5a) How would you modify this formulation if you could only open at most k facilities? 5b) How would you modify this formulation if demand at a given demand location j could be left unsatisfied at a per-unit cost of gj? Hint: You will need a variable for each demand location. These variables need to be part of the first set of constraints for demand as well as the objective.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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5) Consider the facility location problem that we covered in lecture:
n m
n
min z = ΣΣcijXij + Σciyi
Yi
X
i=1 j=1
i=1
n
s.t. Σxij zdj,
1≤j≤m
i=1
m
Σxij ≤ biyi,
1≤ i ≤n,
j=1
x ≥ 0,
y = {0, 1}n
5a)
How would you modify this formulation if you could only open at most k facilities?
5b)
How would you modify this formulation if demand at a given demand location j
could be left unsatisfied at a per-unit cost of gj?
Hint: You will need a variable for each demand location. These variables need to be part of the
first set of constraints for demand as well as the objective.
Transcribed Image Text:5) Consider the facility location problem that we covered in lecture: n m n min z = ΣΣcijXij + Σciyi Yi X i=1 j=1 i=1 n s.t. Σxij zdj, 1≤j≤m i=1 m Σxij ≤ biyi, 1≤ i ≤n, j=1 x ≥ 0, y = {0, 1}n 5a) How would you modify this formulation if you could only open at most k facilities? 5b) How would you modify this formulation if demand at a given demand location j could be left unsatisfied at a per-unit cost of gj? Hint: You will need a variable for each demand location. These variables need to be part of the first set of constraints for demand as well as the objective.
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