Download
1 / 6
60 likes | 205 Views
Optimization Models with Integer Variables. Chapter 6. Introduction. Binary variable: A decision variable that is permitted to take only two possible values, 0 or 1 Usually a 0–1 variable corresponds to an activity that either is or is not undertaken.
E N D
Introduction • Binary variable: • A decision variable that is permitted to take only two possible values, 0 or 1 • Usually a 0–1 variable corresponds to an activity that either is or is not undertaken. • If it equals 1, the activity is undertaken; if it equals 0, the activity is not undertaken.
Solving models with binary variables • Complete enumeration • look at all possible solutions and select the best • impractical because as the number of variables increases the number of possible solutions to enumerate will increase exponentially • a model with 100 binary changing cells will have 2100 possible solutions to enumerate -- 2100 is an extremely large number, so it would take even a very fast computer a long time to check each one of them.
Solving models with binary variables • implicit enumeration • Branch and Bound method • used by Solver in IP models • Branching – systematically creating two problems (branches) setting a given binary variable to 0 or 1 • incumbent solution – current best feasible solution; is a lower bound for a Max problem • Upper bound – the maximum possible objective function for a given branch for a Max problem • Initially LP relaxation serves as the upper bound • If Upper bound < incumbent solution abandon the branch
Solver Tolerance setting A tolerance setting of 5% means that Solver stops as soon as it finds a feasible (integer) solution to the IP model that is within 5% of the current upper bound.
