Question

Listed below are RFPs issued under consideration by AllWeihsBZ Inc. Listed for each is the expected profit from each, the required staff time to develop a proposal, and the probability that the proposal will be accepted and a contract awarded. During the period before the proposals must be accepted there are 114 staff hours available to write proposals. Use an optimization method to identify which projects should be bid on to achieve the optimum measure given in each sub question under the restriction of staff time availability 

a. If the goal is to maximize the sum of probability across all projects bid on, how many projects are bid on? 

b. For the objective in a, what is the total sum of profit of projects bid on? 

c. If the goal is to maximize the raw profit total, how many projects are bid on? 

d. A new goal of 'expected profit' has been proposed where each project has the measure of profit multiplied by its probability. If the goal is to maximize this measure, how many projects are bid on?

Answer 1

a)

Let

X1 = 1, if bid should placed for RFP number 21, otherwise X1 = 0

X2 = 1, if bid should placed for RFP number 35, otherwise X2 = 0

X3 = 1, if bid should placed for RFP number 32, otherwise X3 = 0

X4 = 1, if bid should placed for RFP number 23, otherwise X4 = 0

X5 = 1, if bid should placed for RFP number 67, otherwise X5 = 0

X6 = 1, if bid should placed for RFP number 34, otherwise X6 = 0

X7 = 1, if bid should placed for RFP number 38, otherwise X7 = 0

X8 = 1, if bid should placed for RFP number 41, otherwise X8 = 0

Max .3X1+.5X2+.15X3+.3X4+.18X5+.46X6+.31X7+.8X8

s.t.

18X1+24X2+18X3+35X4+52X5+18X6+10X7+6X8 <= 114

Xi binary

Solution using LINGO is following:

Optimal solution:

X1, X2, X4, X6, X7, X8 = 1

Therefore, except RFP number 32 and 67, all other projects should be bid on.

A total of 6 projects are bid on.

b) Total sum of profits of projects bid on = 46+56+78+49+24+17 = 270

c) Optimization model is following:

Max 46X1+56X2+39X3+78X4+123X5+49X6+24X7+17X8

s.t.

18X1+24X2+18X3+35X4+52X5+18X6+10X7+6X8 <= 114

Xi binary

Solution using LINGO is following:

Optimal solution:

X1, X2, X5, X6 = 1

Therefore, bid should be placed for Project (RFP number) 21, 35, 67 and 34

Total 4 projects are bid on.

d)

Optimization model is following:

Max .3*46X1+.5*56X2+.15*39X3+.3*78X4+.18*123X5+.46*49X6+.31*24X7+.8*17X8 or

Max 13.8X1+28X2+5.85X3+23.4X4+22.14X5+22.54X6+7.44X7+13.6X8

s.t.

18X1+24X2+18X3+35X4+52X5+18X6+10X7+6X8 <= 114

Xi binary

Solution using LINGO is following:

Optimal solution:

X1, X2, X4, X6, X7, X8 = 1

Therefore, except RFP number 32 and 67, all other projects should be bid on.

A total of 6 projects are bid on.