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Question: problem 1 a patient enters the hospital with severe abdominal...

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Problem 1: A patient enters the hospital with severe abdominal pains. Based on past experience Dr. Craig believes there is a 28% chance that the patient has appendicitis (which requires surgery) and a 72% chance that the patient has nonspecific abdominal pains. Dr. Craig may operate on the patient now or wait 12 hours to gain a more accurate diagnosis. In 12 hours, Dr Craig will know for sure whether the patient has appendicitis or nonspecific abdominal pains However, in the meantime, the patients appendix may perforate (if he has appendicitis), thereby making the operation much more dangerous. Dr. Craig has the following information If Dr. Craig performs surgery now and finds out that the patient has nonspecific abdominal pains, the patient may make a full recovery with a probability of 85% or may recover with abdominal pain with the same severity as before. If Dr. Craig performs surgery now and finds out that the patient indeed has appendicitis, the patient may die with probability of 8%; if the patient survives. there is a 70% probability he will fully recover, and otherwise he will recover with abdominal pain with the same severity as before If Dr. Craig waits for 12 hours, there is a probability of 60% she will find out that the patient has nonspecific abdominal pain and does not require surgery. If the patient indeed has appendicitis, after 12 hours of waiting there is a probability of 60% he may suffer from perforated appendix. If the patients appendix perforates. the patient may die with probability 25%, or he may survive with more severe abdominal pain than before. If the patients appendix is not perforated, the patient may die with probability 20%. If the patient survives the operation, he may recover fully with a probability of 80% or may recover with abdominal pain with the same severity as before The patient has the following utilities associated with each of the possible outcomes: Outcome No surgery Full recovery after surgery Recovery from surgery with same pain as before Recovery from surgery with more severe pain than before Death Utility 0.8 0.55 0.4 a) Using a decision tree, determine what Dr. Craig should do to maximize expected utility. b) Suppose that the utility of Recovery from surgery with same pain as before is Up. Determine the value for Up such that the expected utility of performing surgery now is equal to the expected utility of waiting for 12 hours.

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