# Market-Oriented Procurement Planning Leading to a Higher Service Level and Cost Optimization
## Appendix A Formulae of the Conceptual Model  
* Moving average: The simple moving average (SMA) is the non-weighted mean of the previous n data [42]. In the model, the cumulative moving average (CMA) is applied: \[\text{\it Forecast with CMA }=F_{(t+1)}=\frac{1}{n}\sum_{t=1}^{n}\text{\it item demand }(t)\] (1) _with \(n=\text{\it number of days};F_{(t+1)}=\text{\it demand forecast value at time }t+1\)._
* Linear regression: The regression method is usually applicable to a steady course of a time series or a stable trend [43]. It can be defined as follows where \"a\" is the slope, \(t_{\text{\it trend}}\) is the time since the trend demand pattern started, and \"b\" is the value at the time when the trend demand pattern was initiated: \[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\] (2)
* Exponential smoothing: The exponential smoothing method carries out an exponential weighting of the forecast errors to determine the forecast value for the next period [42]: \[\circ\] Exponential smoothing of the first order: based on the literature, the formula used is [43]: \[F_{(t+1)}=\alpha\ \times D_{t}\ +\ (1-\alpha)\times F_{(t)}.\] (3) \[\text{\it with }\ \alpha\ =\ \text{\it smoothing parameter}.\] \(\circ\) Exponential smoothing of the second order: based on the literature, the method developed by [PERSON] is used [42]: \[F_{(t+1)}=L_{(t)}\ +\ T_{(t)}\] (4) \[L_{(t)}=\alpha\ \times T_{t}\ +\ (1-\alpha)\times\left(L_{(t-1)}\ +\ T_{(t-1)}\right)\] (5) \[T_{(t)}=\beta\ \times\left(L_{(t)}-\ L_{(t-1)}\right)\ +\ (1-\beta)\times T_{(t-1)}\] (6) _with \(\text{L}_{(t)}=\text{\it smoothed value for }t;T_{(t)}\ =\text{\it trend estimation}\) for \(t\); \(\beta=\ \text{smoothing parameter for the trend estimation}\)._
* Exponential smoothing of the third order: based on the literature, the method developed by [PERSON] is used [43]: \[F_{(t+1)}=(L_{(t)}\ +\ T_{(t)})\times S_{(t+1-s)}\] (7) \[L_{(t)}=\alpha\times\frac{Y_{(t)}}{S_{(t-s)}}\ +\ (1-\alpha)\times\left(L_{(t-1)}\ +\ T_{(t-1)}\right)\] (8) \[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]0 (9) \[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]1 (10) \[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]2 \(\gamma=\text{\it smoothing parameter for trend estimation}\)._
* Croston Method: a method for sporadic demand patterns [42]: \[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]3 (11)\[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]4 (A12)  
\[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]5 (A13)  
with \(\mathrm{q}=\mathrm{periods}\ \sin\mathrm{ce}\) demand. Methods to measure and provide conclusions regarding the accuracy of the used forecast method [46]:  
\[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]6 (A14)  
\[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]7 (A15)  
\[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]8 (A16)  
_with_  
\(n=\) _number of days;_  
\(D_{(t)}=\) _real demand value at time \(t\)._  
\(F(t)=\) _demand forecast value at time \(t\)._  
The coefficient of variation (CV) is defined as follows [43]:  
\[F_{(t+1)}=a\times t_{\text{\it trend}}\ +\ b.\]9 (A17)  
with:  
\(\sigma(D)=\) standard deviation of demand (\(D\));  
\(D=\) arithmetic average of demand. Reorder Point method and its formulae applied in the conceptual model:  
\[\circ\]0 (A18)  
\[\circ\]1 \[\circ\]2 (A19)  
\[\circ\]3 (A20)  
\[\circ\]4 (A21)  
\[\circ\]5 (A22)  
with \(\overline{F_{(t)}}\) as the average demand forecast during the RT. \[\circ\]6 (A23) \[\circ\]7Calculation of the EOQ with backordering allowed [49]:  
\[\circ\]8  
with \(Q_{E}\) = classic EOQ; \(Q_{B}\) = factor when allowing backordering; \(A\) = annual demand (Units/Year); \(S\) = procurement cost per order (USD); \(C\) = cost per unit depending on the batch size (USD/Unit); I = inventory holding costs (I/Year); and \(\pi\) = backordering costs (USD/Unit).