Rich Vehicle and Inventory Routing Problems with Stochastic Demands

This thesis develops a unified framework for modeling and solving various classes of rich routing problems with stochastic demands, including the VRP and the IRP. The work is inspired by the problem of collecting recyclables from sensorized containers in Geneva, Switzerland. We start by modeling and solving the deterministic single-period version of the problem, which extends the class of VRPs with intermediate facilities. It is formulated as an MILP which is enhanced with several valid inequalities. Due to the rich nature of the problem, general-purpose solvers can only tackle instances of small to medium size. To solve realistic instances, we propose a meta-heuristic approach which achieves optimality on small instances, exhibits competitive performance in comparison to state-of-the-art methods, and leads to important savings in the state of practice. Moreover, it highlights and quantifies the savings from allowing open tours, in which the vehicles' origin and destination depots do not coincide. To integrate demand stochasticity, we extend the problem to an IRP over a finite planning horizon. Demand can be non-stationary and is forecast with any model that provides the expected demands and the standard deviation of the error terms, where the latter are assumed to be iid normal. The problem is modeled as an MINLP, in which the dynamic stochastic information impacts the cost through the probability of container overflows and route failures. The solution methodology is based on Adaptive Large Neighborhood Search (ALNS) which integrates a specialized forecasting model, tested and validated on real data. The computational experiments demonstrate that our ALNS exhibits excellent performance on VRP and IRP benchmarks. The case study, which uses a set of rich IRP instances from Geneva, finds strong evidence of the added value of including stochastic information in the model. Our approach performs significantly better compared to alternative deterministic policies in limiting the occurrence of overflows for the same routing cost. We also analyze the solution properties of a rolling horizon approach in terms of empirical lower and upper bounds. This approach is generalized in a unified framework for rich routing problems with stochastic demands, where we drop the assumption of iid normal error terms. We elaborate on the effects of the stochastic dimension on modeling, with a focus on stock-outs/overflows and route failures, and the cost of the associated recourse actions. Tractability is achieved through the ability to precompute or partially preprocess the bulk of the stochastic information, which is possible for a general inventory policy under mild assumptions. We propose an MINLP formulation, illustrate applications to various problem classes from the literature and practice, and demonstrate that certain problems, e.g. facility maintenance, where breakdown probabilities accumulate over the planning horizon, can be seen through the lens of inventory routing. The case study is based on the waste collection IRP instances cited above and on a new set of instances for the facility maintenance problem. On the first set, we analyze the effects of our assumptions on tractability and the objective function's representation of the real cost. On the second set, we demonstrate the framework's ability to achieve the same level of occurrence of breakdowns for a significantly lower routing cost compared to alternative deterministic policies

The waste collection VRP with intermediate facilities, a heterogeneous fixed fleet and a flexible assignment of origin and destination depot

We consider a complex recyclable waste collection problem that extends the class of vehicle routing problems with intermediate facilities by integrating a heterogeneous fixed fleet and a flexible assignment of origin and destination depot. Several additional side constraints, such as a mandated break period contingent on tour start time, multiple vehicle capacities and site dependencies are also included. This specific problem was inspired by a real-world application and does not appear in the literature. It is modeled as an MILP which is enhanced with several valid inequalities. Due to the rich nature of the problem, state-of-the-art commercial solvers are only able to tackle instances of small to medium size. To solve realistic instances, we propose a local search heuristic capable of systematically treating all problem features and general enough to respond to the varying characteristics of the case study regions for which it is intended. The results show that the heuristic achieves optimality on small random instances, exhibits competitive performance in comparison to state-of-the-art solution methods for special cases of our problem, and leads to important savings in the state of practice. Moreover, it highlights and quantifies the savings from allowing a flexible assignment of origin and destination depot. The data from the state of practice comes from a recyclable waste collection company in Geneva, Switzerland

Vehicle routing for a complex waste collection problem

We consider a complex waste collection problem, where the residents of a certain region dispose of recyclable waste, which is collected using a fixed heterogeneous fleet of vehicles with different volume and weight capacities, fixed costs, unit distance running costs and hourly driver wage rates. Each tour starts and ends at one of several depots, not necessarily the same, and is a sequence of collections followed by disposals at the available recycling plants, with a mandatory disposal before the end of the tour. There are time windows and a maximum tour duration, which is interrupted by a break after a certain interval of continuous work. Moreover, due to the specificities of different collection regions, there are occasional site dependencies. The problem is modeled as a mixed binary linear program and the formulation is enhanced with several valid inequalities and elimination rules. To solve realistic instances, we develop a local search heuristic, which currently embeds much of the functionality of the mathematical model. The heuristic performs well, as indicated by an optimality gap of 2% compared to the exact solution on small instances. Future work will see improving the model formulation to solve larger instances to optimality and expanding the heuristic to include all of the features of the model

Network design of a transport system based on accelerating moving walkways

Pollution, congestion and urbanistic considerations are leading to a change in the use of private vehicles in dense city centers. More frequently, the last-mile is covered with systems such as public transport, car sharing and bike sharing as well as an increase in walking and cycling. Following this trend, we assume a hypothetical scenario where the use of private cars is strongly limited in dense urban areas, and innovative transport modes must be used. This work investigates a futuristic system based on a network of accelerating moving walkways (AMW) to facilitate the movement of pedestrians in city centers where cars have been banned. Unlike constant speed moving walkways, AMWs can reach speeds of up to 15km/h thanks to an acceleration section. This paper presents a rigorous description of the system characteristics from a transportation point of view, develops a heuristic algorithm for the network design problem, and tests it on a real case study. Given a network of urban roads and an origin-destination demand, the optimization algorithm, which combines traffic assignment and supply modification, explores the trade-of curve between the total travel time and capital cost of the infrastructure. The results give practical insight on the possible dimensioning of the system, show the optimal network designs, and how these vary with a reduction of the available budget. This paper investigates for the first time the use of AMWs at a network scale, and provides results useful for analyzing the system feasibility. The results on travel time, investment budget and payback period, indicates that AMWs could be an effective mode of transport in cities

Modeling a waste disposal process via a discrete mixture of count data models

We propose a modeling framework for the data generating process of waste disposal in recyclable waste containers. It is based on a discrete mixture of count data models representing populations depositing dierent quantities in the containers, thus reflecting a realistic underlying behavior. It is tested on real data coming from ultrasound sensors mounted inside the containers and exhibits better in- and out-of-sample performance compared to a simple count data model assuming only one deposit quantity. The purpose of the mixture model is to forecast container waste levels at a future date when collection will take place. It thus becomes the first-step ingredient in a framework for ecient waste collection optimization