Supply chain planning has become a major concern of many companies. It is now well known that optimizing one activity of the supply chain often prevents the achievement of better solutions in others. Therefore, one should consider integrated problems, such as the Production Routing Problem (PRP), in which one performs the joint and simultaneous optimization of production, inventory, distribution, and routing decisions. Most PRP models consider only deterministic data, although uncertainty is a major issue in supply-chain management. Past studies have considered uncertainty in demand, quantity of products returned and quantity of components in each product. Here, we consider a PRP over a finite horizon, with a single capacitated production facility, a single product, a fleet of homogeneous vehicles, and uncertainty in the availability of vehicles. This is a problem setting seldom considered in previous studies, but commonly found in industrial environments.

Our PRP is defined on a complete graph. The plant is located at node 0 and the other nodes represent customers. A single product is produced by the plant with production time-dependent capacity along a finite discrete-time horizon. When production takes place, a fixed setup cost and a variable production cost per unit are incurred. The products can be stored by the plant and by the customers up to an inventory limit, incurring an inventory holding cost per unit.

The distribution is performed using a limited fleet of homogeneous vehicles. For each period, a set of routes starting and ending at the plant is defined. However, the number of available vehicles is an independently distributed random parameter, with respect to periods, and its value depends on the general random event. To obtain a manageable model, we sample scenarios from the random space to empirically define the possible realizations of the random parameter. For a given period, if the minimum number of vehicles required to serve all the customers is not available, some routes cannot be performed, and a recourse policy must be adopted. The recourse policy that we study involves redirecting the customers who cannot be served due to the lack of vehicles; in fact, these clients are outsourced to a third party, which will individually deliver the products to each customer. The goal of the problem is to simultaneously minimize production, inventory, routing, and recourse costs, while respecting inventory limits, and production and vehicle capacities.

We propose a classical stochastic programming two-stage formulation with recourse: production, inventory and routing plans are decided in the first stage, while the recourse decisions belong to the second stage, after the realization of the random event. The objective function minimizes the sum of production, transportation, inventory holding, and expected recourse costs.

To solve efficiently the proposed model, one must exploit the inherent structure of the problem at hand. An obvious approach is to apply Benders decomposition by separating the two stages of the problem. Computational experiments are now under way on instances derived from existing benchmark instances described. Detailed computational results will be reported at the conference.

Classical Dial-a-Ride problem (DARP) is typically formulated on a complete customer-based graph, where vertices represent customer locations and arcs denote the shortest path between them. Further, a unique pair of pickup and dropoff (PD) nodes is associated with each request. We argue that these models might not be responsive to the contemporary transportation needs, hence leading to suboptimal solutions. First, in reality, an actual road network connects customer locations, where the speed on links changes over time, resulting in multiple shortest paths within various intervals throughout the day. Moreover, in modern logistics, flexibility is no longer a feature but a necessity. To be competitive in today's market, carrier companies and on-demand transit providers may need to offer clients a selection of potential pickup and dropoff locations, each with its own time windows, based on availability and constraints. Despite this, the rich vehicle routing problem body of knowledge does not entail any article which explicitly investigates the combination of the aforementioned aspects. Hence, we formally introduce a new class of DARP with added layers of complexity described earlier, termed Generalized Dial-A-Ride Problem (GDARP). This model assumes a set of potential pickup and dropoff locations for each transit request, studied on real road networks with time-dependent travel times (TD-GDARP-RN). We present a Mixed-Integer Programming (MIP) model and formulate the scheduling problem for each vehicle as a Dynamic Programming (DP) problem. To solve the DP to optimality, we propose two algorithms: one employing forward propagation linearly, and the other utilizing a binary tree data structure in both recursive and iterative methods. Solving the DP for each route yields an optimal solution to the NP-Hard, Optimal Start Time Problem (OSTP). Additionally, we present an efficient DP-embedded hybrid adaptive large neighbourhood search (ALNS) metaheuristic that generates high-quality solutions.

A Stochastic Prize Collection Methodology for mobile Clinic Deployment Planning
Mobile clinic deployments are often used to provide healthcare to underserved or disaster-affected populations. Practitioners aim to deploy mobile clinics to reach populations with the most critical healthcare needs. However, during humanitarian operations uncertainty arises in the travel time, usability of roads, and access. To address these challenges, we model mobile clinic deployment as a Two Stage Stochastic Prize Collection Problem, to maximize the benefit offered by mobile clinics while considering the uncertainty. We also propose and study the effect of four recourse policies, that defer in their routing decisions. Results and insights will be presented based on the cases of Indonesia, Iraq, Kenya, and Malawi.

The maintenance of an electricity distribution network involves numerous daily technical interventions. In this problem, we are given a set of interventions each with associated time windows, location, necessary skills and duration, as well as a set of teams of technicians with associated set of skills, each represented by a vehicle. We need to find feasible routes on the interventions for each vehicle, taking into account the time windows and skills, and ensure that each vehicle returns to its departure depot before the end of the day. The primary objective is to maximize the total duration of completed interventions and as a secondary objective, we aim to minimize the overall routing cost. This problem can be formulated as a capacitated vehicle routing problem with time windows. Due to the large number of vehicles and interventions, this results in a large-scale optimization problem, and its operational nature limits the time available for exact solving. Here, we propose a column generation approach where the subproblem decomposes into a subproblem per vehicle and each potential route of a vehicle is considered as a new column in the master problem. To generate these routes, we rely on dynamic programming. Real-world instances from EDF (Electricité de France) of historical technicians' interventions will be used to evaluate the effectiveness of the proposed methods.