2 Problem 2 (50 points) Supermarkets are currently facing unprecedented pressure to replenish their empty shelves due to panic buying. Suppose you have been hired as a logistics manager for a Toilet Paper distributor called TPanic, and your job entails building vehicle routes to serve supermarket locations from their main Distribution Center (DC) located in Atlanta with the objective of minimizing total cost. On a given day, TPanic must serve 8 supermarkets in Atlanta located in Atlantic Station, Virginia Highland, Piedmont Heights, Edgewood, Midtown Atlanta, Downtown Atlanta, East Point and Buckhead. Denote Tij and Cijto be the travel time and travel cost between location i and j, respectively. At the DC, you have enough vehicles to operate and meet all demand. Each vehicle has a capacity of Q packs. Each supermarket requests a given number of TP packs from the depot, denote it by di for i = 1, ..., 8. The delivery for supermarkets must take place in the afternoon and evening shifts between 12pm and 9pm. Model the problem as Vehicle Routing Problem with Time Windows using an arc-based formulation. Make sure to clearly define your decision variables, objective function and constraints. Explain in words what each set of constraints represents. Hint: Use the following decision variables: Xij to indicate whether a vehicle visit node j after node i or not; qi to represent the remaining vehicle capacity after visiting node i, and ti to represent the earliest time the vehicle can depart from node i. Also, think about using Big-M constraints to capture capacity and time restrictions. 2 Problem 2 (50 points) Supermarkets are currently facing unprecedented pressure to replenish their empty shelves due to panic buying. Suppose you have been hired as a logistics manager for a Toilet Paper distributor called TPanic, and your job entails building vehicle routes to serve supermarket locations from their main Distribution Center (DC) located in Atlanta with the objective of minimizing total cost. On a given day, TPanic must serve 8 supermarkets in Atlanta located in Atlantic Station, Virginia Highland, Piedmont Heights, Edgewood, Midtown Atlanta, Downtown Atlanta, East Point and Buckhead. Denote Tij and Cijto be the travel time and travel cost between location i and j, respectively. At the DC, you have enough vehicles to operate and meet all demand. Each vehicle has a capacity of Q packs. Each supermarket requests a given number of TP packs from the depot, denote it by di for i = 1, ..., 8. The delivery for supermarkets must take place in the afternoon and evening shifts between 12pm and 9pm. Model the problem as Vehicle Routing Problem with Time Windows using an arc-based formulation. Make sure to clearly define your decision variables, objective function and constraints. Explain in words what each set of constraints represents. Hint: Use the following decision variables: Xij to indicate whether a vehicle visit node j after node i or not; qi to represent the remaining vehicle capacity after visiting node i, and ti to represent the earliest time the vehicle can depart from node i. Also, think about using Big-M constraints to capture capacity and time restrictions