The Ring Offshore company, in the North Sea, has deployed 13 drilling platforms to be connected through a network of pipelines with a hub assembly whose best position can be determined by solving a SCSE continuous location problem. To this end, the Cartesian coordinates and the average daily flow rate of each drilling platform are reported in Table 3.30. Solve the problem by using the Weiszfeld heuristic (with at least three iterations).

 

Table 3.30 Coordinates and average flow rates of the drilling platforms in the North Sea. Abscissa (km) Ordinate (km) Drilling platform 6 7 9 10 11 12 13 0.00 11.56 5.58 22.60 8.88 37.28 12.72 35.65 9.27 25.56 15.87 31.53 29.72 8.54 0.00 12.45 11.35 17.38 21.56 18.65 5.42 24.32 34.54 28.55 10.12 31.40 Flow rate (quintals/day) 198 191 212 279 205 230 278 198 226 188 244 215 248