Decision Making

Introduction n Basic concepts of Acts, Events and Outcomes and Payoffs n Criteria for Decision Making n Backward Induction n Value of Information n Summary

Basic Concepts in This chapter n Acts are decision maker’s choices. n Under uncertainty, events are particular situations that occur with some chance. n The decision maker has full control over his (her) acts and no control over events. n Both events and acts are affecting outcomes. n Often the decision maker needs to choose an act on more than one occasion and may encounter more than one event. n The decision may be based on a path comprised of a sequence of acts and events. n A point in which a decision maker is making his her act choice is referred to as act fork and is represented by a square. The consumer is choosing a single act out of those stemming from an act fork, clipping the rest. n related events are stemming from an event fork. The event fork is labeled as a circle. Every event at an event fork has a probability of ocurrance. The events are mutually Every event at an event fork has a probability of ocurrance. The events are mutually exclusive. The sum of all probabilities at any event fork is 1. exclusive. The sum of all probabilities at any event fork is 1. It may be worthwhile to map the structure Naturally, acts stem from act fork that signify the point at which maker’s choice take place. It may be worthwhile to map the structure Naturally, acts stem from act fork that signify the point at which maker’s choice take place. n Shapes of feasible sets u Special Types of constraints: u Resource u Specialized Resource and Limit constraints u Equality Constraints u Mixture constraints n Insights and Tips.

Classes of Constraints n In summary we may conclude that there are only 3 types of constraints: u Common reseource u Specialized Resource ( or alternatively expressed Quantity) u Mixture n There are only three directions possible to each constraint u Greater or Greater and Equal u Smaller or Smaller and Equal u Equal

Special Problems and features n Non Feasibility: The feasible set is empty u In this case one must revise some constraint (s) to obtain a non empty feasible set. u Notice, if there is no feasibility, there is no solution, regardless of the objective. n The feasible set is not bound u If the feasible set is not bound in the direction of Improvement of the objective, DOI, there is no solution. In this case one must add constraint (s) to bound the feasible set. u In general, the case of a not bound feasible set is not realistic as it implies that infinite amount of the decision variables are possible. Some constraint (s) were forgotten. However, one can still obtain an optimal solution if the feasible set is bound in the DOI.

Special Problems and Features Contd. n The feasible set may be u A point u Or A segment u or A region in the plane. n The optimal solution may be u An intercept, indicating specialization in Production u A segment of the feasible set, indicating any infinite number of combination of the decision variables are optimal, as long as they are within the segment u A unique point on the feasible set that has two non zero coordinates. In which case both products are produced.