Execution of experiments

In this part the execution of the 12 experiments takes place. First, the model is set according t the requirements of the tests and second, the simulations are performed.

 Model Set up

In order to execute the experimental design on the verified and validated model, this section first is essential to discuss the simulation set up. This refers to defining the warm up time, the length of the simulation and the number of replications for each scenario that has been designed.

As it is already mentioned, there is a warm up time for every scenario that equals to one year. For all scenarios, the simulation period is from 1 January 2013 to 1 January 2015. Hence, with a warm up time of 12 months, the results depict what occurs during January 2014 and January 2015. Thus, the length of the simulation is two years: from 2013 to 2015.

Regarding how many replications are needed in order to gain an outcome that is reliable enough, too few simulation runs can cause unreliable results but too many runs cause waste of time. Due to the initial tests of the model where the model was tested to estimate a sufficient number of replications, it was decided that each scenario will run for 50 replications. Moreover, in order to be certain that the number of replications is correct, one scenario was performed first and used to decide on how many runs are needed in order to get a convergent average and at the same time how long it takes. The scenario that was run for this reason was Scenario 5 that regards the current policy with an IRI of one month for a random product. For this purpose, a random product was selected from the product list for this random scenario. Then, this scenario was executed for 50 replications. The KPI of finished inventories was exported for all the 50 replications. Regarding the plot above, for every replication out of the 50 replications in total, the average inventory value for the random product is calculated.

Figure 43: Average inventory values for the random product

600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 0 10 20 30 40 50 60 A ve rag e In ve n to ry v al u e

Number of replications from 1 to 50

Annual inventory value for 50 replications for one random product for one random scenario

89 In figure 43 the x axis is the number of replications counting from the 1st replication to the 50th replication performed. The y axis shows the annual inventory value of the product. It can be observed that the average inventory value of this product varies very little among the 50 replications and it the average of 50 replications seems sufficient. However, this is not a scientific proof of defining the sufficient number of replications.

Moreover, It has been determined that 50 replications of the simulation model results in an acceptable 95% confidence interval: After performing a set of replications, the average value for a KPI can be determined as well as the accompanying standard deviation within a 95% confidence interval (Verbraeck, 2010). The purpose of a confidence interval is to estimate an unknown population parameter with an indication of how accurate the estimate is and of how confident we are the result is correct. The confidence interval μ around the average outcome is determined using the following equation:

.

In this equation, x is the expectation of the outcome and h is the half width value of the confidence interval. The lower the value for h, the higher the confidence of the outcome is. When 𝑥𝑗 is the result of the j-th replication, the values for x and 𝑠2 for x and x are given by the following equations:

The half width h provides the range in which the outcomes vary from . H can be determined using the following equations:

In order to determine the confidence interval for the created simulation model, μ is being determined using the aforementioned formulas along with excel formulas. Initially, 50 replications are being performed. With high certainty (95%) the result range can be determined in the following table. Statistics Mean 1849,377 Standard deviation 14,642 Sample size 50 Alpha 0,05 Confidence interval 4,058 Upper limit 1853,435 Lower limit 1845,319

There is a 95% chance that the true mean is between 1845,319 and 1853,435

Tabel 11: Calculating the confidence interval

Based on the results of the table, it can be concluded that there is a 95% chance that the true mean is between 1845,319 and 1853,435. Hence, based on the aforementioned, the amount of 50 replications is sufficient to reach an acceptable range of the 95% confidence interval.

90 After the model was set, the simulations took place. Each scenario ran for approximately 45 to 55 minutes. The product list, as mentioned, contains 57 products, thus, the simulation for each run can be considered as quite fast. After having executed all the experiments, the author proceeded in exporting the relevant KPIs for obtaining the results and for being able to analyze them afterwards. The KPIs that are relevant for the sake of this analysis are two: The first one is the final inventory which in S3N can be found in the “Inventory turnover” KPI category under the name “Inventory final product”. This KPI depicts for all 57 ISBNs their final inventory status during one year. The second KPI that is relevant for the analysis belongs to the “Service Level” KPI category and is named “% Delivered on time versus Requested” and expresses the rate of actual sales that were delivered on time to the initial demand that was requested from the customer.