Question

Proposals A, B, C, D, E. F and G are being considered with money flows over 10 years S35,000 $10,000 65,000 $42,000 $12,000 S52,000 $28,000 $7,000 $2,200 $13,000 S9,0 S3,000 Investment 000 $2,400 $11,000 $7,200 Net Annual Benefit Salvage Value $0S5,000 $2,000 $500 0 $1,000 Proposal (A and G) are mutually exclusive, (C and D) are also mutually exclusive, and proposal B depends on C or D. The MARR is set at 9%. a) Formulate the problem with Integer Programming. b) which proposal(s) should be selected if the amount of money available for investment is S100,000?

Answer 1

A.   Problem with IP is that integer programs are (in general) much more difficult to solve than linear programs. It is therefore important to know

   How does an integer programming solver work

   How can we exploit structure to implement efficient methods

B.  
EUAWA = 7000 - 35,000(A/P, 9%, 10) – 3000(A/P, 9%, 10)
   = 7000 – 35000(0.1558) – 3000(0.1558)
   = 7000 – 5453 - 467.4
   =1079.6

EUAWb     = 2200 - 10,000(A/P, 9%, 10)
   = 2200 – 10000(0.1558)
   = 1042

EUAWc         = 13000 - 65,000(A/P, 9%, 10) – 5000(A/P, 9%, 10)
   = 13000 – 65000(0.1558) – 5000(0.1558)
   = 2094

EUAWd         = 9000 - 42,000(A/P, 9%, 10) – 2000(A/P, 9%, 10)
   = 9000 – 42000(0.1558) – 2000(0.1558)
   = 2144.8

EUAWe         = 2400 - 12,000(A/P, 9%, 10) – 500(A/P, 9%, 10)
   = 2400 – 12000(0.1558) – 500(0.1558)
   = 452.5

EUAWg         = 7200 - 28,000(A/P, 9%, 10) – 1000(A/P, 9%, 10)
   = 7200 – 28000(0.1558) – 1000(0.1558)
   = 2681.8

EUAWf     = 11000 - 52,000(A/P, 9%, 10)
   = 11000 – 52000(0.1558)
   = 2898.4

Therefore Proposal/Investment F is the best alternative to select