midterm_notes_190

Shadow price change in the optimal objective function value per unit increase in the right-hand side of a constraint. Sensitivity analysis- The study of how changes in the right-hand side of a constraint in a linear programming problem affect the optimal solution. LP Relaxation- The linear program that results from dropping the integer requirements for the variable in an integer linear program Integer linear programming - A linear program in which all decision variables are required to be integer. Binary constraint -A constraint in which may be dropped variables must have values of either 0 or 1. Redundant constraint- A constraint which may be dropped but still leaves the feasible region that same Surplus- A variable added to the left-hand side of a >= constraint to convert the constraint into an equality. The value of this variable can usually be interpreted as the additional amount over the requirement Feasibility situation in which the solution to the linear programming problem satisfies all the constraints. 100% rule to determine if the optimal solution changes when a change is made more than one coefficient of the objective function. The situation in which the value of the solution may be made infinitely large in a maximization problem without violating any of the constraints. Constraints- restrictions that limit the degree to which the objective can be pursued Decision variables- the controllable inputs in the problem Objective function a function of the decision variable using Max or Min Nonnegativity constraints prevent decision variables from having negative values Linear functions in which each variable appears separate term and is raised to the first power. Feasible solutions that satisfy all the constraints simultaneously, Feasible region shaded region Slack variables are added to the formulation of a linear programming problem to represent the slack or unused capacity associated with the constraint. Supply the set of all interconnected resources involved in producing and distributing a product transportation problem network flow problem that often involves minimizing the cost of shipping goods from a set of origins to a set destination . Network graphical representation of a problem, consisting of nodes interconnected. Nodes- intersection or junction point of a network arcs -lines connecting the nodes in a network dummy origin- an origin added to a transportation problem to make the total supply equal to the total demand. Transshipment problem- an extension for the transportation to distribution involving transfer points and possible shipments between a pair of nodes. Optimal Solution – solutions occur at one of the vertices or corners of the feasible regions. Also called extreme points Graphical Problem Which are the binding constraints where 2 lines meet at the optimal solution. The optimal solution occurs at their intersection Why are they binding? The optimal solution occurs at their intersection Transportation Problem Do you need a dummy node for this problem? no, supply > demand or yes, demand >supply Draw the appropriate network diagram. Define the appropriate decision variables for this problem. Remember NUN for full credit. N U N What is the objective function for this problem? use dimensional analysis. Max Profit 20MX1 + 20MX2 + 35X3 + 25MX4 What are the constraints for this problem? Use dimensional analysis. Use dimensional analysis Sensitivity analysis.