###### Abstract
The same authors suggest considering new models that involve more than one factory, routing finished products to distribution centers or retailers, and scheduling milk collection time. Using the Cascaded Deep Learning model, the authors proposed a mathematical model of mixed integer and bi-objective programming for short life cycle products, whose goal is to minimize transport costs by modeling and analyzing the network path in three levels (supplier, manufacturer, and distribution center and retailer) and intuitively finding the minimum cost path [10]. Studies highlight artificial intelligence as a key tool for optimization. The Polar Fox Optimization Algorithm (PFA), inspired by the hunting behavior of polar foxes, enhances search space exploration with fast convergence and fewer parameter adjustments, excelling in engineering challenges [11]. In aquaculture, integrating the Adaptive Artificial Multiple Intelligence System (AAMIS) with the Design of Experiments (DOE) optimizes growth, costs, and environmental impact in Nile tilapia production [12]. Another research presented a mixed integer programming model to minimize the total CO\({}_{2}\) emissions associated with milk collection vehicle routes. It was based on the total fuel consumption rate, using the load-dependent emission factor and heterogeneous fleet [13]. In a research work involving the dairy supply chain, they applied multi-objective modeling to maximize profits from three levels satisfying the environmental, economic, and social criteria defined in terms of costs. Environmental costs are associated with effluents generated in the production of dairy and emissions of CO2 due to energy consumption and the transportation of raw materials and products, and social costs are related to employees hired to perform activities [14]. Other authors proposed a mixed integer multi-objective mathematical model to maximize the total value of the supply chain, minimize greenhouse gas emissions, and minimize resource consumption. The study was based on a real case of a dairy plant in Iran, aiming to solve issues in production distribution and consider environmental problems. Due to the complexity of the problem, the CPLEX solver did not solve the set of instances within reasonable time. Then, they proposed a heuristic mixing Genetic Algorithms and Fuzzy Self-Learning named Fuzzy Self-Learning NSGA-II (FSL-NSGA-II) [15]. A study examined a case in the dairy supply chain, aiming to maximize total profit by reducing waste, meeting service levels, and optimizing inventory, while balancing production and distribution, integrating a MILP model for production and inventory decisions with Monte Carlo simulation to assess demand uncertainty [16]. The recent review examines the challenges of the dairy supply chain and explores how artificial intelligence addresses issues such as demand forecasting, logistics optimization, and inventory management. Although the study discusses statistical and heuristic techniques applied to AI, it does not mention APS or report any specific studies on the middle-mile in the analyzed literature [17]. In previous studies involving the dairy production chain, the focus of optimization on costs and financial impacts predominates and, in some cases, includes environmental issues. Research efforts typically address situations that seek to improve performance between milk production sites and factories or between factories and retail, allowing for the observation of a gap in addressing challenges between factories and distribution centers, which are essential to business logistics. To carry out this research, we made several technical visits to milk processing industries, where it became evident that planning and optimizing the dairy production chain presents itself as a challenging task. What drew our attention were the high perishable products, precedence relations between products, processing times, and product release. Processing often occurs in factories distant from each other, and semi-finished products are transported between them.