# An Integrated Model for the Harvest, Storage, and Distribution of Perishable Crops
## 1 Introduction  
In the coming years, an increase in global food demand is expected, due to the growth in the world population. This trend has been going on for several decades. Fresh fruit and vegetables are and will be among the most demanded products also because their consumption has several beneficial effects on human health [1, 2]. Therefore, one of today most significant challenges concerns the design and management of efficient fresh-produce supply chains, which can effectively face the variability of demand and prices, the perishable nature of the products, the complexity of the logistic systems [3]. In recent decades, globalization has forced companies all over the world to rethink market strategies in a sustainable and collaborative way, in order to contain costs and offer a higher quality product to customers, who are increasingly demanding and knowledgeable [4]. While in the past there was a tendency to locally and sequentially optimize the various phases of the supply chain, today we are moving towards integrated approaches, which reduce lead times and offer quicker reactions to the frequent market changes [5].  
Aware of this global trend, in this paper we address the integrated and collaborative harvesting inventory distribution problem (HIDP) with perishable products. It belongs to the class of the production-inventory-routing problems, which aim to jointly optimize production, inventory, distribution, and routing decisions. In the most classic configuration, such a problem involves a supplier, who produces a commodity and replenishes a set of customers through the use of a fleet of vehicles, within a well defined time horizon. Then, the most common decisions concern: when and how much to produce, the inventory level at the supplier and/or at each customer, when and how much to deliver, which vehicle routes to use [6, 7].  
Our contribution can be summarized as follows:we propose an optimization model to support in an integrated way an agricultural company in the harvesting, storage, and distribution decisions. The model can be used at the tactical level to define the most profitable configuration of the main operating parameters;
* we propose an optimization model to support horizontal collaboration, in terms of distribution activities, between two or more heterogeneous agri-companies, which share part of their customers. The model can increase profit;
* we propose a heuristic framework which can deal with the two proposed optimization models and invite day-by-day to collaboration, only when profitable for the suppliers.  
The remainder of this paper is organized as follows. Section 2 provides a review of the main contributions in the literature on the use of mathematical models which integrate production and distribution activities in the case of perishable products. In Section 3, two mathematical models are introduced and explained to support in an integrated and collaborative way the decision-making of agri-companies, which deal with harvesting, storage, and distribution activities. In Section 4, we describe our computational experience on a case study and some useful managerial insights. Possible future developments and conclusions are reported in Section 5.