Question: 4. (a 8 points, b 12 points (3x4)) Consider the VRP (without capacity constraints) on a directed graph G=(N,A), where node 1 corresponds to the

4. (a 8 points, b 12 points (3x4)) Consider the VRP (without capacity constraints) on a directed graph G=(N,A), where node 1 corresponds to the depot location. Suppose that there are m vehicles available at the depot and cydenotes the cost of using arc (ij) A. a. Give a mathematical model for the problem. (Hint: Define the decision varibles x,-1 if nodej is visited just after node i; 0 otherwise.) b. Modify your model to satisfy the following restrictions. (Hint: You need to define additional decision varibles to model these restrictions). i. Total distance traveled by a vehicle should not exceed a predetermined value T. ii. Each customer can only be visited in specific time interval (customer i should be visited not earlier than time e, and not later than time /). iii. A truck can visit at most k nodes

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