Question: . . Consider an instance of the vehicle routing problem (VRP) with the following parameters: number of customers = 8 (each customer has unit demand)

. . Consider an instance of the vehicle routing

. . Consider an instance of the vehicle routing problem (VRP) with the following parameters: number of customers = 8 (each customer has unit demand) - 8 ) number of vehicles available - 2 = vehicle capacity - 4 and with the following distance matrix where node is the origin. . 0 0 1 2 3 4 5 6 7 8 0 0 130 34 45.422.7 1946 120 38.5 1 130 0 149.322 102 126.165.33569 2 44.4149.3 032 65 73.2 63 75.5 44 3 45.4 180 320 75 37.3 45.4 51 125 4 22.7 125 65 750 38.1 28 61 168 5 19 126.1 73.237.338.1 0 38 48 125.2 6 46 65.3 63 45.4160 1240 153 68 7 120 190 75.5 56 64 48 153088 8 38.5 69 | 44 125 168 12.4 146 88 0 0 You are asked to employ a cluster-first-route-second (CFRS) procedure to find a feasible solution. Assume that, initially you calculated the clusters as follows: Cluster 1: (1,3,4,7) Cluster 2: (2,5,6,8) (a) (10p) The sequence of a given solution for the first cluster is 0-3-1-7-4-0. Can you improve the tour length of this solution by using a 2-opt swap? Evaluate all possible 2-opt swap operations and identify the most improving 2-opt swap. Report the tour obtained by applying the most improving swap and its length (SHOW YOUR WORK CLEARLY IN ORDER TO GET FULL CREDIT) (b) (10 p) You decided to apply savings algorithm in order to solve a feasible tour for the second cluster only. If the savings matrix is given as follows report the tour obtained by applying the savings algorithm and its length. (SHOW YOUR WORK CLEARLY IN ORDER TO GET FULL CREDIT) 1 2 2 3 4 1 1 2 3 4 5 6 7 8 0 0 14.7153.4 50.7 22.9 110.7215 99.5 25.1 0 0 57.8 2.1 -9.8|27.4 88.938.9 -4.6 47.40 -6.9 27.1 46 114.4 -41.1 27.7-8.3 -6.9 0 3.640.781.7106.8| 22.9 20.2 27.1 3.6 0 27 91 -67.7 110.71 17 46 -91.3-590 13 16.5 60 78.5 109.4 78.7 91 13 0 0 70.5 99.5 28.5 -41.1-106.845.1-61.5 70.5 0 5 6 7 8

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