The Bonsante Drug Company is aiming to develop a new drug which will alleviate t

Question

The Bonsante Drug Company is aiming to develop a new drug which will alleviate the symptoms of arthritis with few side effects. The earlier the company can develop, test and market the drug, the greater will be the returns they will earn in a market which it is thought will be worth billions of pounds.

Two alternative technologies for developing the drug are being considered and, given the resources available to the company, only one of these approaches can be pursued at a given time. The first approach is based on a substance called HMP acid and it is estimated that there is a 0.4 probability that this approach would lead to development of the drug in 5 years, with a 0.6 probability that the development would take 7 years. There is more uncertainty about the development time of the second approach, which is based on a derivative of the chemical, zylogen. It is estimated that the use of this chemical has a 0.3 probability of leading to completion of development in as little as 3 years. If development has not been completed in this period then a decision would have to be made between switching to the HMP acid technology or attempting to modify the zylogen approach. It is thought that the modification has a 0.8 probability of leading to completion after a further 2 years.

If the modification has still not led to completion after the further 2 years a decision would then have to be made between switching to the HMP acid approach or persevering with zylogen for a further 7 years, by which time it is assumed that successful development is certain to have been achieved.

Assuming that the objective of Bonsante's directors is to minimize the expected development time of the drug, determine their optimum policy.

Explanation / Answer

Solution

For HMP acid based approach, the completion time is 5 years with probability 0.4 and

7 years with probability 0.4. So, expected completion time is: (5 x 0.4) + (7 x 0.6) = 6.2 years

Zylogen derivative based approach, since there are 3 step-wise decision options, we need to do backward calculation as follows:

The last phase: when Zylogen is not completed within 3 years initially and then if it is modified taking another 2 years but not completed, there are two options, namely,

Switch over to HMP with expected completion time of 6.2 years or pursue Zylogen further to complete in another 7 years.

Since 6.2 < 7, if Zylogen is modified taking another 2 years but not completed, the option at this phase is to go for HMP.        

Going to the next forward phase of deciding whether to modify Zylogen when it has not been complete within the initial 3 years, there are two possibilities, namely, modified version completes within 2 years with probability 0.8 or modification does not complete in 2 years with a probability of 0.2. In latter case, as already seen above, decision was to go for HMP with an expected completion time of 6.2 years. Expected completion time when Zylogen is modified

= (2 x 0.8)+{(2 + 6.2) x 0.2}[the earlier decision under the last phase is after the modification did not complete within 2 years and hence the completion time must be increased by those 2 years]

= 3.24.

As has already been established first, expected completion time for HMP is 6.2 years. Since

3.24 < 6.2, decision at this phase is modify Zylogen and if it does not complete in 2 years go for HMP and the expected completion time is 3.24 years   

Now, in the very first phase, two possibilities exist: Zylogen completes within initial 3 years with probability 0.3 or does not complete within 3 years wih probability 0.7. in the latter possibility, as already established, the expected completion time is 3.24 years. Thus, expected completion time for Zylogen = (3 x 0.3) + (3.24 x 0.7) = 3.168 years

Finally, since the expected completion time for HMP is 6.2 which is greater than the expected completion time of 3.24 years for Zylogen, the final decision is:

Go for Zylogen derivative based approach and if the work is not completed within 3 years, modify it taking another 2 years and still not complete switch over to HMP based approach.

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