(c) In class we talked about how to model constraints like "either condition A holds or condition B holds (or both)". How about when you have three conditions? For example, how to model "at least one of the following three conditions should hold": (i) 3x1 +x2 > 5; (ii) 2x1+2x2 > 4; (iii) x1+3x2 > 5? (If you use big-M inequalities here, you do not need to specify the values for the big-M parameters.)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter11: Simulation Models
Section: Chapter Questions
Problem 68P
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Short Answer / Please only answer part C ONLY PART “C” please
(a) When you solve an integer programming problem (suppose it is a maximization prob-
lem), how do you obtain an upper bound on the optimal objective value? How do you
obtain a lower bound?
(b) Suppose you use a binary variable ya to represent whether or not event A will happen,
and use a binary variable yB to represent whether or not event B will happen. How
do you model the following logic constraint using an inequality?
If A happens = then B must happen
(c) In class we talked about how to model constraints like "either condition A holds
or condition B holds (or both)". How about when you have three conditions? For
example, how to model “at least one of the following three conditions should hold":
(i) 3.x1+x2 > 5; (ii) 2x1+2x2 > 4; (iii) x1+3x2 > 5? (If you use big-M inequalities
here, you do not need to specify the values for the big-M parameters.)
Transcribed Image Text:(a) When you solve an integer programming problem (suppose it is a maximization prob- lem), how do you obtain an upper bound on the optimal objective value? How do you obtain a lower bound? (b) Suppose you use a binary variable ya to represent whether or not event A will happen, and use a binary variable yB to represent whether or not event B will happen. How do you model the following logic constraint using an inequality? If A happens = then B must happen (c) In class we talked about how to model constraints like "either condition A holds or condition B holds (or both)". How about when you have three conditions? For example, how to model “at least one of the following three conditions should hold": (i) 3.x1+x2 > 5; (ii) 2x1+2x2 > 4; (iii) x1+3x2 > 5? (If you use big-M inequalities here, you do not need to specify the values for the big-M parameters.)
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