Optimal Service Time Windows

Because customers must usually arrange their schedules to be present for home services, they desire an accurate estimate of when the service will take place. However, even when firms quote large service time windows, they are often missed, leading to customer dissatisfaction. Wide time windows and frequent failures occur because time windows must be communicated to customers in the face of several uncertainties: future customer requests are unknown, final service plans are not yet determined, and when fulfillment is outsourced to a third party, the firm has limited control over routing procedures. Even when routing is performed in-house, time windows typically do not receive explicit consideration. In this paper, we show how companies can communicate reliable and narrow time windows to customers in the face of arrival time uncertainty. Under mild assumptions, our main result characterizes the optimal policy, identifying structure that reduces a high-dimensional stochastic non-linear optimization problem to a root-finding problem in one dimension. The result inspires a practice-ready heuristic for the more general case. Relative to the industry standard of communicating uniform time windows to all customers, and to other policies applied in practice, our method of quoting customer-specific time windows yields a substantial increase in customer convenience without sacrificing reliability of service, providing results that nearly achieve the lower bound on the optimal solution. Our results show that (i) time windows should be tailored to individual customers, (ii) time window sizes should be proportional to the service level, (iii) larger time windows should be assigned to earlier requests and smaller time windows to later requests, (iv) larger time windows should be assigned to customers further from the depot of operation and smaller time windows to closer customers, and (v) two time windows for one customer are helpful in some cases

Time and timing in vehicle routing problems

The distribution of goods to a set of geographically dispersed customers is a common problem faced by carrier companies, well-known as the Vehicle Routing Problem (VRP). The VRP consists of finding an optimal set of routes that minimizes total travel times for a given number of vehicles with a fixed capacity. Given the demand of each customer and a depot, the optimal set of routes should adhere to the following conditions: ?? Each customer is visited exactly once by exactly one vehicle. ?? All vehicle routes start and end at the depot. ?? Every route has a total demand not exceeding the vehicle capacity. The travel times between any two potential locations are given as input to the problem. Consequently, the total travel is computed by summing up the travel time over the chosen routes. In reality, carrier companies are faced with a number of other issues not conveyed in the VRP. The research in this thesis introduces a number of realistic variants of the VRP. These variants consider the VRP as a core component and incorporate additional features. By definition the VRP is NP-hard. Throughout the years a vast amount of research was aimed at developing both exact and heuristic solution procedures. Building on this established literature, solution procedures are developed to fit the variants proposed in this thesis. The standard VRP considers that the travel time between any pair of locations is constant throughout the day. However, congestion is present in most road networks. Considering traffic congestion results in time-dependent travel times, where the travel time between two location depends not only on the distance between them but also on the time of day one chooses to traverse this distance. Time-dependent travel times are considered in Chapters 2 and 3 of this thesis. Thus, in these Chapters we incorporate the time dimension into the VRP. The standard VRP does not take into account any customer service aspect. The customers are presumed to be available to receive their goods upon arrival of the vehicles. However, a number of carrier companies quote their expected arrival time to their customers. We introduce the concept of self-imposed time windows (SITW). SITW reflect the fact that the carrier company decides on when to visit the customer and communicates this to the customer. Once a time window is quoted to a customer the carrier company strives to provide service within this time window. SITW differ from time windows