## 4 Results
### Forrester Diagram and Mathematical Equations  
To create the Forrester diagram, the causal diagram was taken as a reference. The process performed to obtain package demand and the time required to comply with such demand are shown in Figure 6. The packages offered by the organization are four, and each one is constituted by different products and quantities.  
Figure 5: Causal diagram for the production process.  
The packaging process is activated by a production order subjected to the demand ordered by the final consumer. This production order indicates the necessary kilograms of the set of products for each package. When the order is launched, picking is performed where only the products required are taken to subsequently carry out the demand. All merchandise goes through the packaging area with a unit in kilograms to convert them to products between those that each product weighs according to their characteristics. After that, the packages go through an inspection, and, finally, to the conservation area to be distributed on time and form. It is important to highlight that any type of package conveys the same process.  
Package 1 is formed by noodles (400 g), spaghetti (400 g), elbow macaroni (400 g), rice (500 g), beans (1 kg), and canned tuna fish (280 g). Package 2 contains whole milk (2.1 L), fruit ring multigrain cereal (200 g), wheat cereal (150 g), and frosted corn flake cereal (200 g). Package 3 contains noodles (400 g), spaghetti (400 g), elbow macaroni (400 g), rice (500 g), beans (1 kg), canned tuna fish (280 g), coffee (50 g), and cooking oil (0.475 L). Lastly, Package 4 needs noodles (400 g), spaghetti (400 g), elbow macaroni (400 g), rice (1 kg), beans (1 kg), and canned tuna fish (420 g). To obtain the production order, the demand per weight of each item must be multiplied. In this manner, the total kilograms necessary to satisfy the order are known. Subsequently, the kilograms of each product are added, as well as adding the necessary kilograms of cold products. The order is only launched once a day.  
Mathematical equations. Jointly with the Forrester diagram, the values of each variable are inserted to make the mathematical equation by the parameter and variable interaction. A segment of equations is described by type (auxiliary level, inflow, outflow, as well as some important parameters).  
Level equations: Level equations are generated starting from the relationship and influence of the variables, parameters, and/or inflow on each one of the level variables. It should be made clear that each level variable and inflow are influenced by the increase in time (\(dt\)) established in the model:  
\[CW1\ (t+dt)=CW1\ (0)\int_{0}^{t}[Pi\ (t)]dt \tag{1}\]  
where:  
\(CW1=\) Conservation warehouse  
\(Pi=\) Packages inspected  
\[P\ (t+dt)=P\ (0)\int_{0}^{t}[CT\ (t)-Pf(t)]dt \tag{2}\]  
where:  
\(P=\) Packaging  
\(Ct=\) Capacity of tray in Kg  
\(Pf=\) Packages with food in Kg  
Figure 6: Forrester diagram of the packaging process.  
\[Pi\left(t+dt\right)=Pi\left(0\right)\int_{0}^{t}[P\left(t\right)-Pfi(t)]dt \tag{3}\]  
where:  
\(Pi\) = Package inspection  
\(P\) = Packages  
\(P\)_fi_ = Packages inspected  
Inflow and outflow equations: these flows of the level varieties (stock, conveyor, queue, oven) bring about information, in this case, the number of product kilograms to satisfy the order.  
\[Pick\left(0\right)=Init\ Pi\left(t\right)\text{, \  
(3) Electricity (light) = MXP 79.7157; (4) Sale price of Package_1 = MXP 212.52; (5) Cold product = 1.7 kg (the prices are in Mexican pesos (MXP)).