Pure Integer Programming Example 1: Harrison Electric Company (4 of 8) Graphical LP Solution Pure Integer Programming Example 1: Harrison Electric Company (3 of 8) Objective: maximize profit = $600C + $700F subject to 2C + 3F = 0 and integer where C = number of chandeliers to be produced F = number of ceiling fans to be produced 30 hours of final assembly time available.Pure Integer Programming Example 1: Harrison Electric Company (2 of 8) Final assembly time (6 hours per chandelier and 5 hours per fan).Wiring ( 2 hours per chandelier and 3 hours per ceiling fan).Produces two expensive products popular with renovators of historic old homes:.Pure Integer Programming Example 1: Harrison Electric Company (1 of 8) General Integer Variables:Pure Integer Programming Models The values of the objective function coefficients relatively small.The values of the positive decision variables are relatively large, and.Is rounding ever done? Yes, particularly if:.Enumerating all the integer solutions is impractical because of the large number of feasible integer points.Why not enumerate all the feasible integer points and select the best one? Integer Programming Example Graphical Solution of Maximization Model Maximize Z = $100x1 + $150x2 subject to: 8,000x1 + 4,000x2 $40,000 15x1 + 30x2 200 ft2 x1, x2 0 and integer Optimal Solution: Z = $1,055.56 x1 = 2.22 presses x2 = 5.55 lathes Feasible Solution Space with Integer Solution Points A feasible solution is ensured by rounding down non-integer solution values but may result in a less than optimal (sub-optimal) solution.Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution.Some Features of Integer Programming Problems Rounding to integer values may result in:.If an integer model is solved as a simple linear model, at the optimal solution non-integer values may be attained.are perfectly valid for these variables as long as these values satisfy all model constraints.) Actual value of this integer variable is limited by the model constraints.Only additional requirement in IP model is one or more of the decision variables have to take on integer values in the optimal solution.No real difference in basic procedure for formulating an IP model and LP model.A model with general integer variables (IP) has objective function and constraints identical to LP models.Some decision variables are binary, and other decision variables are either general integer or continuous valued.Mixed binary integer programming problems.Variables must have solution values of either 0 or 1.All decision variables are of special type known as binary.Pure binary (or Zero - One) integer programming problems.Non-integer variables can have fractional optimal values.Some, but not all, decision variables must have integer solutions.All decision variables must have integer solutions. ![]() ![]() Binary variables can only take on either of two values: 0 or 1.General integer variables can take on any non-negative, integer value that satisfies all constraints in the model.Algorithms that solve integer linear models do not provide valuable sensitivity analysis results. ![]()
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