Management Science: Scientific approach to solving management problems. Decision making and problem solving based on quantitative analysis. Origins: Operations Research in World War II . logistics, transportation, scheduling. Quantitative Analysis – Model Development, Representation of reality. Less time-consuming, Less expensive, Enables what-if analyses. Deterministic: Values of parameters known and cannot vary. Probabilistic or Stochastic: Values of parameters uncertain and subject to variation. Graphical Solution Procedure: Graphical procedure applies only to problems with 2 decision variables. Plot the constraint lines on a graph. Determine the feasible region (solutions that satisfy all constraints. Determine the optimal solution by solving the appropriate simultaneous equations. Extreme Points Feature of LP optimal solutions: The optimal solution to an LP problem is always at an extreme point (also called corner point) of the feasible region. Optimal solution can be obtained by computing the objective function value for each extreme point and choosing the one with the best value. Unbounded: If the value of the objective function may be made infinitely large (for a max problem) without violating any of the constraints. Usually indicates a problem in formulation (e.g., omitted constraint). Surplus Variables: A surplus variable represents excess quantity for a ≥ constraint. Surplus variables are ≥ 0 and make no contribution to the objective function. Constraints with slack or surplus = 0 are called binding constraints. Solver Answer Report: Gives values of decision variables and objective function at optimal. Slack: Difference between LHS and RHS of a constraint. Answer report gives slack pertaining to the optimal solution. Sensitivity Analysis: Study how changes in the model parameters affect the optimal solution. Consider one change at a time. Ex: RHS value of constraint (e.g., labor hours available). Range of optimality: Range of values over which the current optimal solution point will remain optimal. Solver gives range in terms of allowable increase and allowable