# Benefit Optimization of Short Food Supply Chains for Organic Products: A Simulation-Based Approach
## 4 Simulation-Based Multi-Objective Optimization of SFSC
### Research Methodology  
The general outline of our methodology is shown in Figure 3, and is described in detail below:  
* Statement of the problem: the proportion of delivery to different types of consumers can effectively increase the profits of local farmers;
* Objectives: supporting the decisions of local farmers in the delivery strategy using simulation modeling and an optimization module;
* Tools: computer simulation software, including the Arena environment with the optimization module;  
* Input variables:
* Number of sold products: \(n\)
* Product type: \(p_{i}\), \(i\in\{1,2,3,\ldots,n\}\)
* Prices for products: \(c_{i}\), \(i\in\{1,2,3,\ldots,n\}\)
* Delivery amount: \(d_{i}\) (kilograms per delivery for each \(p_{i}\)), \(i\in\{1,2,3,\ldots,n\}\)
* Number of destined markets: \(m\)
* Market type: \(t_{j}\), \(j\in\{1,2,3,\ldots,m\}\)
* Delivery quantities: \(q_{j}\) (for each market type \(t_{j}\)), \(j\in\{1,2,3,\ldots,m\}\)
* Distance from the market: \(h_{j},j\in\{1,2,3,\ldots,m\}\)
* Transport cost for 1 km: \(k\)
* Cost of unsold products: \(cu_{i}\), \(i\in\{1,2,3,\ldots,n\}\)
* Demand considering uncertainty (for each product type in each market in kilograms): \(u_{ij}\) (triangular distribution), \(i\in\{1,2,3,\ldots,n\}\)
* Control parameters:
* Delivery proportion: \(Pr_{j}\) (percent of delivery for each market type \(t_{j}\)) \(\sum_{j=1}^{m}Pr_{j}=\)100%, \(j\in\{1,2,3,\ldots,m\}\)
* Output variables:
* Number of sold products in each category: \(s_{i}\), \(i\in\{1,2,3,\ldots,n\}\)
* Number of unsold products in each category: \(us_{i}\), \(i\in\{1,2,3,\ldots,n\}\)
* Profit: \(f=\sum_{i=1}^{n}s_{i}\times c_{i}-\sum_{j=1}^{m}k\times h_{j}-\sum_{i=1}^{n}us_ {i}\times cu_{i}\), \(i\in\{1,\,2,\,3,\ldots,\,n\}\), \(j\in\{1,\,2,\,3,\ldots,m\}\) *  
Figure 2: A fragment of the analyzed model of short food supply chain in Arena software (Rockwell Software, version 14.0, Austin, TX, USA).  
Experiments: performed using discrete event simulation software to analyze the current values of variables with the established delivery proportion. Additionally, it calculates the values of output variables transferred to the optimization module;
* Optimization: the optimization module changes the control parameters, which include the delivery proportion to the different markets. For these new parameters, the simulation model calculates a new value for the criterion functions. In this way, the scope for potential optimal solutions is analyzed (Figure 3).  
To find an optimal delivery strategy, the simulation model calculates criterion functions, which can be the profit of the local farmer, the number of unsold products (economic factors), the shortest road route or usage of green transport (environmental factors), or number of persons employed in the transport of goods (social factor). In our case, we only considered economic factors.  
One local farmer from the West Pomeranian Voivodeship in Poland (SFSC presented in Figure 4) served as a test bench for the analysis.  
In the analyzed short food supply chain, a local farmer cells their products in three abovementioned markets: face-to-face, spatially proximal, and spatially extended markets. The farmer cultivates three main types of organic products and sells them in season (3 months) on the markets: tomatoes (sold for 3 months), apples (sold for 3 months), and potatoes (sold for 2 months).  
Figure 4: Analyzed short food supply chain: a local farmer from West Pomeranian Voivodeship.  
Figure 3: Practical methodology used to support decisions in the short food supply chain using simulation modeling and an optimization module.