Ensayos a nivel de laboratorio para la elaboración de adhesivos

The model as described before, is implemented in Excel. The model constructed is new and can’t be

checked, verified, and validated by comparing it to an existing system. However, in order to increase validity and credibility of the model, we have used several techniques during construction of the model and to verify the model, as adduced by Law (2015).

Prior to the construction of the model, we have visited a supplier of Thales which is focused on the development of AM. During this visit, we spoke with AM experts specialised in the machine capabilities and material properties. They were willing to give a lot of information about these subjects. Additionally, they gave their opinion about the use of AM in the future and the cost development of AM. Besides, for

this research we went to ‘Formnext’, an international exhibition in Frankfurt on the next generation of

manufacturing technologies mainly focussed on AM. During the exhibition, we spoke experts out of all fields of AM. From machine builders, to consultants who advice companies how to use AM in an effective way. We discussed subjects related to the development of the costs of AM, the difference in design costs between CM and AM, and production lead times associated with AM processes.

With all this information and knowledge gathered in different ways we started to develop a model. During the development period, we have consulted people from different disciplines within Thales, about their opinion on several points which are of importance regarding the model.

Finally, we presented the model to people with knowledge of additive manufacturing as well as knowledge of the parts produced for Thales. They concluded, the model seems to be valid given the

assumptions. Additionally, we have consulted Thales’s supplier who is working on the development of

AM, to give their opinion about the model. They concluded, the model seems to be valid as well. Besides these qualitative techniques, we have constructed a spreadsheet in which we can simulate the number of one-off parts demanded as discrete events. With the use of a random number generator between 0 and 1, and the probability that a specific number of parts demand will occur we simulated the number of parts demanded during every period of the life cycle. The number of parts demand during each period is simulated as follows:

∑ (𝜆𝑁)𝑞 𝑞! ∗ 𝑒−𝜆𝑁 𝑥 𝑞=0 > 𝑟𝑎𝑛𝑑𝑜𝑚 𝑛𝑢𝑚𝑏𝑒𝑟 ≤ (1 − ∑ (𝜆𝑁)𝑞 𝑞! ∗ 𝑒−𝜆𝑁 ∞ 𝑞=𝑥+1 )

The value of x, for which this holds is the expected number of parts demanded during that period. In addition, all applicable costs subject to the specific number of parts demanded can be easily calculated. Besides, based on the simulation we can simulate several life cycles in order to determine all kind of results with respect to the average number of parts in inventory, the average period in which AM is used for the first time in case it is applied. Therefore, we will use this simulation in Chapter 7, where we make an analysis of the model.

In order to verify the model, we have cut the model into different components. First we have analysed the production costs during the life cycles. Since we assume, demand follows a Poisson distribution we can calculate the expected demand during the life cycle. By means of a simulation model, we can determine the average period in which CM is replaced for AM. Based on these numbers, we are able to determine the average production costs. Hereafter, we included the preparation costs of the two methods and compared the results of the model, with those of the simulation. Thirdly, we added the costs of special tooling. Finally, we added the costs of inventory together with the costs as a result of

downtime. Since these two cost components are dependent on each other, we can’t check them

separately.

We will run 10.000 life cycles for this simulation for different values of different parameters. In this way, we are able to check different components of the model separately, as adduced by Law (2015). We start with input values, causing that only CM will be used during the entire life cycle. Hereafter, we adjust the input in such a way only AM will be used. Finally, we will run a simulation in which AM might start at a random moment during the life cycle. The settings for the simulation are based on average values of parts within Thales, as described in Appendix 3. If we compare the costs of our simulation runs, with those of the costs according the model we find no differences greater than 0,48%, see Appendix 8. Based on this difference, we conclude that the model is implemented properly in excel and it gives the same results as the SDP model.

6.7

Conclusion

In this this chapter, we constructed a model which is able to determine the optimal period to start with AM as manufacturing method. Additionally, the model determines the optimal number of parts which should be produced to put in inventory, in order to minimize costs. The total life cycle of a part is divided into multiple periods. At the start of every period, decisions have to made at the beginning of every period. The method to solve such an optimization problem is stochastic dynamic programming, which is used for the construction of the model. The cost factors taken into account are:

 Production costs  Downtime costs

 Preparation costs of the manufacturing methods  Costs associated with inventory

 Salvage value of inventory

The model is validated using experts in the field of additive manufacturing. Besides, with the use of a discrete simulation model, we have verified the working of the model.