Subclass W 1 model validation

Input parameters of demand are generated using an underlying regression equation (equation (4.3)), defined and validated in §4.3.3 to meet all the assumptions of multiple regression and be a good fit of the data. Inflows are calculated by a size-mix allocation calculation which is shown in a previous study to not be significantly different from the Retailer’s calculated inflows [40]. The weighting parameter for dynamic size profile adjustments, γ = 1, are used to ensure no adjustment to the Retailer’s calculated size profile occurs and the simulation model is reflective of a static size profile system. Using formula (4.5), at least one simulation replication is required for Subclass W1. Given the availability of computer resources, the proposed model is replicated 10 times to increase confidence in the output and the average is reported on.

Reliability of the proposed simulation model is quantified by considering the ICC values, obtained via IBM SPSS 25 [16]; presented in Table 4.16 where each group and ICC measure, apart from the week single ICC (0.828); are excellent (> 0.9). The reliability of week single ICC measure is still considered good (> 0.8) and the average consistency of actual week sales and simulated week sales are excellent.

Group Single measure ICC Average measure ICC Cronbach’s Alpha (α) Week 0.828 0.906 0.904 Store 0.992 0.996 0.997 Size 0.957 0.978 0.991

Table 4.16: Groups of ICC values for Subclass W1sales generated via the proposed simulation model, compared to the Retailer’s real sales. A value of γ = 1 was used.

Given the reported ICC values and the high measures of internal consistency, the proposed simulation model when generating sales for Subclass W1are considered a reliable representation of the real system. Validity of the system must be determined, before the proposed simulation model may be used to analyse the effect of dynamic size profile adjustments.

Total sales generated by the proposed simulation model for W1 amount to 154 068.7 units, on average, with a standard deviation of 119.2 units. This value is 5.6% higher than the real systems total sales (145 904), as recorded by the Retailer and 0.31% less than the average total sales of the validated existing model (154 546.3). As the proposed simulation model total sales are within the expected values of total sales, the proposed model is considered valid and reliable with regards to objective of this study and it is concluded the effect of dynamic size profile adjustments on total sales may be analysed with confidence for Subclass W1.

Graphical comparison of data

This section presents a graphical comparison between the real system total sales, as recorded by the Retailer; and total sales generated by the proposed simulation model for Subclass W1. Scatter plots present a comparison between system sales, indicating the strength of correlation for total sales grouped by weeks, stores and sizes. Figure 4.11 presents total weekly sales as recorded by the Retailer and as generated by the simulation model for W1. There is some noticeable variation between the two systems total sales, with points lying on either side of the line of best fit. The value of R2 is 0.6826, indicating that the relationship is not too strong, but is still acceptable. Points above the line indicate an overestimation and points below, an underestimation in total sales. An outlier indicated at point (B), is recorded for the first week

4.4. Black-box validation 51 0 2 000 4 000 6 000 8 000 10 000 12 000 14 000 0 5 000 10 000 15 000 B

Real system week total

Sim ulation mo del w eek total

Figure 4.11: Scatter plot of correlation between total real system week sales and total simulated week sales for Subclass W1. The simulation was performed using γ = 1.

of July. Demand in July was underestimated by regression equation (4.3), which as reported in the scatter plot results in an underestimation of sales.

0 200 400 600 800 1 000 0 200 400 600 800 1 000 1 200 C

Real system store total

Sim ulation mo del store total

Figure 4.12: Scatter plot of correlation between total real system store sales and total simulated store sales for Subclass W1. The simulation was performed using γ = 1.

Figure 4.12 presents the relationship between total sales on a store level for the two systems under consideration (real system and proposed model). The majority of points are clustered towards the lower left-hand corner, simply indicating that the majority of stores sell under 600 units of W1 for the season, 2014. The correlation between systems is strong, indicated by the closeness of points to the line of best fit and an R2 = 0.9872. An outlier at point (C), indicated an overestimation of sales for the store (Store 338). Actual sales recorded by the Retailer at this store are equivalent to 935 units for the season, which is overestimates by approximately 164 units in the simulation model.

Total sales in Figure 4.13 indicate a very good fit of sales for each size. The value of R2 = 0.9979, indicates an almost perfect fit of the simulated sales to the actual sales. Total sales are overestimated because demand was overestimated by regression equation (4.3). On average the

14 00016 00018 00020 00022 00024 00026 00028 00030 000 20 000

25 000 30 000

Real system size total

Sim ulation mo del size total

Figure 4.13: Scatter plot of correlation between total real system size sales and total simulated size sales for Subclass W1. The simulation was performed using γ = 1.

size sales generated by the simulation model are about 7% higher than actual size sales recorded by the Retailer for 2014.

Total sales generated by the proposed simulation model have a relatively strong correlation with the real system total sales for weeks, and an excellent correlation for store and size sales. Furthermore, total sales for 2014 are as expected and it is concluded that the proposed model is accepted as valid and reliable, thus completing black-box validation for Subclass W1.