# Market-Oriented Procurement Planning Leading to a Higher Service Level and Cost Optimization
## Appendix B Formulae of Key Performance Indicators (KPIs)  
Parameters referring to a specific scenario are those that define the scenario itself and are exogenous variables:  
* Cumulated Demand (products): This represents the cumulated demand to be satisfied in a certain period: \[\text{{\it Cumulated Demand}}\ (\text{{\it products}})\ =\sum_{t=1}^{n}\text{{\it Demand at time period}}\ t.\] (11)  
System efficiency indicators refer to the efficiency parameters that are needed to reach the required satisfaction rate and service level:  
* MAD of the forecast (products): This is the sum of the absolute values that come from the difference between the real and forecast demands for the simulation periods [42]. This sums the values of the forecast errors and divides the sum by the number of periods. MAD is a useful method to show the forecast error in the same units of the time series data [42]. In the model, the weekly production order is leveled based on a monthly forecast and used to place production orders: \[\text{{\it MAD forecast production order}}\ (\text{{\it products}})=\frac{\sum_{t=1}^{n} \left|D\ (t)-F\ (t)\right|}{\sum_{t=1}^{n}t}\] (12)
* Average WIP stock (products): This is the average stock after production until the end-customer. Inventory is also one of the most important drivers in a distribution network [51]. Inventory always involves storage costs; therefore, stock levels should be minimized while assuring the service level that was established for the customers in the strategy of the company: \[\varnothing\ \text{Average {\it WIP stock}}\ (\text{{\it products}})=\frac{\sum_{t=1}^{n} \text{{\it Stock at the warehouses at time}}\ t}{\sum_{t=1}^{n}t}\] (13)
* Average stock at Tier 1 producer and at original equipment manufacturer (OEM) producer (products): This applies the same formula as for the average WIP stock when considering only the specific warehouses of Tier 1 or OEM producers. * Utilization rate of employees (%): This is the percentage of the nominal capacity of the employees that is used to perform the warehouse activities. Utilization is another important KPI. It definesthe rate of capacity that is currently being used [51]. In this case, it defines the capacity utilization of those employees that perform the warehouse activities: \[ \begin{array}{c}\text{{Utilization rate of employees }}(\%)=\frac{\sum_{t=1}^{n}\text{ Capacity used}}{\sum_{t=1}^{n}\text{ Nonunital Capacity}}\times 100\%\\ =\frac{\sum_{t=1}^{n}\text{Capacity used}}{\sum_{t=1}^{n}\text{Capacity per employee }*\text{Number of employees}}\times 100\%\end{array} \] (100)
* On-time delivery (OTD) (%): This represents the percentage of the quantity delivered on time for a certain period. It is a quantity-oriented KPI that describes the customer demand percentages that could be satisfied directly from the stock in a certain period [42]. The difference with the service level (%) relapse is in consideration of the single product and not on the whole demand to meet in each week: \[\text{OTD }(\%)=\frac{\sum_{t=1}^{n}\text{Products delivered on time}}{\sum_{t=1}^{n}\text{Total products ordered}}\times 100\%.\] (101)
* Service level (%): This represents the percentage of weeks in which the demand is satisfied. It is the probability of demand fulfillment in a certain period with the stock in the warehouses. It also considers the accumulated backlog. Therefore, it is a quantity- and time-oriented KPI [42]. It represents the percentage of weeks in which the clients were fully served with all the products they ordered. It is considered as an unmet demand in those cases when the delivered quantity to the customers was not sufficient to supply the customer demand for the current period and the customer's backlog from previous weeks: \[\text{{Service Level }}(\%)=\frac{\sum_{t=1}^{n}\text{Weeks }\text{without product backlog}}{\sum_{t=1}^{n}t}\times 100\%.\] (102)
* Average procurement quantity (products): This represents the average quantity ordered along a certain period: \[