6. Model verification and validation 51
6.1. Verification 51
7.2.2. Optimal solution implemented 58
The current solution does not have to be the option where the total costs of ownership are the least possible. Since no evaluation of the TCO happened when the contract started, it is interesting to see whether the hospital’s fleet would change when the total costs of ownership are considered in the choice of adding or removing a device. Therefore the optimization is applied to the current situation with the parameters of Hospital A. Based on this input the threshold values can be calculated, where after the optimal number of devices is determined based on the expected demand.
The optimal number of devices is again determined by the use of the threshold values. In the calculations for the optimization, the prices and the replacement interval for equipment in a category that are used are the averages of the price and replacement interval of the currently installed equipment. The devices that will be installed in the MES contract according to the optimization also have this same value . This is done since removing a more expensive model instead of a cheaper device, would give a distorted picture.
Based on the values of all parameters, the threshold value for having versus
devices is determined for every equipment category. The outcomes of the model are shown in Appendix J.
By combining the expected demand in all periods with the threshold values found by the model. It is possible to determine the optimal number of devices for Hospital A at every period for all equipment categories. The number of devices in the optimal situation is shown in Table 21.
1 2 3 4 5 6 7 8 9 10 11 12 US 2 2 2 2 2 2 2 2 2 2 2 2 MRI 1 1 1 1 1 1 1 1 1 1 2 2 CT 1 1 1 1 1 1 1 1 1 1 1 1 Angio 1 1 1 1 1 1 1 1 1 1 1 1 C-Arm 1 1 1 1 1 1 1 1 1 1 1 1 Mammo 1 1 1 1 1 1 1 1 1 1 1 1
Table 21: Recommended number of devices in every period and category for Hospital A
Based on the number of devices, the recommended opening hours are calculated. These hours are visible in Appendix I. The TCO that is associated with the solution described above is calculated by the model and listed below in Table 22. In order to calculate the TCO associated with the optimal solution, it is assumed that all required devices at period 1 are installed by Siemens for the first time in that period, so no equipment of a third party is taken into account. The proportion of every cost element in the TCO of the optimal solution is visible in Figure 15.
Optimal situation NPV of TCO
Optimal situation incl. indexation € 41.109.812,59
Optimal situation excl. indexation € 40.069.898,16
Table 22: TCO value of proposed solution (optimal)
Since there is already equipment installed at the hospital at the beginning of the contract, which cannot be removed immediately since equipment can only be removed after the replacement interval, the optimal solution is not realistic in the first periods. Therefore, next performed experiment is with the installed base of the current situation at period 1, and with the assumption that removals are only allowed after the replacement period of the already installed equipment. Based on these restrictions, the number of devices over the period of 12 years is determined and given in Table 23. The daily opening hours associated with the new recommended number of devices are shown in Appendix I.
1 2 3 4 5 6 7 8 9 10 11 12 US 5 5 4 2 2 2 2 2 2 2 2 2 MRI 1 1 1 1 1 1 1 1 1 1 2 2 CT 1 1 1 1 1 1 1 1 1 1 1 1 Angio 3 3 3 3 3 3 3 3 2 1 1 1 C-Arm 3 3 3 3 3 3 3 3 3 2 1 1 Mammo 1 1 1 1 1 1 1 1 1 1 1 1
Table 23: Recommended number of devices starting with the installed base at period 1
Now all required data is known, it is possible to calculate the TCO of the solution again. Just like the implementation of the data of the current installed base, the TCO is calculated with and without the use of indexation.
Starting with installed base at p=1 NPV of TCO Optimal situation incl. indexation € 40.258.708,85
Optimal situation excl. indexation € 39.111.776,06
Table 24: TCO value of proposed solution (optimal, starting with installed base)
It is remarkable that the TCO of the optimal situation, combined with the installed base at period 1 gives a lower TCO than the optimal solution. This could be explained by the fact that in the excising situation equipment is installed in the first periods where only maintenance costs have to be paid
since the equipment costs are only included from the moment of first install in the contract. This first install might occur in this situation in, for example, the sixth period and therefore there are no costs for the purchase of that device over the first five periods. This effect is also visible in the graph that represents the shares of every cost element to the value of the TCO in Figure 15, since the equipment has only a share of 12% compared to a 17% share in the optimal situation. The graph in Figure 15 is also based on the indexed TCO, in order to compare the current and optimal solution better.
When looking at the share of the cost elements in the TCO of the current situation and the optimal solution with the installed base as starting point, it is clear that the costs for labour account for a bigger part in the optimal solution. Since the optimal solution suggests in many cases to have less devices, the opening hours will increase in order to meet the expected demand. When the opening hours are extended till over the regular hours, the labour costs will increase. This causes the effect visible in the shares of the cost element labour.
Figure 15: Shares of all cost elements in different experiments
The used treatment times in the above described experiments are averages of the realized treatment times over a few years. Some values of treatment times are numbers which are not possible to use when planning a department. For example, the treatment time on the MRI is determined to be 28 minutes. However, the MRI department makes in practice appointments of 30 minutes. Where other departments, like the Bucky, are able to plan approximately 8 patients in an hour. So in that situation the treatment time is representative. The case of Hospital A is also evaluated with appointment adjusted treatment times. The used treatment times are shown in Appendix J.
The result of the TCO calculation is based on the adjusted treatment times for the current and the optimal situation with both having the installed base at period 1 as starting point. The results, including and excluding indexation, are shown in Table 25. The associated threshold values and the number of devices are given in Appendix I.
€ - € 5,00 € 10,00 € 15,00 € 20,00 € 25,00 € 30,00 € 35,00 € 40,00 € 45,00
Current situation Optimal start blanco Optimal start installed base TCO M ill io n s Experiment Floor/Space Disposables Energy Labour Direct Downtime Extra MES Service Maintenance Acquisition 7% 20% 4% 27% 0% 3% 24% 15% 5% 22% 4% 33% 0% 3% 16% 17% 7% 22% 4% 33% 0% 2% 20% 12% € 44.222.647,63 € 41.109.812,59 € 40.258.708,85
Adjusted treatment times Current situation Optimal situation
Incl. indexation € 45.151.973,15 € 42.120.137,50
Excl. indexation € 43.584.865,57 € 40.858.420,75
Table 25: TCO value of proposed solution (adjusted treatment times, starting with installed base)