Learning from Operations Course: Bank Portfolio Management

Question No 2: Bank Portfolio Management

Decision Variables:

XA: Amount (in million) invested in bond type A (Municipal)

XB: Amount (in million) invested in bond type B (Agency)

XC: Amount (in million) invested in bond type C (Government)

XD: Amount (in million) invested in bond type D (Government)

XE: Amount (in million) invested in bond type E (Municipal)

Objective Function: Maximize After-tax Earnings

Maximize Z = (4.3 XA + 2.7 XB + 2.5 XC + 2.2 XD + 4.5 XE) / 100

Subject to constraints:

Funds available

XA + XB + XC + XD + XE <= 10 million

Government and Agency Bonds in Portfolio Mix

XB + XC + XD >= 4 million

Quality of Portfolio Mix:

(2XA + 2XB + XC + XD + 5XE)/(XA + XB + XC + XD + XE) <= 1.4

=> (0.6XA + 0.6XB – 0.4XC – 0.4XD + 3.6XE) <= 0

Maturity of Portfolio Mix:

(9XA + 15XB + 4XC + 3XD + 2XE)/ (XA + XB + XC + XD + XE) <= 5

=> (4XA + 10XB - XC - 2XD - 3XE) <= 0

Non-negativity:

XA , XB , XC , XD , XE >= 0

Solution:

Maximum Earnings After-tax : $298363.63

Q4. Warehouse Distribution Problem

Variables:

i ∈{1=Liverpool ,2=Brighton }

j ∈{1=Newcastle ,2=Brmingham ,3=London ,4= Exeter }

k ∈{1= C1,2= C2,3= C3,4= C4,5= C5,6= C6 }

x_ij=quantity delivered from i factory to j deport

y_ik=quantity delivered from i factory to k customer

z_jk=quantity delivered from j depot to k customer

〖Cap〗_i=Capacity of factory i

T_j=Throughput of Depot j

R_k=Requirement of customer k

〖Cx〗_ij=Cost of transport from factory i to depot j

〖Cz〗_jk=Cost of transport from deport j to customer k

〖Cy〗_ik=Cost of transport from factory i to cutomer k

Objective: Minimize overall cost

Min z=∑_(i=1)^2▒∑_(j=1)^4▒〖〖Cx〗_ij.x_ij+