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.

This paper addressed an important variant of two-dimensional cutting stock problem. The objective was not only to minimize trim loss, as in traditional cutting stock problems, but rather to minimize the number of machine setups. This additional objective is crucial for the life of the machines and affects both the time and the cost of cutting operations. Since cutting stock problems are well known to be NP-hard, we proposed an approximate method to solve this problem in a reasonable time. This approach differs from the previous works by generating a front with many interesting solutions. By this way, the decision maker or production manager can choose the best one from the set based on other additional constraints. This approach combined a genetic algorithm with a linear programming model to estimate the optimal Pareto front of these two objectives. The effectiveness of this approach was evaluated through a set of instances collected from the literature. The experimental results for different-size problems show that this algorithm provides Pareto fronts very near to the optimal ones.

The Multiple Traveling Salesmen Problem is to deliver goods to a set of customers thanks to several travelling salesmen with known demands within minimizing the total salesman transportation cost while satisfying the delivery demands. Here, each salesman's subset of customers and service or visit' processing time are determined in advance. Many variants of this problem with different formulations and solving methods are provided in literature. In particular, the Synchronized m-TSP is defined where some customers are common for more than one salesman and must be entirely visited at the same time, simultaneously and not in sequence. The Synchronized m-TSPTW considering synchronization and time windows constraints is defined in Dohn (2011). This paper deals with Synchronized-mTSPTW within an application to Home Health Care (HHC) scheduling problem. Vehicles and customers are modified respectively by caregivers and patients. Time windows and synchronization are given as patients' availability preferences and caregivers' synchronization. The Synchronized-mTSPTW is NP-hard since TSPTW is NP-Hard. In this paper, we provide a new MILP considering the HHC routing problem as a special Resource-Constrained Project Scheduling Problem (RCPSP) with fixed resources (patients) and mobile resources (caregivers). A derived two-stage MILP heuristic is also provided to improve the computation times, especially for big instances.

In this paper, we focus on the Synchronized Multiple Traveling Salesmen Problem with Time Windows (Synchronized-m-TSPTW) within an application to Home Health Care (HHC) scheduling problem under uncertain processing and setup times. The general Synchronized-m-TSPTW consists on delivering goods to a set of customers thanks to several traveling salesmen with known demands. In the considered application, each salesmans subset of customers and service are known in advance, but visit processing times and setup times are uncertain. Vehicles and customers are modified respectively by caregivers and patients. Time windows and synchronization are given as patients availability preferences and caregivers synchronization. The Synchronized-mTSPTW with known parameters is NP-hard. An efficient Mixed Integer Linear Program is proposed in (Masmoudi and Mellouli 2014) to solve the HHC scheduling problem in its certain version. In this paper, we extend the considered problem by considering the uncertainty of processing times and setup times. Thus, we formulate and solve the problem as a robust Resource-Constrained Project Scheduling Problem (Robust-RCPSP) with fixed resources (patients), and mobile resources (caregivers). We use a scenario-based model to represent the uncertain processing and setup times and min-max objective to generate robust solutions that withstand the uncertainty in the worst-case. The experimental results show that the CPU time of the Robust-MILP formulation for the uncertain problem is closed to the CPU time of the MILP for nominal problem. The feasibility of the solution is insured for all scenarios for a set of instances. The cost of robustness increases as the level of uncertainties increases.