buy additional barrels of oil. On the market there are 1000 barrels of Medium Oil, and 1000 barrels of Brent blend available at the same price we used in the model. Extend the model to answer the question: given our initial stock as before, how much extra of these oils should we buy and how much of the different gasoline types should we make to maximize our profit? 2) Modify the model further: assume a storage cost of 1 cent/barrel has to be paid for oil not used for production. We have four types of refined oils and we need to blend (some of) them into three types of gasoline to maximize profit. Type of oil available quantity barrel 5000 2400 Brent Blend(BB) MediumOils (MO) WestTexas (WT) LightOils (LO) Type of gasoline price $/barrel 12 A B C 18 10 4000 1500 min oil type ΜΟ WT price $/barrel 97 12 6 max % oil type % 20 MO 30 40 ΜΟ 50 # Blending data #set OILTYPE := BB MO WT LO; #set GASOLINES: A B C; param: OILTYPE: BB MO WT LO param a :- BB 5000 MO 2400 WT 4000 LO 1500 ; param: GASOLINES: A B C param Q - WT A 0.3 MO C 0.5 ; param q = MO A 0.2 WT B 0.4 ; US7 с 9 12 6; P :- 12 18 10; param p[GASOLINES} >=0; #unit selling price of gasolines param Q{OILTYPE, GASOLINES} >-0, <1, default 1; #Q[i,j] is the maximum fraction of type i oil #that can be used when making gasoline j param qfi in OILTYPE, j in GASOLINES} >=0, <= Q[i, j], default 0; #q[i,j] is the minimum fraction of type i oil #that must be used when making gasoline j # VARS var x {OILTYPE, GASOLINES} >= 0; var y {GASOLINES}; var z{i in OILTYPE}, <= a[i]; # OBJECTIVE FUNCTION maximize totalprofit: #x[i,j] is the amount of type i oil used to make gasoline j #amounts of gasolins produced #amounts of oils used in the process sum{j in GASOLINES} p[j] *y[j] # CONSTRAINTS subject to usedoil{i in OILTYPE}: sum{j in GASOLINES} x[i,j] = z[i]; sum {i in OILTYPE} c[i] * z[i]; #subject to availabilityfi in OILTYPE}: #z[i]<= a[i]; subject to conservation{j in GASOLINES}: sum{i in OILTYPE} x[i,j] = y[j]; subject to maxlimit{i in OILTYPE, j in GASOLINES}: x[i, j] <= Q[i,j] * y[j]; subject to minrequirement {i in OILTYPE, j in GASOLINES}: q[i, j]y[j]; x[i, j] # execution option solver cplex; data blending.dat; solve; display {i in OILTYPE, j in GASOLINES: x[i,j]>0} x[i,j]; display{j in GASOLINES: y[j]>0} y[j]; display {i in OILTYPE: z[i]>0} z[i]; 1) Modify the blending model and data file. Assume that you also have $2000 to buy additional barrels of oil. On the market there are 1000 barrels of Medium Oil, and 1000 barrels of Brent blend available at the same price we used in the model. Extend the model to answer the question: given our initial stock as before, how much extra of these oils should we buy and how much of the different gasoline types should we make to maximize our profit? 2) Modify the model further: assume a storage cost of 1 cent/barrel has to be paid for oil not used for production. We have four types of refined oils and we need to blend (some of) them into three types of gasoline to maximize profit. Type of oil available quantity barrel 5000 2400 Brent Blend(BB) MediumOils (MO) WestTexas (WT) LightOils (LO) Type of gasoline price $/barrel 12 A B C 18 10 4000 1500 min oil type ΜΟ WT price $/barrel 97 12 6 max % oil type % 20 MO 30 40 ΜΟ 50 # Blending data #set OILTYPE := BB MO WT LO; #set GASOLINES: A B C; param: OILTYPE: BB MO WT LO param a :- BB 5000 MO 2400 WT 4000 LO 1500 ; param: GASOLINES: A B C param Q - WT A 0.3 MO C 0.5 ; param q = MO A 0.2 WT B 0.4 ; US7 с 9 12 6; P :- 12 18 10; param p[GASOLINES} >=0; #unit selling price of gasolines param Q{OILTYPE, GASOLINES} >-0, <1, default 1; #Q[i,j] is the maximum fraction of type i oil #that can be used when making gasoline j param qfi in OILTYPE, j in GASOLINES} >=0, <= Q[i, j], default 0; #q[i,j] is the minimum fraction of type i oil #that must be used when making gasoline j # VARS var x {OILTYPE, GASOLINES} >= 0; var y {GASOLINES}; var z{i in OILTYPE}, <= a[i]; # OBJECTIVE FUNCTION maximize