A major supermarket is updating its delivery network. They have 2 main warehouses (W1 and W2)...

     

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A major supermarket is updating its delivery network. They have 2 main warehouses (W1 and W2) and 23 stores at locations (1-23). Each day they must carry out a daily delivery from their two warehouses to all 23 stores, with the vehicles returning to the ware- houses at the end of the day. The geographical locations of the sites are shown below, with exact distances over the page: 100- 80 60 40 20 17 3 20 W2 15 10 21 2 23 14 13 16 19 12 Wi 18 0 20 40 60 (An Excel version of this data will be available on Canvas.) 80 100 There are two types of vehicle that the supermarket can use: Cost per mile | Maximum stores it can supply Van Lorry 1 2 16 Given the aim is to minimise the total daily costs, find the best strategy such that every store receives its delivery and the warehouses have the correct number of vehicles at the end of the day to carry out the deliveries the following day. Questions: Which stores should each warehouse supply? How many vans or lorries does each warehouse require? What routes should each vehicle take? What is the total cost? The distances from site i to site j, in miles, rounded to the nearest mile, are given in the table below (table is symmetrical): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 W1 W2 1 0 23456789 50 0 87 95 0 74 56 48 0 46 10 85 47 0 41 47 52 34 37 0 47 92 76 90 85 58 0 54 55 40 25 45 13 65 0 32 51 56 47 43 13 46 23 0 10 38 18 102 70 23 51 84 62 51 0 11 28 26 77 50 20 25 66 37 26 26 0 12 39 84 75 85 78 52 8 60 40 77 58 0 13 47 79 49 63 70 36 29 39 27 77 53 27 0 14 48 66 39 44 57 20 47 20 18 68 43 43 19 0 15 75 98 28 64 88 51 52 45 49 100 74 53 29 32 0 16 89 112 33 76 102 66 60 60 64 115 89 62 42 46 15 0 17 63 28 76 31 21 38 94 40 48 44 34 88 74 57 85 99 0 18 21 71 96 91 68 57 36 69 45 58 49 29 49 58 78 90 83 0 19 32 69 62 66 62 34 25 41 21 65 43 19 15 25 44 57 70 34 0. 20 90 78 36 22 69 49 97 37 60 91 69 93 69 51 59 69 53 105 76 0 21 30 20 93 63 21 41 75 53 41 11 16 67 66 58 89 104 41 51 54 83 0 22 12 38 90 69 36 40 58 53 34 27 20 50 55 52 81 95 54 32 41 88 18 0 23 66 79 21 42 68 33 59 24 35 83 58 56 30 18 22 36 63 75 41 40 74 69 0 W1 19 66 80 78 61 44 28 54 31 57 41 20 34 42 63 75 74 15 19 91 48 30 59 0 W2 73 83 15 42 72 38 64 28 41 89 63 63 36 24 23 35 66 81 48 37 79 75 7 66 0 Sheet1 Part 2 Data (2...)_2014979516 P Q R S T U V W X Y 1234 3 4 100 5 69 6 90 7 80 8 70 9 60 10 11 50 12 40 13 30 14 20 15 10 16 17 0 + 0 20 18 19 2222 04 40 40 60 80 100 120 A B B D E LL F G H J K 1 Y Column for Python: TSP_GA.py 2345 1 54.139172 10.163014 ) ) (54.1391723668124,10.1630144708565), 2 5.1631179 18.371369 ( ) (5.16311785475916,18.3713689888664), 3 58.107734 97.325872 ( (58.1077341232713,97.325872003479), 4 16.606639 73.675291 6 5 10.921515 26.902626 7 6 40.283043 49.005961 ) ) ) (16.6066387616466,73.6752906752222), (10.9215147296463,26.9026260431418), ) (40.2830425950062,49.0059611185157), 8 7 95.906795 31.253792 ( ) (95.9067950103118,31.2537921390593), 9 8 38.806885 61.849634 ( (38.8068853736467,61.8496341187066), 10 9 50.773628 41.712299 11 10 16.121045 4.1741521 ) ) (50.7736281603872,41.7122988413166), (16.1210451723109,4.17415211185698), 12 11 30.572526 25.664161 ( ) (30.5725260368337,25.6641613944403), 13 12 88.654185 28.603406 ( ) (88.6541848293903,28.6034058450262), 14 13 76.158333 52.060102 ( (76.1583329812348,52.0601020081577), 15 14 16 15 57.99079 58.290169 80.11801 80.742421 17 16 90.879028 90.976906 ) ) ) (57.9907902884404,58.2901693224847), (80.1180100459334,80.7424210060046), ) (90.879027610417,90.9769056531731), 18 17 2.5872075 45.808494 ( ) (2.58720752188314,45.8084939684228), 19 18 74.049801 2.9861312 ( (74.0498005304951,2.98613115772289), 20 19 21 20 22 21 23 22 71.709117 37.258171 22.371917 94.530747 24.101122 11.066581 ) ) (71.7091166549543,37.2581705831028), (22.3719171429327,94.5307472331531), ( (24.1011220595671,11.0665812260669), 42.278001 9.1418604 ( ) (42.2780005223912,9.14186038530076), 24 23 25 W1 26 W2 58.328059 76.159076 71.253598 18.212685 ) (58.3280585995255,76.1590760811723), (71.2535984441914,18.2126848196072), 57.242195 82.668761 ( (57.2421947321968,82.6687611686287), 27 28 A major supermarket is updating its delivery network. They have 2 main warehouses (W1 and W2) and 23 stores at locations (1-23). Each day they must carry out a daily delivery from their two warehouses to all 23 stores, with the vehicles returning to the ware- houses at the end of the day. The geographical locations of the sites are shown below, with exact distances over the page: 100- 80 60 40 20 17 3 20 W2 15 10 21 2 23 14 13 16 19 12 Wi 18 0 20 40 60 (An Excel version of this data will be available on Canvas.) 