You work at Amazon and are asked to extend the facility location that makes sure every customer in Georgia is within an hour of a delivery dispatch location.

The current model is a standard set-covering model and is as follows:

a.) Write down constraint(s) that would prevent more than q customers from being assigned to one location. You will need to add a new variable for assignments.

b.) Management would like to add a delivery cost to the model based on how far customers are from the assigned dispatch locations. Define a parameter to represent this.

c.) Write down a revised objective function that includes both the costs for selecting a dispatch location and delivery.

Sets Vi: candidate dispatch locations V2: customer locations Parameters T: time limit (1 hour) tij: time to travel between dispatch location i E Vand customerj E V2 i iftij ST lo otherwise fixed cost of locating dispatch location i E V. dij Decision variables: 11 if locate at i E V 10 otherwise y:= { Minimize fiyi ievi subject to aij y; 2 1, j = V2 ievi Yi {0,1}, i e Vi Sets Vi: candidate dispatch locations V2: customer locations Parameters T: time limit (1 hour) tij: time to travel between dispatch location i E Vand customerj E V2 i iftij ST lo otherwise fixed cost of locating dispatch location i E V. dij Decision variables: 11 if locate at i E V 10 otherwise y:= { Minimize fiyi ievi subject to aij y; 2 1, j = V2 ievi Yi {0,1}, i e Vi