in the widely studied VRP with time windows (VRPTW), as the latter are exogenous constraints. In Chapters 4 and 5 SITW are endogenous decisions in stochastic environments. Thus, in addition to the sequencings decisions required by the VRP further timing decisions are needed. This thesis extends the VRP in two major dimensions: time-dependent travel times and self-imposed time windows. In reality carrier companies are faced with various uncertainties. The presented models incorporated some of these uncertainties by addressing three stochastic aspects: (I) In Chapter 3 stochastic service times are considered. (II) In Chapter 4, stochasticity in travel time is modeled to describes variability caused by random events such as car accidents or vehicle break down. (III) Finally, in Chapter 5 the objective was to construct a long term plan for providing consistent service to reoccurring customers. Stochasticity in this thesis is treated in an a priori manner. The plan, consisting of routes and timing decisions where necessary, is determined beforehand and is not modified according to the realization of the random events. Chapter 2 addresses environmental concerns by studying CO2 emissions in a timedependent vehicle routing problem environment. In addition to the decisions required for the assignment and scheduling of customers to vehicles, the vehicle speed limit is considered. The emissions per kilometer as a function of speed, is a function with a unique minimum speed v*. However, we show that limiting vehicle speed to this v* might be sub-optimal, in terms of total emissions. We adapted a Tabu search procedure for the proposed model. Furthermore, upper and lower bounds on the total amount of emissions that may be saved are presented. Quantifying the tradeoff between minimizing travel time as opposed to CO2 emissions is an important contribution. Another important contribution lies in incorporating fuel costs in the optimization. As fuel costs are correlated with CO2 emissions, Chapter 2 shows that even in today’s cost structure limiting vehicle speeds is beneficial. Chapter 3 defines the perturbed time-dependent VRP (P-TDVRP) model which is designed to handle unexpected delays at the various customer locations. A solution method that combines disruptions in a Tabu Search procedure is proposed. In Chapter 3 we identify situations capable of absorbing delays. i.e. where inserting a delay will lead to an increase in travel time that is less than the delay length itself. Based on this, assumptions with respect to the solution structure of P-TDVRP are formulated and validated. Furthermore, most experiments showed that the additional travel time required by the P-TDVRP, when compared to the travel time required by the TDVRP, was justified. In Chapter 4 the notion of self imposed time windows is defined and embedded in the VRP-SITW model. The objective of this problem is to minimize delay costs (caused by late arrivals at customers) as well as traveling time. The problem is optimized under various disruptions in travel times. The basic mechanism of dealing with these disruptions is allocating time buffers throughout the routes. Thus, additional timing decisions are taken. The time buffers attempt to reduce potential damage of disruptions. The solution approach combines a linear programming model with a local search heuristic. In Chapter 4, two main types of experiments were conducted: one compares the VRP with VRP-SITW while the other compares VRPTW with VRPSITW. The first set of experiments assessed the increase in operational costs caused by incorporating SITW in the VRP. The second set of experiments enabled evaluating the savings in operational costs by using flexible time windows, when compared to the VRPTW. Chapter 5 extends the customer service dimension by considering the consistent vehicle routing problem. Consistency is defined by having the same driver visiting the same customers at roughly the same time. As such, two main dimensions of consistency are identified in the literature, driver- and temporal consistency. In Chapter 5, driver consistency is imposed by having the same driver visit the same customers. Furthermore, we impose temporal consistency by SITW. A stochastic programming formulation is presented for the consistent VRP with stochastic customers. An exact solution method is proposed by adapting the 0-1 integer L- shaped algorithm to the problem. The method was able to solve the majority of test instances to optimality

