## 4 Results
### Current Model Simulation  
Based on the variables determined for the model and causal diagram, the dynamics simulation model was formulated by using Stella(r) Architect software. The model was structured based on the mathematical equations used to calculate the different variable values. The considerations taken into account for the designed model were as follows: wholesale demand (kg) when less or equal to 1300 kg; that is, demand less than or equal to the capacity in kilograms of the Ford Transit vehicle. The demand for wholesale is up to 8000 kg; that is, the C2 truck capacity is considered in kilograms. Under these considerations, a package needed to be specified as a container with the following measurements: 0.60 m (length), 0.32 m (width) and 0.40 cm (height). The different products are then placed inside and delivered to the customers. Due to the dimensions of the container, the space within the transportation vehicle units is restricted: the possible volume to be transported is 0.0768 m\({}^{3}\). The base model is structured in a logical way, representing the real structure of the system under study (the distribution process), consisting of loading activities, transporting the product to customers, unloading and delivering the product to customers. Figure 3 shows the varying wholesale demand using the Ford Transit vehicle. Figure 3: Base model in Stella® Architect. TC = Transit client; T = Transit cargo vehicle. Figure 2: Causal loop distribution process diagram under study. In the model for the current scenario, a single load, route and unloading is considered, and the products are delivered to only one customer. The model considers delivery to several customers on the same route: it may carry out distribution to one, two or three customers. Product loading is performed only once when all the goods to be delivered to all the customers are loaded. Moreover, the distance traveled in the routes to reach each location is considered, as well as the unloading maneuvers that are conducted individually. Figure 4 shows the inherent wholesale delivery costs. The costs considered in goods distribution, including the truck driver's salary, vehicle maintenance, tire wearing, diesel consumption and tolls in a given case, are all considered. These costs are added to obtain the total distribution cost. The proposed model is based on variables and parameters, for which different equations were required. The determination of the type of variables was also necessary according to the symbols suggested in [11]; that is, level, auxiliary, flow or parameter variables. Below is a summary of the variables based on their category:  
**Level:**  
\[WiTl(t)=WiTl\;(0)+\int_{0}^{t}[Wmlf(t)-WmOf\;(t)]dt \tag{1}\]  
where \(WiTl\) = wholesale items, total load; \(WmIf\) = wholesale meat, input flow; \(WmOf\) = wholesale meat, output flow. \[R1 LT(t)=R1 LT(0)+\int_{0}^{t}[R1 WmIf(t)\;R2 WmOf\;(t)]dt \tag{2}\]  
where \(R1 LT\) = Route 1, load transport; \(R1 WmIf\) = Route 1, wholesale meat input flow; \(R2 WmOf\) = Route 2, wholesale meat output flow. \[R1 LTd(t)=R1 Ltd(0)+\int_{0}^{t}[R1 WmfdOf(t)]dt \tag{3}\]  
where \(R1 LTd\) = Route 1, load, transport deliveries; \(R1 WmfdOf\) = Route 1, wholesale meat, final delivery output flow. **Auxiliary:**  
\[Tt(t)=Ltpe\;(t)\times D(t) \tag{4}\]  
Figure 4: Wholesale distribution costs structure in the Transit vehicle. TC = Transit client; TWS = Transit wholesale; T = Transit cargo vehicle. where \(Tt=\) transit time; \(Ltpe=\) loading time per employee; \(D=\) demand. \[Ct\ (t)=(C1d/TVs) \tag{5}\]  
where \(Ct=\) cooking time (time during which wholesale products remain in the Transit vehicle); \(C1d=C1\) distance; \(TVs=\) Transit vehicle speed. \[WmC\ (t)=[(WmC+TwC+DC+S+TbC)\times(LDgt)\times(Dl)]\ TTnt \tag{6}\]  
where \(WmC=\) wholesale maintenance cost; \(TwC=\) tire wearing cost; \(DC=\) diesel cost; \(S=\) salary; \(TbC=\) toll cost; \(LDgt=\) loading time; \(DI=\) deliveries; \(TTnt=\) Transit truck number of trips.