Question

Tazer management now has concluded that the company cannot devote enough money to research and development to undertake all of these projects. Only $1.5 billion is available, which may be not enough for all the projects. The first row of table shows the amount needed (in millions of dollars) for each of these projects. The second row estimates each project’s probability of being successful. If a project is successful, it is estimated that the resulting drug would generate the revenue shown in the third row. Thus, the expected revenue (in the statistical sense) from a potential drug is the product of its numbers in the second and third rows, whereas its expected profit is this expected revenue minus the investment given in the first row. These expected profits are shown in the bottom row of table. The objective is to choose the projects that will maximize the expected profit while satisfying the budget constraint.

a. Formulate algebraic form for this problem. (Please clearly define all the decision variables, clearly write down the objective function and each constraints)

TABLE Data for the Tazer Project Selection Problem

	Project
	1 (Up)	2 (Stable)	3 (Choice)	4 (Hope)	5 (Release)
R&D investment ($million)*	450	300	620	510	200
Success rate	60%	30%	30%	20%	45%
Revenue if successful ($million)	1,400	1,200	2,200	3,000	600

Answer 1

Decision variable

Let,

yi = 1 if project i is selected else 0

Objective is to maximize expected profit so Objective function Z = Max (60%*1400-450)*y1+(30%*1200-300)*y2+(30%*2200-620)*y3+(20%*3000-510)*y4+(45%*600-200)*y5

= Max 3901+60y2+40y3+90y4+70y5

subject to,

450y1+300y2+620y3+510y4+200y5 <= 1500 (Budget)

yi = binary

Solving in olver we get,

Project 1,2,4 and 5 are to be selected in order to maximize expected profit

maximized profit = 610 million

Solver screenshot

Solver formula