Mathematical optimization and learning models to address uncertainties and sustainability of supply chain management

As concerns about climate change, biodiversity loss, and pollution have become more widespread, new worldwide challenges deal with the protection of the environment and the conservation of natural resources. Thus, in order to empower sustainability and circular economy ambitions, the world has shifted to embrace sustainable practices and policies. This is carried out, primarily, through the implementation of sustainable business practices and increased investments in green technology. Advanced information systems, digital technologies and mathematical models are required to respond to the demanding targets of the sustainability paradigm. This trend is expanding with the growing interest in production and services sustainability in order to achieve economic growth and development while preventing their negative impact on the environment. A significant step forward in this direction is enabled by Supply Chain Management (SCM) practices that exploit mathematical and statistical modeling to better support decisions affecting both profitability and sustainability targets. Indeed, these targets should not be approached as competing goals, but rather addressed simultaneously within a comprehensive vision that responds adequately to both of them. Accordingly, Green Supply Chain Management (GSCM) can achieve its goals through innovative management approaches that consider sustainable efficiency and profitability to be clearly linked by the savings that result from applying optimization techniques. To confirm the above, there is a growing trend of applying mathematical optimization models for enhancing decision-making in pursuit of both environmental and profit performance. Indeed, GSCM takes into account many decision problems, such as facility location, capacity allocation, production planning and vehicle routing. Besides sustainability, uncertainty is another critical issue in Supply Chain Management (SCM). Considering a deterministic approach would definitely fail to provide concrete decision support when modeling those kinds of scenarios. According to various hypothesis and strategies, uncertainties can be addressed by exploiting several modeling approaches arising from statistics, statistical learning and mathematical programming. While statistical and learning models accounts variability by definition, Robust Optimization (RO) is a particular modeling approach that is commonly applied in solving mathematical programming problems where a certain set of parameters are subject to uncertainty. In this dissertation, mathematical and learning models are exploited according to different approaches and models combinations, providing new formulations and frameworks to address strategic and operational problems of GSCM under uncertainty. All models and frameworks presented in this dissertation are tested and validated on real-case instances

A mixed integer programming model for a continuous move transportation problem with service constraints (Un método de programación mixta entera para un problema de transportación de movimiento continuo con restricciones de servicio)

Abstract. We consider a Pickup and Delivery Vehicle Routing Problem (PDP) commonly encountered in real-world logistics operations. The problem involves a set of practical complications that have received little attention in the vehicle routing literature. In this problem, there are multiple vehicle types available to cover a set of pickup and delivery requests, each of which has pickup time windows and delivery time windows. Transportation orders and vehicle types must satisfy a set of compatibility constraints that specify which orders cannot be covered by which vehicle types. In addition we include some dock service capacity constraints as is required on common real world operations. This problem requires to be attended on large scale instances (orders ≥ 500), (vehicles ≥ 150). As a generalization of the traveling salesman problem, clearly this problem is NP-hard. The exact algorithms are too slow for large scale instances. The PDP-TWDS is both a packing problem (assign order to vehicles), and a routing problem (find the best route for each vehicle). We propose to solve the problem in three stages. The first stage constructs initials solutions at aggregate level relaxing some constraints on the original problem. The other two stages imposes time windows and dock service constraints. Our results are favorable finding good quality solutions in relatively short computational times. Resumen. En la solución de problemas combinatorios, es importante evaluar el costobeneficio entre la obtención de soluciones de alta calidad en detrimento de los recursos computacionales requeridos. El problema planteado es para el ruteo de un vehículo con entrega y recolección de producto y con restricciones de ventana de horario. En la práctica, dicho problema requiere ser atendido con instancias de gran escala (nodos ≥100). Existe un fuerte porcentaje de ventanas de horario activas (≥90%) y con factores de amplitud ≥75%. El problema es NP-hard y por tal motivo la aplicación de un método de solución exacta para resolverlo en la práctica, está limitado por el tiempo requerido para la actividad de ruteo. Se propone un algoritmo genético especializado, el cual ofrece soluciones de buena calidad (% de optimalidad aceptables) y en tiempos de ejecución computacional que hacen útil su aplicación en la práctica de la logística. Para comprobar la eficacia de la propuesta algorítmica se desarrolla un diseño experimental el cual hará uso de las soluciones óptimas obtenidas mediante un algoritmo de ramificación y corte sin límite de tiempo. Los resultados son favorables

Scheduling for Timely Passenger Delivery in a Large Scale Ride Sharing System

Taxi ride sharing is one of the most promising solutions to urban transportation issues, such as traffic congestion, gas insufficiency, air pollution, limited parking space and unaffordable parking charge, taxi shortage in peak hours, etc. Despite the enormous demands of such service and its exciting social benefits, there is still a shortage of successful automated operations of ride sharing systems around the world. Two of the bottlenecks are: (1) on-time delivery is not guaranteed; (2) matching and scheduling drivers and passengers is a NP-hard problem, and optimization based models do not support real time scheduling on large scale systems. This thesis tackles the challenge of timely delivery of passengers in a large scale ride sharing system, where there are hundreds and even thousands of passengers and drivers to be matched and scheduled. We first formulate it as a mixed linear integer programming problem, which obtains the theoretical optimum, but at an unacceptable runtime cost even for a small system. We then introduce our greedy agglomeration and Monte Carlo simulation based algorithm. The effectiveness and efficiency of the new algorithm are fully evaluated: (1) Comparison with solving optimization model is conducted on small ride sharing cases. The greedy agglomerative algorithm can always achieve the same optimal solutions that the optimization model offers, but is three orders of magnitude faster. (2) Case studies on large scale systems are also included to validate its performance. (3) The proposed greedy algorithm is straightforward for parallelization to utilize distributed computing resources. (4) Two important details are discussed: selection of the number of Monte Carlo simulations and proper calculation of delays in the greedy agglomeration step. We find out from experiments that the sufficient number of simulations to achieve a “sufficiently optimal solution” is linearly related to the product of the number of vehicles and the number of passengers. Experiments also show that enabling margins and counting early delivery as negative delay leads to more accurate solutions than counting delay only

