info372-ip-practice-sol - INFO 372 Practice Integer...

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INFO 372 Practice – Integer Programming Solutions A young couple, Alice and Bob, want to divide their main household chores (marketing, cooking, dishwashing, and laundering) between them so that each has two tasks but the total time they spend on the household duties is kept to a minimum. Tasks are cannot be split. Their efficiencies on these tasks differ, where the time each would need to perform the task is given by the following table: Grocery Shopping Cooking Dishwashing Laundry Alice 4.5 hours 7.8 hours 3.6 hours 2.9 hours Bob 4.9 hours 7.2 hours 4.3 hours 3.1 hours Time Needed per Week per person per task (Note each task will be assigned to a single person). a) Formulate a BIP model for this problem. a) M A = 1 if Alice does the marketing (grocery shopping); 0 if she doesn’t M B = 1 if Bob does the marketing (grocery shopping); 0 if he doesn’t C A = 1 if Alice does the cooking; 0 if she doesn’t C B = 1 if Bob does the cooking; 0 is he doesn’t D A = 1 if Alice does the dishwashing; 0 if she doesn’t D B = 1 if Bob does the dishwashing; 0 if he doesn’t L A = 1 if Alice does the laundry; 0 if she doesn’t L B = 1 if Bob does the laundry; 0 is he doesn’t Minimize: T = 4.5M A + 7.8C A + 3.6D A + 2.9L A + 4.9M B + 7.2C B + 4.3D B + 3.1L B s.t. M A + C A + D A + L A = 2 (Alice must have 2 chores) M B + C B + D B + L B = 2 (Bob must have 2 chores) M A + M B = 1 (Someone must go to the market) C
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info372-ip-practice-sol - INFO 372 Practice Integer...

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