10.1 Integer Programming and LP relaxation
f(L) 2C f(x) and C r(L) 6C r(y). Proof: For any two customers j 1 and j 2 that were picked in Step 1, S j 1 \S j 2 = ;. Consider the facility cost incurred by one execution of Steps 1 through 4. Let jbe the customer chosen in Step 1, and let ibe the facility chosen in Step 2. Since ~xis part of a feasible solution, 1 P k2S j x~ k. So, f i f i P ...
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