Oxymoron, a large pharmaceutical firm, is developing a new iPhone app that will test for COVID-19.  While the company has currently developed a version that is 80 percent reliable, they know that the reliability of their app (and the corresponding value) will continue to increase as further investment and research is made.  

However, the firm knows that competitors are working on similar products and only the first firm to enter the market with an iPhone app for detecting COVID will be successful.   As a result, Oxymoron managers assume that only the first firm to enter the market will earn a positive return; all other firms will earn nothing (and immediately terminate their development efforts).

Managers at Oxymoron estimate that the time for a competitor to enter the market is a random variable with pdf     Given the nature of this development project, the company can launch their product at any time where the value of the app is a function of the cumulative amount spent prior to launch time.  We assume that this function, denoted by , is concave, increasing, bounded from above, and .

The company wants to decide on the appropriate cash flow f(t) at any time t (assuming that the project has not been terminated prematurely).  Oxymoron also wants to know the expected time to market; that is, when should they expect to enter the market (given that a competitor has not entered first). 

In addition, top management at Oxymoron has placed constraints on the maximum allowable cash flow at any time t (denoted by ), the maximum allowable expected development time (denoted by ) and the total available budget (denoted by B). 

a) Given that an amount h(t) has been spent on this project to time t and no competitor has yet entered the market, formulate Oxymoron’s problem at time t to find the optimal cash flow and expected time to market that maximizes the expected value of this project.

b) Show that the optimal solution in part (a) has the form (find the conditions for t)

                                         

c)  This problem is analogous to a continuous knapsack problem (a well known problem in OR).  Briefly describe the continuous knapsack problem and how it is related to this problem

d)  Substituting the solution in part (b) into the optimization problem formulated in part (a), characterize the optimal solution for the Oxymoron management (i.e., that maximizes the expected value of this project).

Answer rating: 100% (QA)

a Oxymorons problem at time t is to find the optimal cash flow and expected time to market that maximizes the expected value of the project given that ht has been spent on the project to time t and no ... View the full answer