When discussing VRP heuristics, we talked about how both TSP Partitioning and Sweep make use of the Next Fit bin packing heuristic. In a couple of sentences, discuss why Next Fit is a better choice than First Fit or Best Fit to use within the context of these VRP heuristics. HINT: This is not related to the ability to immediately dispatch closed vehicles; there is another discussion we have had about this in class a few times. Table 1: Customer lot sizes (tons) and X-Y coordinates Y 5 2 4 4 Cust Lot size X 1 4 3 2 3 4 5 6 7 APPENDIX 8 9 10 9 6 3 7 11 2 4 8 1 3 10 8 7 7 2 7 4 6 0 8 3 6 0 3 0 1 2 3 4 5 6 7 8 9 10 Table 2: Travel distances (based on Euclidean distances between x-y coordinates) 0 3 4 10.8 8.9 9.1 7.1 7.3 5.4 2.0 5.1 3.6 10.8 8.9 7.0 10.6 3.6 9.2 4.0 6.7 9 8 7 6 5 4 3 2 1 1 5.1 3.6 9.1 7.1 7.8 6.7 2.2 6.1 5.8 5.4 1 2 3.6 3.6 7.3 5.4 4.5 524 7.2 1.4 5.7 2.2 22 3.2 2.0 5.0 5.0 8.1 3.6 NH 7.2 4.1 446 4 4.1 4.1 6.1 2.2 177 5.7 52 2.2 5 7.0 7.8 4.5 5.0 4.1 8.0 5.8 6.0 3.0 3.2 10 6 10.6 6.7 7.2 5.0 4.1 8.0 7.1 2.0 8.5 5.1 5 7 3.6 2.2 1.4 8.1 6.1 5.8 7.1 5.8 3.6 4.0 8 9.2 6.1 5.7 3.6 2.2 6.0 2.0 5.8 6.7 3.2 9 4.0 5.8 2.2 7.2 5.7 3.0 8.5 3.6 6.7 3.6 2 6 8 10 12 Figure 1: Graphical depiction of instance (labels are customer indices) 10 6.7 5.4 3.2 4.1 2.2 3.2 5.1 4.0 3.2 3.6 Consider the vehicle routing problem defined by the data in Table 1 (Appendix), where the lot size in tons and the x and y coordinates are provided for each of 10 customers. Suppose the depot is located at the origin (0,0) and each vehicle has the capacity to hold 15 tons of goods. A complete distance matrix is provided in Table 2 and a graphical depiction is in Figure 1 (both in Appendix). Use this information to answer all questions in this assignment.