Consistent Time Window Assignments for Stochastic Multi-Depot Multi-Commodity Pickup and Delivery

In this paper, we present the problem of assigning consistent time windows for the collection of multiple fresh products from local farmers and delivering them to distribution centers for consolidation and further distribution in a short agri-food supply chain with stochastic demand. We formulate the problem as a two-stage stochastic program. In the first stage, the time windows are assigned from a set of discrete time windows to farmers and in the second stage, after the demand is realized, the collection routes are planned by solving yet a newly introduced multi-depot multi-commodity team orienteering problem with soft time windows. The objective is to minimize the overall travel time and the time window violations. To solve our problem, we design a (heuristic) progressive hedging algorithm to decompose the deterministic equivalent problem into subproblems for a sampled set of demand scenarios and guide the scenarios toward consensus time windows. Through numerical experiments, we show the value of considering demand uncertainty over solving the deterministic expected value problem and the superiority of our approach over benchmarks when it comes to reducing the routing cost as well as the inconvenience for farmers

Optimizing transportation systems and logistics network configurations : From biased-randomized algorithms to fuzzy simheuristics

242 páginasTransportation and logistics (T&L) are currently highly relevant functions in any competitive industry. Locating facilities or distributing goods to hundreds or thousands of customers are activities with a high degree of complexity, regardless of whether facilities and customers are placed all over the globe or in the same city. A countless number of alternative strategic, tactical, and operational decisions can be made in T&L systems; hence, reaching an optimal solution –e.g., a solution with the minimum cost or the maximum profit– is a really difficult challenge, even by the most powerful existing computers. Approximate methods, such as heuristics, metaheuristics, and simheuristics, are then proposed to solve T&L problems. They do not guarantee optimal results, but they yield good solutions in short computational times. These characteristics become even more important when considering uncertainty conditions, since they increase T&L problems’ complexity. Modeling uncertainty implies to introduce complex mathematical formulas and procedures, however, the model realism increases and, therefore, also its reliability to represent real world situations. Stochastic approaches, which require the use of probability distributions, are one of the most employed approaches to model uncertain parameters. Alternatively, if the real world does not provide enough information to reliably estimate a probability distribution, then fuzzy logic approaches become an alternative to model uncertainty. Hence, the main objective of this thesis is to design hybrid algorithms that combine fuzzy and stochastic simulation with approximate and exact methods to solve T&L problems considering operational, tactical, and strategic decision levels. This thesis is organized following a layered structure, in which each introduced layer enriches the previous one.El transporte y la logística (T&L) son actualmente funciones de gran relevancia en cual quier industria competitiva. La localización de instalaciones o la distribución de mercancías a cientos o miles de clientes son actividades con un alto grado de complejidad, indepen dientemente de si las instalaciones y los clientes se encuentran en todo el mundo o en la misma ciudad. En los sistemas de T&L se pueden tomar un sinnúmero de decisiones al ternativas estratégicas, tácticas y operativas; por lo tanto, llegar a una solución óptima –por ejemplo, una solución con el mínimo costo o la máxima utilidad– es un desafío realmente di fícil, incluso para las computadoras más potentes que existen hoy en día. Así pues, métodos aproximados, tales como heurísticas, metaheurísticas y simheurísticas, son propuestos para resolver problemas de T&L. Estos métodos no garantizan resultados óptimos, pero ofrecen buenas soluciones en tiempos computacionales cortos. Estas características se vuelven aún más importantes cuando se consideran condiciones de incertidumbre, ya que estas aumen tan la complejidad de los problemas de T&L. Modelar la incertidumbre implica introducir fórmulas y procedimientos matemáticos complejos, sin embargo, el realismo del modelo aumenta y, por lo tanto, también su confiabilidad para representar situaciones del mundo real. Los enfoques estocásticos, que requieren el uso de distribuciones de probabilidad, son uno de los enfoques más empleados para modelar parámetros inciertos. Alternativamente, si el mundo real no proporciona suficiente información para estimar de manera confiable una distribución de probabilidad, los enfoques que hacen uso de lógica difusa se convier ten en una alternativa para modelar la incertidumbre. Así pues, el objetivo principal de esta tesis es diseñar algoritmos híbridos que combinen simulación difusa y estocástica con métodos aproximados y exactos para resolver problemas de T&L considerando niveles de decisión operativos, tácticos y estratégicos. Esta tesis se organiza siguiendo una estructura por capas, en la que cada capa introducida enriquece a la anterior. Por lo tanto, en primer lugar se exponen heurísticas y metaheurísticas sesgadas-aleatorizadas para resolver proble mas de T&L que solo incluyen parámetros determinísticos. Posteriormente, la simulación Monte Carlo se agrega a estos enfoques para modelar parámetros estocásticos. Por último, se emplean simheurísticas difusas para abordar simultáneamente la incertidumbre difusa y estocástica. Una serie de experimentos numéricos es diseñada para probar los algoritmos propuestos, utilizando instancias de referencia, instancias nuevas e instancias del mundo real. Los resultados obtenidos demuestran la eficiencia de los algoritmos diseñados, tanto en costo como en tiempo, así como su confiabilidad para resolver problemas realistas que incluyen incertidumbre y múltiples restricciones y condiciones que enriquecen todos los problemas abordados.Doctorado en Logística y Gestión de Cadenas de SuministrosDoctor en Logística y Gestión de Cadenas de Suministro

Mixing quantitative and qualitative methods for sustainable transportation in Smart Cities

L'abstract è presente nell'allegato / the abstract is in the attachmen

Applications of biased-randomized algorithms and simheuristics in integrated logistics