Methodologies for Solving Integrated Transportation and Scheduling Problems

This research proposes novel solution techniques to optimize two real-world problems in the area of scheduling and transportation. We first consider a model for optimizing the operations of dredges. In this problem, scheduling and assignment decisions are integrated across a finite planning horizon. Additional constraints and problem elements explicitly considered include, but are not limited, to environmental work window restrictions, budget limitations, dredge operation rates and schedule-dependent dredge availability. Our approach makes use of Constraint Programming (CP) to obtain quality and robust solutions within an amount of time small enough to be useful to practitioners. The expanded feature set of the methodology presented makes our solution tool the most comprehensive and flexible decision-making framework for dredge scheduling in existence. The second transportation and logistics problem considered in this dissertation considers a unified variation of the Vehicle Routing Problem (VRP). This work offers a powerful yet flexible tool to model and solve real-world problems, each with their specifications, constraints, and requirements. We review existing VRP problems from the literature and propose new VRP variants that differ from the existing ones by the consideration of hours of service regulation on the active and drive hours of drivers in a single or multiple shifts. Real-world instances of these problems consist of thousands of customer locations and hundreds of vehicles. To ensure the quality of the solutions, we compare the performance of our approach with CPLEX on several benchmark instances from the literature. Finally, the third chapter of this work focuses on a comprehensive analysis of the methodology presented in Chapter 4. Specifically, sensitivity analysis regarding the parameters driving the performance of the heuristics is performed. Also, we propose a Genetic Algorithm (GA) to solve the VRP variants in Chapter 3 and provide a computational study of its performance against CPLEX and the approaches in Chapter 3

A Hybrid Approach to the Optimization of Multiechelon Systems

In freight transportation there are two main distribution strategies: direct shipping and multiechelon distribution. In the direct shipping, vehicles, starting from a depot, bring their freight directly to the destination, while in the multiechelon systems, freight is delivered from the depot to the customers through an intermediate points. Multiechelon systems are particularly useful for logistic issues in a competitive environment. The paper presents a concept and application of a hybrid approach to modeling and optimization of the Multi-Echelon Capacitated Vehicle Routing Problem. Two ways of mathematical programming (MP) and constraint logic programming (CLP) are integrated in one environment. The strengths of MP and CLP in which constraints are treated in a different way and different methods are implemented and combined to use the strengths of both. The proposed approach is particularly important for the discrete decision models with an objective function and many discrete decision variables added up in multiple constraints. An implementation of hybrid approach in the ECLiPSe system using Eplex library is presented. The Two-Echelon Capacitated Vehicle Routing Problem (2E-CVRP) and its variants are shown as an illustrative example of the hybrid approach. The presented hybrid approach will be compared with classical mathematical programming on the same benchmark data sets

Requirement for C-130 Aircraft in the Intratheater Korean Scenario

In an effort to provide a timely and reasonably accurate methodology for determining C-130 intratheater airlift requirements, this research concentrated on a rough-cut capacity approach using a straight forward linear programming spreadsheet model. To provide more detailed analysis, a more sophisticated linear program was investigated. Specifically, the spreadsheet model calculated the minimum number of C-130s required to carry required cargo, passenger, and aeromedical loads based on user-defined daily requirements. For a given scenario, inputs include the daily requirements and the expected capacity for C-130 aircraft, trucks, and 22-car trains. Included in the capacity inputs are the number of daily cycles or trips expected from a given mode of transportation. The model is automatically formulated based on these inputs and is solved using a spreadsheet solver. Graphical results are provided. This spreadsheet model is analyzed for a 20-day period, but any planning horizon can be used with modifications. Since the spreadsheet does not perform a parametric analysis, the data used in the spreadsheet formulation was input into the LINDO solver in order to perform parametric analyses

Multi-Robot Pickup and Delivery via Distributed Resource Allocation

In this article, we consider a large-scale instance of the classical pickup-and-delivery vehicle routing problem that must be solved by a network of mobile cooperating robots. Robots must self-coordinate and self-allocate a set of pickup/delivery tasks while minimizing a given cost figure. This results in a large, challenging mixed-integer linear problem that must be cooperatively solved without a central coordinator. We propose a distributed algorithm based on a primal decomposition approach that provides a feasible solution to the problem in finite time. An interesting feature of the proposed scheme is that each robot computes only its own block of solution, thereby preserving privacy of sensible information. The algorithm also exhibits attractive scalability properties that guarantee solvability of the problem even in large networks. To the best of our knowledge, this is the first attempt to provide a scalable distributed solution to the problem. The algorithm is first tested through Gazebo simulations on a ROS 2 platform, highlighting the effectiveness of the proposed solution. Finally, experiments on a real testbed with a team of ground and aerial robots are provided