totalprofit: #x[i,j] is the amount of type i oil used to make gasoline j #amounts of gasolins produced #amounts of oils used in the process sum{j in GASOLINES} p[j] *y[j] # CONSTRAINTS subject to usedoil{i in OILTYPE}: sum{j in GASOLINES} x[i,j] = z[i]; sum {i in OILTYPE} c[i] * z[i]; #subject to availabilityfi in OILTYPE}: #z[i]<= a[i]; subject to conservation{j in GASOLINES}: sum{i in OILTYPE} x[i,j] = y[j]; subject to maxlimit{i in OILTYPE, j in GASOLINES}: x[i, j] <= Q[i,j] * y[j]; subject to minrequirement {i in OILTYPE, j in GASOLINES}: q[i, j]y[j]; x[i, j] # execution option solver cplex; data blending.dat; solve; display {i in OILTYPE, j in GASOLINES: x[i,j]>0} x[i,j]; display{j in GASOLINES: y[j]>0} y[j]; display {i in OILTYPE: z[i]>0} z[i]; 1) Modify the blending model and data file. Assume that you also have $2000 to buy additional barrels of oil. On the market there are 1000 barrels of Medium Oil, and 1000 barrels of Brent blend available at the same price we used in the model. Extend the model to answer the question: given our initial stock as before, how much extra of these oils should we buy and how much of the different gasoline types should we make to maximize our profit? 2) Modify the model further: assume a storage cost of 1 cent/barrel has to be paid for oil not used for production. We have four types of refined oils and we need to blend (some of) them into three types of gasoline to maximize profit. Type of oil available quantity barrel 5000 2400 Brent Blend(BB) MediumOils (MO) WestTexas (WT) LightOils (LO) Type of gasoline price $/barrel 12 A B C 18 10 4000 1500 min oil type ΜΟ WT price $/barrel 97 12 6 max % oil type % 20 MO 30 40 ΜΟ 50 # Blending data #set OILTYPE := BB MO WT LO; #set GASOLINES: A B C; param: OILTYPE: BB MO WT LO param a :- BB 5000 MO 2400 WT 4000 LO 1500 ; param: GASOLINES: A B C param Q - WT A 0.3 MO C 0.5 ; param q = MO A 0.2 WT B 0.4 ; US7 с 9 12 6; P :- 12 18 10; param p[GASOLINES} >=0; #unit selling price of gasolines param Q{OILTYPE, GASOLINES} >-0, <1, default 1; #Q[i,j] is the maximum fraction of type i oil #that can be used when making gasoline j param qfi in OILTYPE, j in GASOLINES} >=0, <= Q[i, j], default 0; #q[i,j] is the minimum fraction of type i oil #that must be used when making gasoline j # VARS var x {OILTYPE, GASOLINES} >= 0; var y {GASOLINES}; var z{i in OILTYPE}, <= a[i]; # OBJECTIVE FUNCTION maximize totalprofit: #x[i,j] is the amount of type i oil used to make gasoline j #amounts of gasolins produced #amounts of oils used in the process sum{j in GASOLINES} p[j] *y[j] # CONSTRAINTS subject to usedoil{i in OILTYPE}: sum{j in GASOLINES} x[i,j] = z[i]; sum {i in OILTYPE} c[i] * z[i]; #subject to availabilityfi in OILTYPE}: #z[i]<= a[i]; subject to conservation{j in GASOLINES}: sum{i in OILTYPE} x[i,j] = y[j]; subject to maxlimit{i in OILTYPE, j in GASOLINES}: x[i, j] <= Q[i,j] * y[j]; subject to minrequirement {i in OILTYPE, j in GASOLINES}: q[i, j]y[j]; x[i, j] # execution option solver cplex; data blending.dat; solve; display {i in OILTYPE, j in GASOLINES: x[i,j]>0} x[i,j]; display{j in GASOLINES: y[j]>0} y[j]; display {i in OILTYPE: z[i]>0} z[i]; 1) Modify the blending model and data file. Assume that you also have $2000 to buy additional barrels of oil. On the market there are 1000 barrels of Medium Oil, and 1000 barrels of Brent blend available at the same price we used in the model. Extend the model to answer the question: given our initial stock as before, how much extra of these oils should we buy and how much of the different gasoline types should we make to maximize our profit? 2) Modify the model further: assume a storage cost of 1 cent/barrel has to be paid for oil not used for production.

Answer rating: 100% (QA)

Answer 1 We can modify the blending model and data file to accommodate the additional barrels of oil We can add two additional columns to the data file one for the quantity of Medium Oil and one for t... View the full answer