Transportation and logistics (T&L) activities play a vital role in the development of many businesses from different industries. With the increasing number of people living in urban areas, the expansion of on-demand economy and e-commerce activities, the number of services from transportation and delivery has considerably increased. Consequently, several urban problems have been potentialized, such as traffic congestion and pollution. Several related problems can be formulated as a combinatorial optimization problem (COP). Since most of them are NP-Hard, the finding of optimal solutions through exact solution methods is often impractical in a reasonable amount of time. In realistic settings, the increasing need for 'instant' decision-making further refutes their use in real life. Under these circumstances, this thesis aims at: (i) identifying realistic COPs from different industries; (ii) developing different classes of approximate solution approaches to solve the identified T&L problems; (iii) conducting a series of computational experiments to validate and measure the performance of the developed approaches. The novel concept of 'agile optimization' is introduced, which refers to the combination of biased-randomized heuristics with parallel computing to deal with real-time decision-making.Las actividades de transporte y logística (T&L) juegan un papel vital en el desarrollo de muchas empresas de diferentes industrias. Con el creciente número de personas que viven en áreas urbanas, la expansión de la economía a lacarta y las actividades de comercio electrónico, el número de servicios de transporte y entrega ha aumentado considerablemente. En consecuencia, se han potencializado varios problemas urbanos, como la congestión del tráfico y la contaminación. Varios problemas relacionados pueden formularse como un problema de optimización combinatoria (COP). Dado que la mayoría de ellos son NP-Hard, la búsqueda de soluciones óptimas a través de métodos de solución exactos a menudo no es práctico en un período de tiempo razonable. En entornos realistas, la creciente necesidad de una toma de decisiones "instantánea" refuta aún más su uso en la vida real. En estas circunstancias, esta tesis tiene como objetivo: (i) identificar COP realistas de diferentes industrias; (ii) desarrollar diferentes clases de enfoques de solución aproximada para resolver los problemas de T&L identificados; (iii) realizar una serie de experimentos computacionales para validar y medir el desempeño de los enfoques desarrollados. Se introduce el nuevo concepto de optimización ágil, que se refiere a la combinación de heurísticas aleatorias sesgadas con computación paralela para hacer frente a la toma de decisiones en tiempo real.Les activitats de transport i logística (T&L) tenen un paper vital en el desenvolupament de moltes empreses de diferents indústries. Amb l'augment del nombre de persones que viuen a les zones urbanes, l'expansió de l'economia a la carta i les activitats de comerç electrònic, el nombre de serveis del transport i el lliurament ha augmentat considerablement. En conseqüència, s'han potencialitzat diversos problemes urbans, com ara la congestió del trànsit i la contaminació. Es poden formular diversos problemes relacionats com a problema d'optimització combinatòria (COP). Com que la majoria són NP-Hard, la recerca de solucions òptimes mitjançant mètodes de solució exactes sovint no és pràctica en un temps raonable. En entorns realistes, la creixent necessitat de prendre decisions "instantànies" refuta encara més el seu ús a la vida real. En aquestes circumstàncies, aquesta tesi té com a objectiu: (i) identificar COP realistes de diferents indústries; (ii) desenvolupar diferents classes d'aproximacions aproximades a la solució per resoldre els problemes identificats de T&L; (iii) la realització d'una sèrie d'experiments computacionals per validar i mesurar el rendiment dels enfocaments desenvolupats. S'introdueix el nou concepte d'optimització àgil, que fa referència a la combinació d'heurístiques esbiaixades i aleatòries amb informàtica paral·lela per fer front a la presa de decisions en temps real.Tecnologies de la informació i de xarxe

Exact Two-Step Benders Decomposition for Two-Stage Stochastic Mixed-Integer Programs

Many real-life optimization problems belong to the class of two-stage stochastic mixed-integer programming problems with continuous recourse. This paper introduces Two-Step Benders Decomposition with Scenario Clustering (TBDS) as a general exact solution methodology for solving such stochastic programs to optimality. The method combines and generalizes Benders dual decomposition, partial Benders decomposition, and Scenario Clustering techniques and does so within a novel two-step decomposition along the binary and continuous first-stage decisions. We use TBDS to provide the first exact solutions for the so-called Time Window Assignment Traveling Salesperson problem. This is a canonical optimization problem for service-oriented vehicle routing; it considers jointly assigning time windows to customers and routing a vehicle among them while travel times are stochastic. Extensive experiments show that TBDS is superior to state-of-the-art approaches in the literature. It solves instances with up to 25 customers to optimality. It provides better lower and upper bounds that lead to faster convergence than related methods. For example, Benders dual decomposition cannot solve instances of 10 customers to optimality. We use TBDS to analyze the structure of the optimal solutions. By increasing routing costs only slightly, customer service can be improved tremendously, driven by smartly alternating between high- and low-variance travel arcs to reduce the impact of delay propagation throughout the executed vehicle route