Question

Investment	Condition
1	None
2	Only if 1
3	Only if 1
4	Must if 1 and 2
5	Not if 1 or 2
6	Not if 1 or 3
7	Only if 2 and Not 3

The board of directors of a large manufacturing firm is considering a set of investments shown in the following table. Let Ri be the total revenue from investment i and Ci be the cost to make investment i. The board wishes to maximize the total revenue and invest no more than a total of M dollars. Formulate this model as a Binary Integer Programming Problem (BIP). Define your decision variables, and write down the algebraic formulation of the model. (Explain what is BIP also provide solution in details )

Answer 1

BIP model is formulated as below:

Decision variables:

Let Xi = 1, if investment i is chosen, otherwise Xi = 0

Objective function:

Maximize R1X1+R2X2+R3X3+R4X4+R5X5+R6X6+R7X7

s.t.

Constraints:

C1X1+C2X2+C3X3+C4X4+C5X5+C6X6+C7X7 <= M

X1-X2 >= 0 (Only if 1)

X2-X3 >= 0 (Only if 2)

X4-X1-X2 >= 0 (Must if 1 or 2, means invetment 4 is selected, only if either 1 or 2 is selected, but not both 1 and 2)

X1+X2+X5 <= 1 (Not if 1 or 2)

X2+X3+X6 <= 2 (Not if 2 and 3)

X2-X7 >= 0 (Only if 2

X3+X7 <= 1 (and not 3)

  

Xi binary