Data, models, and decisions: the fundamentals of management by Dimitris Bertsimas

By Dimitris Bertsimas

The publication combines subject matters from generally designated quantitative topics: probability/statistics and optimization types, into one unified therapy of quantitative equipment and versions for administration and enterprise. The e-book stresses these basic techniques which are most crucial for the sensible research of administration judgements: modeling and comparing uncertainty explicitly, knowing the dynamic nature of decision-making, utilizing historic info and restricted info successfully, simulating advanced structures, and allocating scarce assets optimally.

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Starting from any one of the "final" nodes of the decision tree, we proceed backwards. As we have already seen, the EMV of node E is $11,580. 7. Similarly, the EMV of node D is also $11,580, which we write above node D. 7. 7 Solution of the decision tree. We next examine decision node C, which corresponds to the event that Bill receives a job offer from Vanessa's firm. At this decision node, there are two choices. The first choice is for Bill to accept the offer from Vanessa's firm, which has an EMV of $14,000.

Page 14 If we test a variety of values of c in the spreadsheet representation of the decision tree, we will notice that the current optimal decision strategy (which is to reject John's job offer, and to accept a job offer from Vanessa's firm if it is offered) remains the same for all values of c less than c = $2,578. 10 shows the output of the spreadsheet when c = $2,578. For values of c above c = $2,578, the EMV of node B becomes less than $12,000, which results in a new optimal decision strategy of accepting John's job offer.

Unlike a decision node, where the decision-maker gets to select which branch to opt for, at an event node the decision-maker has no such choice. Rather, one can think that at an event node, "nature" or "fate" decides which outcome will take place. The outcome branches that emanate from an event node must represent a mutually exclusive and collectively exhaustive set of possible events. By mutually exclusive, we mean that no two outcomes could ever transpire at the same time. By collectively exhaustive, we mean that the set of possible outcomes represents the entire range of possible outcomes.

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