As it is known, simulation models cannot be validated. There is no procedure, how we could verify that the model operates correctly (i.e. realistically). We can only in-crease confidence that the model most likely works as it should. And that was tried to be done as well as possible, by designing the model structure based on literature find-ings. That is, the model should be as realistic as the literature is, or in practice, the simplified version of it. In this respect, the model is subject to critique, whether it is structurally realistic. The structural realism was tried to be increased throughout the modeling process by receiving feedback from the reviewers and supervisor of this thesis and adjusting the model structure accordingly.
Even in pure technical respect, we cannot be totally sure that the model works cor-rectly in practice. As the complexity or just the amount of features in the model is increased, the likelihood of bugs in the final code is highly increased. In practice, it would take too much time to check every line of the code and verify that those are correct. Even if this was done and all the technical bugs were corrected, in the end, semantic errors would still be very likely. That is the reality of computer program-ming.
Therefore, the most practical way to increase confidence that the model works as in-tended is to check that the model does not crash while running test simulations and qualitatively analyze that the test results are believable. A few million simulations were run during the whole process of making the model. If the model crashed in any of those simulations, the bugs causing this were corrected. In the end, the model did not crash with any of the tested parameter combinations, except for the ones that are unrealistic, and the model does not have to work with those (for example, prices can-not be negative so negative prices do can-not have to be tested). And if there were any unbelievable results or the model could not produce something that was expected, the model was modified accordingly. Of course, there is a danger here: dynamic systems are not necessarily predictable as dynamic phenomena can be totally realistic while being totally unexpected. However, in this particular case in which maintenance strat-egy is considered, we are rather familiar with the associated systemic phenomena.
Therefore, in the end, the model was considered to be working as it should by the au-thor, supervisor and the reviewers of this thesis.
4 THE RESULTS OF THE MODELING
The final model came out so that it has quite a lot of depth in it. This means, first of all, it is not practical to present all the results the model could actually produce due to lack of space. Not all the results are really interesting in analyzing maintenance strat-egy, so the most relevant results were chosen. Secondly, it would not be practically possible to present all the results in the matter of time: running the model with all the possible parameter combinations (i.e. inputs for the simulation runs) could take a few weeks with the processing power the author had available (24 core processor, each core clocked at 2,4 GHz). To retrieve the results presented below, the model had to be run for a few days. Therefore, the final parameter combinations had to be chosen based on the interest of analyzing different phenomena and qualitative analysis on which of the parameters are contributing to specific phenomena the most.
The interest was to analyze, how changing of different parameters affect the optimal maintenance point for a machine. Here, the optimal maintenance point is defined to be the one that, in which the maintenance being conducted, results in greatest profita-bility through time for either the customer or the maintenance company. The mainte-nance point is kept constant through the whole simulation. To ease the analysis a bit, only two parameters are varied at once between simulation runs, while others are kept constant.
As being a conceptual AB model, the absolute values the model produces are of little interest themselves. Instead, the changes in the absolute values tell us more about the dynamics of the system. So, the actual result from this whole analysis is a qualitative explanation on what happens to profitability (i.e. how profitability changes) if we change different parameters.
In the table 14, the initialization of the model and inputs to the simulations are pre-sented. In the table 15 all the actual tests that were run are presented and explained. In the figures 12 - 18 the results from these simulations are visualized. The results are analyzed and the implications of these results for decision making and science are elaborated.
A few quick notes should be mentioned about the upcoming figures in this chapter.
The dimensions in the figures relate to the parameters that were varied in the simula-tions (presented in the table 15). The color scheme is set to be so that the warmer the color, the higher the cumulative profits and vice versa. In addition, in the bottom of each figure is a two dimensional contour plot, which highlights the differences in cu-mulative profits. Finally, there are additional figures in the appendix 3, in which min-imum and maxmin-imum values and standard deviations in the average values are pre-sented of each of the following cases. Referring to these additional figures, it is safe to say that enough confidence was gained that the conclusions to be made are believ-able.
Table 14. The AB model details.
Model details Explanation of the model details
Initialization
At the start of all the simulations, the number of agents and their state variables are:
1 Maintenance company: operating as usual
0 Workers
20 Customers: operating as usual
20 Machines: running
Inputs
All the parameters that were not varied between simulation runs and that were not changed within a simulation were:
Parameter Value
Base wear from maintenance 0.05
Delay in movement to workplaces 2
Delay in recruitment 7
How many percent the minimum and maximum degradation time differ from the average
0.1
How much cost of work time increases in a year 0.05
How often expected values regarding the states of the machines are updated 10 How often requested maintenance tasks are processed 2
How often salaries of the workers are paid 15
Initial average degradation time for machines 2*365
Initial cost of work time 3
Maximum revenue the machine can output 1
Minimum accepted degradation time for a machine 100
Minimum decimal precision in degradation rate iteration 100
Output ability decrease factor 1.05
Output of a worker on a time step 10
Payment time given for customers 30
Risk factor 1 000 000
Wear from delaying maintenance factor 0.8
Table 15. The actual simulations that were run with the model with the given input parameters (the ones that were varied, while others being constant).
