## 4 Manufacturing Process Case Study
### Key Performance Indicators (KPIs) for the Case Study  
The main reasons for organizations to undertake activities is to save money, increase profit, and influence other important factors, such as quality, delivery time, and delivery reliability, which are essential for competitiveness [17]. The results will be quantitative, allowing for the evaluation of the response according to the key performance indicators of defining parameters of a specific scenario, process efficiency indicators, product indicators, and economic parameters. Parameters referring to a specific scenario are those that define the scenario itself, and they are exogenous variables:  
* Cumulated demand (tons): this represents the cumulated demand to be satisfied in a certain period: \[\text{{{Cumulated Demand} }(tons)}\ =\sum_{t=1}^{n}\text{{Demand at time period}},\] (1)
* Information availability (% information needed): this represents the information received of the total information needed to manufacture the production orders in a certain period: \[\text{{{Information availability} }(\%\ \text{information needed})}\ =\frac{{{Information\ available }(tons)}}{{{Information\ needed}(tons)}},\] (2)
* Material procurement reliability (% material needed): this represents the available material input of the total of material input required to produce the orders planned in a certain period: \[\text{{{Material availability} }(\%\ \text{{{material\ needed}})}\ =\frac{{{Material\ available }(tons)}}{{{Material\ required}(tons)}}},\] (3)
* Energy availability (% energy needed): this represents the available energy input of the total of energy input required to produce the orders planned in a certain period: \[\text{{{Energy\ availability} }(\%\ \text{{{energy\ needed}})}\ =\frac{{{Energy\ available }(tons)}}{{{Energy\ required}(tons)}}},\] (4)
* Capital equipment (% capital equipment needed): this represents the available capital equipment of the total of capital equipment required to produce the orders planned in a certain period: \[\text{{{Personnel\ Availability} }(\%\ \text{{{capital\ equipment\ needed})}}\ =\frac{{{Capital\ equipment\ available }(tons)}}{{{Capital\ equipment\ required}(tons)}}},\] (5)
* Personnel availability (products): this represents the available staff of the total of human resources required to produce the orders planned in a certain period: \[\text{{{Personnel\ Availability} }(\%\ \text{{{personnel\ needed})}}\ =\frac{{{ Personal\ available }(tons)}}{{{Personnel\ required}(tons)}}},\] (6)  
Process efficiency indicators refer to the efficiency parameters that are needed to reach the required satisfaction rate and service level:  
* OEE (overall equipment effectiveness): This is a well-known measurement method that combines availability, performance, and quality for the evaluation of equipment effectiveness in the manufacturing industry [34]. The OEE index machine stands in comparison with an ideal machine that always runs at full speed and capacity, while at the same time producing good quality products [25]. Although the data of overall effectiveness of equipment seem very simple, extracting useful information from a series of calculations is an important and difficult task [35,36]. \[OEE=Availability\times Performance\ \times\ Quality, \tag{7}\]
* The next three rates are used for both the manufacturing system and process step:Availability factor: In detail, the availability factor measures the time loss due to breakdowns, set-up, adjustment, and other stoppages [19]. It is traditionally calculated using [PERSON]'s [37] formula as shown below [34]. However, in this paper, it is calculated as a multiplication of the areas availabilities. \[\varnothing\;\text{Availability}=\frac{\textit{Net Available Time}-\textit{ Downtime Losses}}{\textit{Net Available Time}}\;\;\times 100\%, \tag{8}\]  
Performance rate: This takes into account \"speed loss\". Reasons for this can be substandard materials, operator inefficiency, and job conditions.