## 4 Case Study: The Disposal in Finland
The different solutions are labeled based on the reference point used and the value of the parameter \(q\). For example, the solution r1q1 is the result obtained by using the reference point 1 and \(q=1\). Moreover, the reference point 1 is labeled with r1. In Step 3, two solutions are selected to be presented for the decision-maker for the closer inspection. The number of presented solutions \(s\) is restricted to two in order to aid the decision maker's task to select best out of only two options and in order to keep the presentation clear. At each iteration, one solution with a smaller value of \(q\) and one with a larger value of \(q\) are presented and different values of \(q\) are demonstrated in order to exemplify the variety of solutions. Next, we present four iterations of MITSPA. Iteration 1. At the first iteration, the decision maker begins by investigating the trade-off between operation time of the encapsulation facility and the cooling times of assemblies by deciding to start with the unachievable reference point such that the operation time is short and the cooling time is long. The two solutions chosen for reference point 1 are shown in Figure 2a together with reference point 1. The solution obtained by using value \(q=1\) (r1q1) shown in the green line corresponds to the early starting time of disposal. The solution obtained by using value \(q=9\) (r1q9) shown in the orange line corresponds to the late starting time of the disposal. In Figures 2b,c, the corresponding disposal schedules are given. The solution r1q9, has the shortest possible encapsulation time but the maximum cooling time is long. The solution r1q9, like r1q1, has a high maximum number of assemblies in the storage (see the objective (1)), but the maximum and average storage times (the objectives (2) and (3)) are slightly shorter. The solution r1q9 does not allow any empty positions in canisters while the solution r1q1 does (see (4)), but the encapsulation ends much later (see (5)) in the solution r1q9 than in r1q1. However, the operation time of the encapsulation facility (see (6)) is shorter in the solution r1q9 than in r1q1. When the disposal facility-related objectives (see (7) and (8)) are compared, the solution r1q9 needs a smaller area than the solution r1q1. Moreover, the solution r1q9 is cheaper than the reference, while the solution r1q1 is more expensive than the reference (see (9)). Mainly due to the significant difference in the costs, the decision maker selects the solution r1q9 as the current solution \(f_{1}\)  
Figure 1: The objective values of 9 solutions obtained using the reference point 1. Iteration 2. In order to learn more about the trade-off between the operation time of the encapsulation facility and the cooling time, another reference point (reference point 2) is selected. In this case, the reference point is achievable. Now we try to find solutions such that the operation time is longer and cooling time shorter. The two solutions chosen for reference point 2 are shown in Figure 2(a) and the corresponding disposal schedules in Figure 2(b),c. Again, the solution obtained with the small value \(q=1\) (r2q1) represents the early starting time of the disposal. This is depicted with the green line in Figure 2(a) while the orange line depicts the solution obtained using value \(q=9\) (r2q9) corresponding to the late starting time of the disposal. If we compare the disposal schedules in Figure 2(b),c to the schedules for reference point 1 given in Figure 1(b),c, we notice some similarity. Even though the starting and ending times differ as well as the total number of canisters, the solutions with the parameter \(q\) value 1 and value 9 have the same shape. The smaller \(q\) suggests the schedule such that first, we encapsulate a small number of canisters per period and the number of canisters is growing while the time goes by, whereas the larger \(q\) recommends the schedule where all the canisters are encapsulated within two periods.