LINEAR PROGRAMMING

Introduction n Introduction: n objective n Constraints n Feasible Set n Solution

Problem Solving n Solution procedure on Page n Insight to Problem Setting 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.