{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Class_Notes_Part_5

# Class_Notes_Part_5 - Class Notes for DMOR Set 5 Integer...

This preview shows pages 1–9. Sign up to view the full content.

Class Notes for DMOR: Set 5 Integer programming and dynamic programming. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
What is an integer program? Linear programming problem, with the additional statement that all variables must be in- teger. Mixed-integer program: some, but not all, of the variables must be integer. Special case: binary programming problems or 0/1 programming problems. All variables must equal to zero or one. Minimize x 1 + 2 x 2 subject to 2 x 1 + 2 x 2 9 x 1 - x 2 1 x 1 , x 2 0 and integer. 2
What can you do with IP’s? Clearly, some variables cannot be split. Consider this problem. A 24-hour call center expects c i calls during hour i , for i = 1 , . . . , 24 (see table below). Each employee on hand can handle one call per hour. We can hire full-time employees at \$100 per day, and part-time employees at \$65 per day. A full-time employee works four straight hours, takes an hour break, and then works four more consecutive hours. A part-time employee works four consecutive hours and then goes home. We wish to hire enough employees to cover all calls at all times, but we want to minimize costs. Devise a model to minimize hiring costs. Hour Demands Hour Demands 1 53 13 423 2 17 14 587 3 48 15 654 4 94 16 581 5 85 17 442 6 226 18 312 7 186 19 251 8 337 20 80 9 293 21 77 10 319 22 79 11 397 23 50 12 419 24 24 LP Solution: IP Solution: 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Using binary variables. But with the clever use of binary variables, we can do a lot more than just require that solutions take integer values. For instance, we can state logical restrictions like: item selection if/then constraints on - off toggles either - or constraints omit a particular solution 4
Pennies Game We have a four by four grid, and ten pennies. Place each penny in a distinct cell of your grid, so that the sum of pennies in each row and each column is an even number. Variables: Constraints: (No objective: Minimize 0) Reference: http://www.chlond.demon.co.uk/academic/puzzles.html 5

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
“Lights Puzzle” Once again, we have a four by four grid, with some lights on and some lights off. If we select a square, then all lights in its row and column toggle their on/off status. We want to turn all the lights on, using the fewest number of cell selections. Reference: http://www.chlond.demon.co.uk/Lights.html Variables: Constraints: Objective: 6
The Knapsack Problem We have a backpack and a set of items that we would like to include in the pack. Have n items to put in the backpack. Item i is worth v i value to me, but weighs w i pounds. I can only carry P pounds. Formulation: 7

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Production and Inventory With Setup Problem is to develop a production plan that minimizes total cost and meets all demand on time. Here is the problem data. T = The number of time periods. a t = The setup cost at time t = 1 , . . . , T . Note that we have to pay this cost of production at time t is positive.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 26

Class_Notes_Part_5 - Class Notes for DMOR Set 5 Integer...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online