###### Abstract  
This paper presents multiple readings to solve a vehicle routing problem with pickup and delivery (VRPPD) based on a real-life case study. Compared to theoretical problems, real-life ones are more difficult to address due to their richness and complexity. To handle multiple points of view in modeling our problem, we developed three different Mixed Integer Linear Programming (MILP) models, where each model covers particular constraints. The suggested models are designed for a mega poultry company in Tunisia, called CHAHIA. Our mission was to develop a prototype for CHAHIA that helps decision-makers find the best path for simultaneously delivering the company's products and collecting the empty boxes. Based on data provided by CHAHIA, we conducted computational experiments, which have shown interesting and promising results.  
vehicle routing problem; pickup and delivery; optimization; mixed integer linear programming +
Footnote †: journal: Applied Sciences  
meat product outlets every day. The various orders issued daily to serve these outlets are delivered in boxes owned by CHAHIA. The logistics of product delivery and box pickup are complicated and generates high costs since boxes are subject to loss (according to CHAHIA). Such losses could lead to stock shortages when filling and preparing products for delivery. Therefore, these boxes require a full-fledged management process when modeling the VRPPD for the company. The real VRPPD that we are dealing with differs from traditional VRPPDs in several aspects. First, our proposed models allow multiple visits to customers on the same day. In addition, each customer could be served by multiple vehicles during the same day. Furthermore, we have included CHAHIA's specificities, which are not well addressed in the literature.  
This paper develops three different Mixed Integer Linear Programming models (MILP) for CHAHIA VRPPD, handling multiple points of view. The first model is a VRP with a Simultaneous Pickup and Delivery (VRPSPD). It ensures that the pickup and delivery are performed simultaneously, without leaving any empty boxes with any customers. The second model is a flexible VRPPD. It provides two options for pickup and delivery operations, separately and/or simultaneously. The third one is a VRPSPD ensuring simultaneous pickup and delivery. However, it provides flexibility to drop and leave some boxes, which will be consequently penalized. The proposed models are benchmarked based on data provided by CHAHIA. We claim that in practice, defining a VRPPD problem is much more laborious than solving it due to the fact that the same problem could be viewed from different angles, observations, perspectives, and preferences. The multiple VRPPD readings could lead to different objective functions by focusing or ignoring certain details, data aggregations, and setting assumptions (see Figure 1).  
The remainder of this paper is organized as follows. Section 2 reviews the related literature. Section 3 describes the VRPSPD (\(MILP1\)). The flexible VRPPD (\(MILP2\)) is detailed in Section 4. Section 5 describes the VRPSPD with two additional alternatives which are, ignoring pickups and penalizing the loss (\(MILP3\)). Section 5 details the experimental framework. Section 6 discusses the limitation of the paper. Finally, Section 7 concludes the paper and opens new perspectives.