## 5 Computational Study  
We adopted a configuration quite similar to the one considered in [29], where authors have implemented their models in the IBM ILOG CPLEX Optimization Studio (Version: 12.6). All the experiments were conducted on a computer with an Intel(R) Core (TM) i7-7700 [EMAIL_ADDRESS] GHz and 8 GB memory under the Windows 10 Pro system. As we highlighted earlier in the introduction section, our work is dedicated to a poultry company in Tunisia, called CHAHIA. Due to a confidentiality issue, CHAHIA has fed our research work with limited data. Based on the collected data, we created a set of instances. To make sure that data features are diversified, we created 44 instances. Several factors have been used to calibrate the quality of solutions, enhance the solving process, and diversify the benchmark of instances. These factors are as follows:  
* The types of demands, i.e., the quantities of required goods (low/medium/high). * The number of boxes for customers (delivery and initial balance) and their dispersion. * The number of customers to be served. * The geographic dispersion of customer locations (distance between customers). * The number of vehicles. * The vehicle capacities: we considered, small (S) with 1.4 tons, and big (B) with 3 tons. Tables 1-3 represent the computational results provided by our proposed models. The results are shown in terms of objective function value (cost), computational time to reach solutions, and number of iterations. Results show that \(MILP2\) achieves the lowest objective function values compared to both \(MILP1\) and \(MILP3\). This achievement is mainly due to its flexibility and high number of specifications that it covers. In case of low demand or low number of boxes to be picked up, both \(MILP1\) and \(MILP3\) provide similar costs. However, if the demand or box numbers increase, \(MILP3\) outperforms \(MILP1\) and provides the lowest travel cost. This fact shows that sometimes it would be more profitable to leave some boxes instead of collecting them. We recall that the left boxes could be collected in future trips, otherwise, a penalization is considered. In case we reduce the cost of left boxes by relying on the possibility to recover them in the future with better conditions, \(MILP3\) will provide the lowest cost for the majority of instances. Moreover, if we change the capacity of vehicles from small to big, such as in instances \"inst5.2.004\" and \"inst5.2.005\", which are the same in fact, \(MILP1\) and \(MILP3\) diversify and provide different value costs, however, \(MILP2\) remains unchangeable. Furthermore, if we increase both, the demand to be between 151 Kg and 500 Kg per customer, and the number of customers to exceed 18, \(MILP3\) becomes the most efficient model. With regard to the computational time performance indicator, \(MILP3\) converges quickly. Contrariwise, \(MILP2\) consumes more time to provide optimal solutions. In case the number of customers exceeds six, \(MILP2\) remains incapable of retrieving an optimum solution during a reasonable period of time (i.e., less than 3600 min). With regard to the number of served customers, \(MILP1\) and \(MILP3\) provide a better performance compared to \(MILP2\). It is noticeable that when the number of vehicle stops for pickup or delivery increase, it will affect the quality of poultry products from CHAHIA. This affection is related to the unstable air conditioning of the vehicle refrigeration cabin. Therefore, it is recommended to reduce the number of load breaks. The different readings of the same problem led to an interesting diversification in terms of travel cost, computational time, and number of served customers.