80 100 There are two types of vehicle that the supermarket can use: Cost per mile | Maximum stores it can supply Van Lorry 1 2 16 Given the aim is to minimise the total daily costs, find the best strategy such that every store receives its delivery and the warehouses have the correct number of vehicles at the end of the day to carry out the deliveries the following day. Questions: Which stores should each warehouse supply? How many vans or lorries does each warehouse require? What routes should each vehicle take? What is the total cost? The distances from site i to site j, in miles, rounded to the nearest mile, are given in the table below (table is symmetrical): 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 W1 W2 1 0 23456789 50 0 87 95 0 74 56 48 0 46 10 85 47 0 41 47 52 34 37 0 47 92 76 90 85 58 0 54 55 40 25 45 13 65 0 32 51 56 47 43 13 46 23 0 10 38 18 102 70 23 51 84 62 51 0 11 28 26 77 50 20 25 66 37 26 26 0 12 39 84 75 85 78 52 8 60 40 77 58 0 13 47 79 49 63 70 36 29 39 27 77 53 27 0 14 48 66 39 44 57 20 47 20 18 68 43 43 19 0 15 75 98 28 64 88 51 52 45 49 100 74 53 29 32 0 16 89 112 33 76 102 66 60 60 64 115 89 62 42 46 15 0 17 63 28 76 31 21 38 94 40 48 44 34 88 74 57 85 99 0 18 21 71 96 91 68 57 36 69 45 58 49 29 49 58 78 90 83 0 19 32 69 62 66 62 34 25 41 21 65 43 19 15 25 44 57 70 34 0. 20 90 78 36 22 69 49 97 37 60 91 69 93 69 51 59 69 53 105 76 0 21 30 20 93 63 21 41 75 53 41 11 16 67 66 58 89 104 41 51 54 83 0 22 12 38 90 69 36 40 58 53 34 27 20 50 55 52 81 95 54 32 41 88 18 0 23 66 79 21 42 68 33 59 24 35 83 58 56 30 18 22 36 63 75 41 40 74 69 0 W1 19 66 80 78 61 44 28 54 31 57 41 20 34 42 63 75 74 15 19 91 48 30 59 0 W2 73 83 15 42 72 38 64 28 41 89 63 63 36 24 23 35 66 81 48 37 79 75 7 66 0 Sheet1 Part 2 Data (2...)_2014979516 P Q R S T U V W X Y 1234 3 4 100 5 69 6 90 7 80 8 70 9 60 10 11 50 12 40 13 30 14 20 15 10 16 17 0 + 0 20 18 19 2222 04 40 40 60 80 100 120 A B B D E LL F G H J K 1 Y Column for Python: TSP_GA.py 2345 1 54.139172 10.163014 ) ) (54.1391723668124,10.1630144708565), 2 5.1631179 18.371369 ( ) (5.16311785475916,18.3713689888664), 3 58.107734 97.325872 ( (58.1077341232713,97.325872003479), 4 16.606639 73.675291 6 5 10.921515 26.902626 7 6 40.283043 49.005961 ) ) ) (16.6066387616466,73.6752906752222), (10.9215147296463,26.9026260431418), ) (40.2830425950062,49.0059611185157), 8 7 95.906795 31.253792 ( ) (95.9067950103118,31.2537921390593), 9 8 38.806885 61.849634 ( (38.8068853736467,61.8496341187066), 10 9 50.773628 41.712299 11 10 16.121045 4.1741521 ) ) (50.7736281603872,41.7122988413166), (16.1210451723109,4.17415211185698), 12 11 30.572526 25.664161 ( ) (30.5725260368337,25.6641613944403), 13 12 88.654185 28.603406 ( ) (88.6541848293903,28.6034058450262), 14 13 76.158333 52.060102 ( (76.1583329812348,52.0601020081577), 15 14 16 15 57.99079 58.290169 80.11801 80.742421 17 16 90.879028 90.976906 ) ) ) (57.9907902884404,58.2901693224847), (80.1180100459334,80.7424210060046), ) (90.879027610417,90.9769056531731), 18 17 2.5872075 45.808494 ( ) (2.58720752188314,45.8084939684228), 19 18 74.049801 2.9861312 ( (74.0498005304951,2.98613115772289), 20 19 21 20 22 21 23 22 71.709117 37.258171 22.371917 94.530747 24.101122 11.066581 ) ) (71.7091166549543,37.2581705831028), (22.3719171429327,94.5307472331531), ( (24.1011220595671,11.0665812260669), 42.278001 9.1418604 ( ) (42.2780005223912,9.14186038530076), 24 23 25 W1 26 W2 58.328059 76.159076 71.253598 18.212685 ) (58.3280585995255,76.1590760811723), (71.2535984441914,18.2126848196072), 57.242195 82.668761 ( (57.2421947321968,82.6687611686287), 27 28