# An Integrated Model for the Harvest, Storage, and Distribution of Perishable Crops
## 2 Literature Review  
The reduction in total operating cost achieved by coordination of production and distribution planning can range from 3% to 20%, as reported in the pioneristic work of [PERSON] and [PERSON] [8]. The integration of production and distribution activities can bring innumerable advantages, such as reduction in delivery time, increase in product quality for the benefit of customer satisfaction, improvement in the overall performance of the food supply chain [9]. The study of [PERSON] et al. [10] highlights the economic advantages in using an integrated approach compared to a decoupled one. Moreover, the coordination of the different steps of the supply chain has a very positive environmental impact, limiting pollution [11] and food waste [12]. As reported in [13; 14], a very large part of food waste is currently due to inefficiencies in the fresh food supply chain. The coordination of production, storage and distribution activities is much more complex and critical when the supply chain deals with perishable products. Perishability and shelf-life are among the main issues for achieving sustainability and efficiency in food logistiscs [15]. According to [PERSON] et al. [16], a good is perishable if at least one of the following three conditions takes place, during a well defined time horizon: (i) its physical status considerably worsens, (ii) the value perceived by customers decreases, (iii) there is a risk of possible future reduced functionality according to some authority. Products such as fruits, vegetables, and flowers are characterized by continuous deterioration [17], which influences the profits achievable from their sale to customers. Basically, the selling price is not constant, but depends on the quality, which usually begins to decline immediately after production, or harvesting in the case of agricultural products [18]. In the case of fresh fruits and vegetables, the expiry date is not printed, then their shelf-life is defined loose because it can be only estimated based on some information (e.g., physical status, date of harvesting) [10]. For all these reasons, a branch of research which concerns the inventory management with deteriorating items has developed over the years. The work of [PERSON] [19] was pioneering, while for some quite recent studies, see [20; 21; 22]. In the following, we analyize the most relevant contributions in the literature, where the decisions about production, inventory, and routing of perishable products are optimized. We point out that more detailed information about the production-inventory-routing problems can be found in some comprehensive reviews, see [5; 23; 24]. [PERSON] et al. [25] propose a mixed integer linear programming (MILP) model for planning the production and distribution activities in a multi-level food supply chain. The total costs are minimized, namely production, transportation, storage, disposal, and cooling costs for transportation equipment and storage facilities. The authors mainly focus on product quality, whose decay is strongly related to the temperature along the chain. In particular,they include linear or exponential product quality degradation models in their MILP. The aim is to find a sort of trade-off between quality preservation costs and costs for waste. Since the proposed modelling approach refers to a generic food supply chain configuration, it can succesfully be applied in several food industries. [PERSON] et al. (2018) consider a two-echelon supply chain, where a single supplier distributes a single product to a set of retailers, using a fleet of homogeneous vehicles. They propose a MILP model, which supports the decision-making of the supplier about the production plan, the customers' delivery time, the routing in each period of the planning horizon. The vehicles loading costs are explicitly taken into account. Considering the computational complexity of the problem, the authors propose a two-phase algorithm to solve it efficiently.