Input parameters Explanation
Price for maintenance, time-based: from 0.2 to 2 with the increment of 0.2
The price for maintenance is set to time-based: that is, there is an X % margin the maintenance company is putting on top of the time cost of the maintenance task.
The time cost is defined to be the salary a maintenance worker has to be paid for the time he maintained a machine. The margin is varied from 20 % to 200 % with the increment of 20 % between different simulation runs.
Minimum accepted condition is the maintenance point in which all the customers want the maintenance tasks to be done. So, in an individual simulation, all the customers are having the same minimum accepted condition for their machines and the value is varied between simulations.
Simulation runs: 500 000 Replications per data point: 1000
Price for maintenance, value-based: from 0.05
The price for maintenance is set to value-based: that is, there is an X % share the maintenance company is taking away from the customers’ profits. The profits of the customers are defined to be the revenue in between the latest and the upcom-ing maintenance task subtracted by the latest maintenance cost. When the first maintenance task is conducted, the profit equals the revenue of the customer, as no previous maintenance costs have been realized. The share is varied from 5 % to 95 % with the increment of 10 % between different simulation runs.
Minimum accepted condition is the maintenance point in which all the customers want the maintenance tasks to be done.
Simulation runs: 500 000 Replications per data point: 1000
Pricing (price is
Error range in machine condition measurement determines how accurate estima-tions the maintenance company is able to get from inspecestima-tions. Error is defined to be a percentage point value (on the same scale as the machine condition) that the expected condition of a machine can differ from the actual condition to either lower or higher direction. Error range is varied between one to 50 percentage points with increment of one percentage point.
Minimum accepted condition is the maintenance point in which all the customers want the maintenance tasks to be done.
Simulation runs: 250 000 Replications per data point: 100
Pricing (price is
Error range in machine condition measurement determines how accurate estima-tions the maintenance company is able to get from inspecestima-tions. Error range is varied between one to 50 percentage points with increment of one percentage point.
Minimum accepted condition is the maintenance point in which all the customers want the maintenance tasks to be done.
Simulation runs: 250 000 Replications per data point: 100
4.1 Profitability when pricing is time-based
In the figures 12 and 13 we can see the effect of different time-based prices on the cumulative profits of the customers and the maintenance company while the custom-ers are having different maintenance points. From the customer’s point of view, the optimal maintenance point range is pretty clear, as the peak in cumulative profits is rather constant. However, some shift in the optimal point occurs as the price for maintenance is increased, and that also reduces the profitability in the optimal maintenance point, of course. In addition, if we analyze profitability in different maintenance points, profitability increases exponentially to the optimal maintenance point, from where it starts to fall faster than it rose till the optimal maintenance point.
That is, after the customers have raised the maintenance point requirement over the optimal point, the effect of that decision is bigger and more negative on the profitabil-ity than to having a lower maintenance point.
Figure 12. The effect of the price for maintenance (time-based) and the minimum ac-cepted condition for machines on the average cumulative profits for the customers.
From the point of view of the maintenance company in the same situation as above, the profitability behaves almost inversely. The best situation for the maintenance
company is to have the highest possible price, of course, but it is also desirable that the customers want to drive their machines till they break down. The profitability de-creases exponentially while increasing the maintenance point until the point (or a bit above) in which the customers had their optimal maintenance point. And from there on, the profitability increases again, but nowhere near as with the lower maintenance points.
Figure 13. The effect of the price for maintenance (time-based) and the minimum ac-cepted condition for machines on the average cumulative profits for the maintenance company.
4.2 Profitability when pricing is value-based
In the figures 14 and 15 the analysis perspective is the same as in the previous figures 12 and 13, but the pricing is set to value-based. This change has some fundamental effects on the system response. Beginning from the customer’s point of view, the change is not that evident, as the profitability curve behaves almost the same way as in time-based pricing. However, with the higher values of price and minimum accept-ed condition, the profitability starts to increase again after the slump in the worst maintenance point. Of course, profitability does not increase to acceptable levels, but
reveals a different system response compared to the situation with time-based pricing.
Overall, the optimal maintenance point can be easily located. It shifts to a bit lower level as the price is increased than it shifted when time-based price was increased.
Figure 14. The effect of the price for maintenance (value-based) and the minimum accepted condition for machines on the average cumulative profits for the customers.
The effect of changing pricing logic from time-based to value-based is more evident on the profitability of the maintenance company. With low prices the profitability curve is quite similar to the one with time-based pricing: it is not desirable to the maintenance company to operate in the optimal maintenance point for the customers.
But as the price is increased, it happens that the optimal maintenance point for the maintenance company starts to shift towards the optimal maintenance point for the customers. This is due to the following: a bigger price means a bigger share of the customers’ profits is provided for the maintenance company, meaning that it is de-sired for the maintenance company that the customers are as profitable as possible.
That is, it is a win-win situation for both parties to operate in the optimal maintenance point for the customer.
Figure 15. The effect of the price for maintenance (value-based) and the minimum accepted condition for machines on the average cumulative profits for the mainte-nance company.
4.3 Condition measurement error and profitability in time-based pricing