Real life comparison
In 2010 the Austrian Red Cross gave us an actual route plan for region ; the data used in the earlier subsection is from 2008. The data set consists of 368 jobs, 293 clients, and 53 nurses. For one particular day the actual routing plan leads to a solution value of 3,703 minutes of traveling time. We got information about the service durations, visiting times, and starting points. The number of time-critical jobs is estimated to 10% of the jobs with a qualification level of 3 by the Austrian Red Cross. Jobs with a qualification level of 1 and 2 are usually not time-critical. In case that 10% of the jobs with a qualification level of 3 have to be visited within 120 minutes, a solution of 2,014 minutes can be obtained, which is an improvement of 45.6%. These solution values have been computed with parameter setup . Due to missing data the following results are all computed with this setup. Table 4 presents the results of a sensitivity analysis, in which the number of time-critical jobs with a qualification level of 3 and the service times of all jobs are increasing. This analysis was made because we were interested if it is possible to increase the service times and still get feasible solutions. The focus of our optimization lies mainly in reducing the traveling times which further leads to a reduction in working times. However, the working times of the nurses are constant. Therefore, more time can be spent at the serviced clients or new clients can be visited, which is the focus in the next analysis, presented in Table 5. The results in Table 4 show that all feasible solutions are better than the solution value of the current routing. However, if all jobs are time-critical it is not possible to find feasible solutions if the service time increases by 20%. Figure 2 shows these results as a graph. If the value is set to infinite (Table 4, Table 5, Figure 2, and Figure 3) no feasible solution was obtained.