# A Study on the Vehicle Routing Planning Method for Fresh Food Distribution
## 2 Problem Description and Model Construction
### Problem Description  
On the O2O e-commerce platform, fresh products account for over 50% of sales. Because of the time constraints in the delivery of fresh products, as well as customers' requirements for quality and rapid delivery, it is common to establish a front warehouse to deliver to customers in demand within the coverage range. A single front warehouse covers an area within a radius of five kilometers. Compared to traditional distribution models, it directly delivers from the front warehouse to consumers, eliminating preservation and sales processes of intermediate wholesalers, supermarkets, and markets, achieving rapid delivery of fresh products and ensuring a positive shopping experience for customers. Currently, leading warehouses are mostly distributed in cities. By continuously establishing leading warehouses to cover a wider range of consumers, cold chain logistics costs can be effectively shared. A supply chain model of leading warehouses is shown in Figure 1. This article mainly studies how to maximize the benefits of logistics distribution through a two-level planning front warehouse location scheme and terminal path planning from the front warehouse to the point of the customer. Given the distribution vehicle information, volume, distribution and demand of customer service points, time windows, and other information, in addition to not exceeding the volume constraints of the front warehouse and load of the cold chain distribution vehicle, location selection is based on the distribution and demand of customer points. Distribution vehicles can service multiple customer points from the front warehouse, with each customer point being served by only one vehicle and only once. The bi-level programming mathematical model is constructed as follows. Upper model. In the cold chain logistics network for distributing fresh agricultural products, the location and quantity of the front warehouses are determined based on the degree of customer dispersion and the distribution of fresh agricultural products from the primary network node to the secondary network node. A reasonable location can achieve full coverage of nearby demand points and greatly improve vehicle delivery efficiency. The upper objective function includes the cost of building a front warehouse, vehicle transportation costs, refrigeration costs, cargo damage costs and time window penalty costs. The objective is to minimize the total cost of the system. The mathematical model is shown in Equation (8). \[ \begin{array}{l}\min Z=\sum\limits_{h\in H}\sum\limits_{i\in I}Y_{h}(C_{h}+T _{h})+\sum\limits_{c\in R\in h}C_{ch}d_{ch}Y_{h}+\sum\limits_{k\in K}\sum \limits_{c\in E}C_{rk1}t_{ch}x_{k}+\\ \sum\limits_{k\in K}C_{ik1}x_{ch}^{k}+\theta_{1}\omega_{1}\sum\limits_{k\in K} \sum\limits_{h\in H}x_{k1}g_{ch}(1-e^{-\delta t_{ch}})+\theta_{2}\omega_{h} \sum\limits_{h\in I}\sum\limits_{i\in I}x_{k2}g_{hi}(1-e^{-\delta t_{hi}})\\ +\sum\limits_{k\in K}\sum\limits_{l\in I}\sum\limits_{l\in I}c_{lk2}x_{ij}^{k}+ \sum\limits_{k\in K}\sum\limits_{ij\in H\cup L}C_{p}d_{ij}x_{ij}^{k}+\sum \limits_{i\in I}\beta_{1}\max\{ET_{i}-t_{t},0\}+\sum\limits_{i\in I}\beta_{1} \max\{t_{t}-LT_{i},0\}\end{array}  \tag{8}\]