Stochastic programming for City Logistics: new models and methods

The need for mobility that emerged in the last decades led to an impressive increase in the number of vehicles as well as to a saturation of transportation infrastructures. Consequently, traffic congestion, accidents, transportation delays, and polluting emissions are some of the most recurrent concerns transportation and city managers have to deal with. However, just building new infrastructures might be not sustainable because of their cost, the land usage, which usually lacks in metropolitan regions, and their negative impact on the environment. Therefore, a different way of improving the performance of transportation systems while enhancing travel safety has to be found in order to make people and good transportation operations more efficient and support their key role in the economic development of either a city or a whole country. The concept of City Logistics (CL) is being developed to answer to this need. Indeed, CL focus on reducing the number of vehicles operating in the city, controlling their dimension and characteristics. CL solutions do not only improve the transportation system but the whole logistics system within an urban area, trying to integrate interests of the several. This global view challenges researchers to develop planning models, methods and decision support tools for the optimization of the structures and the activities of the transportation system. In particular, this leads researchers to the definition of strategic and tactical problems belonging to well-known problem classes, including network design problem, vehicle routing problem (VRP), traveling salesman problem (TSP), bin packing problem (BPP), which typically act as sub-problems of the overall CL system optimization. When long planning horizons are involved, these problems become stochastic and, thus, must explicitly take into account the different sources of uncertainty that can affect the transportation system. Due to these reasons and the large-scale of CL systems, the optimization problems arising in the urban context are very challenging. Their solution requires investigations in mathematical and combinatorial optimization methods as well as the implementation of efficient exact and heuristic algorithms. However, contributions answering these challenges are still limited number. This work contributes in filling this gap in the literature in terms of both modeling framework for new planning problems in CL context and developing new and effective heuristic solving methods for the two-stage formulation of these problems. Three stochastic problems are proposed in the context of CL: the stochastic variable cost and size bin packing problem (SVCSBPP), the multi-handler knapsack problem under uncertainty (MHKPu) and the multi-path traveling salesman problem with stochastic travel times (mpTSPs). The SVCSBPP arises in supply-chain management, in which companies outsource the logistics activities to a third-party logistic firm (3PL). The procurement of sufficient capacity, expressed in terms of vehicles, containers or space in a warehouse for varying periods of time to satisfy the demand plays a crucial role. The SVCSBPP focuses on the relation between a company and its logistics capacity provider and the tactical-planning problem of determining the quantity of capacity units to secure for the next period of activity. The SVCSBPP is the first attempt to introduce a stochastic variant of the variable cost and size bin packing problem (VCSBPP) considering not only the uncertainty on the demand to deliver, but also on the renting cost of the different bins and their availability. A large number of real-life situations can be satisfactorily modeled as a MHKPu, in particular in the last mile delivery. Last mile delivery may involve different sequences of consolidation operations, each handled by different workers with different skill levels and reliability. The improper management of consolidation operations can cause delay in the operations reducing the overall profit of the deliveries. Thus, given a set of potential logistics handlers and a set of items to deliver, characterized by volume and random profit, the MHKPu consists in finding a subset of items which maximizes the expected total profit. The profit is given by the sum of a deterministic profit and a stochastic profit oscillation, with unknown probability distribution, due to the random handling costs of the handlers.The mpTSPs arises mainly in City Logistics applications. Cities offer several services, such as garbage collection, periodic delivery of goods in urban grocery distribution and bike sharing services. These services require the planning of fixed and periodic tours that will be used from one to several weeks. However, the enlarged time horizon as well as strong dynamic changes in travel times due to traffic congestion and other nuisances typical of the urban transportation induce the presence of multiple paths with stochastic travel times. Given a graph characterized by a set of nodes connected by arcs, mpTSPs considers that, for every pair of nodes, multiple paths between the two nodes are present. Each path is characterized by a random travel time. Similarly to the standard TSP, the aim of the problem is to define the Hamiltonian cycle minimizing the expected total cost. These planning problems have been formulated as two-stage integer stochastic programs with recourse. Discretization methods are usually applied to approximate the probability distribution of the random parameters. The resulting approximated program becomes a deterministic linear program with integer decision variables of generally very large dimensions, beyond the reach of exact methods. Therefore, heuristics are required. For the MHKPu, we apply the extreme value theory and derive a deterministic approximation, while for the SVCSBPP and the mpTSPs we introduce effective and accurate heuristics based on the progressive hedging (PH) ideas. The PH mitigates the computational difficulty associated with large problem instances by decomposing the stochastic program by scenario. When effective heuristic techniques exist for solving individual scenario, that is the case of the SVCSBPP and the mpTSPs, the PH further reduces the computational effort of solving scenario subproblems by means of a commercial solver. In particular, we propose a series of specific strategies to accelerate the search and efficiently address the symmetry of solutions, including an aggregated consensual solution, heuristic penalty adjustments, and a bundle fixing technique. Yet, although solution methods become more powerful, combinatorial problems in the CL context are very large and difficult to solve. Thus, in order to significantly enhance the computational efficiency, these heuristics implement parallel schemes. With the aim to make a complete analysis of the problems proposed, we perform extensive numerical experiments on a large set of instances of various dimensions, including realistic setting derived by real applications in the urban area, and combinations of different levels of variability and correlations in the stochastic parameters. The campaign includes the assessment of the efficiency of the meta-heuristic, the evaluation of the interest to explicitly consider uncertainty, an analysis of the impact of problem characteristics, the structure of solutions, as well as an evaluation of the robustness of the solutions when used as decision tool. The numerical analysis indicates that the stochastic programs have significant effects in terms of both the economic impact (e.g. cost reduction) and the operations management (e.g. prediction of the capacity needed by the firm). The proposed methodologies outperform the use of commercial solvers, also when small-size instances are considered. In fact, they find good solutions in manageable computing time. This makes these heuristics a strategic tool that can be incorporated in larger decision support systems for CL

Integrated network flow model for a reliability assessment of the national electric energy system

Electric energy availability and price depend not only on the electric generation and transmission facilities, but also on the infrastructure associated to the production, transportation, and storage of coal and natural gas. As the U.S. energy system has grown more complex and interdependent, failure or degradation on the performance of one or more of its components may possibly result in more severe consequences in the overall system performance. The effects of a contingency in one or more facilities may propagate and affect the operation, in terms of availability and energy price, of other facilities in the energy grid. In this dissertation, a novel approach for analyzing the different energy subsystems in an integrated analytical framework is presented, by using a simplified representation of the energy infrastructure structured as an integrated, generalized, multi-period network flow model. The model is capable of simulating the energy system operation in terms of bulk energy movements between the different facilities and prices at different locations under different scenarios. Assessment of reliability and congestion in the grid is performed through the introduction and development of nodal price-based metrics, which prove to be especially valuable for the assessment of conditions related to changes in the capacity of one or more of the facilities. Nodal price-based metrics are developed with the specific objectives of evaluating the impact of disruptions and of assessing capacity expansion projects. These metrics are supported by studying the relationship between nodal prices and congestion using duality theory. Techniques aimed at identifying system vulnerabilities and conditions that may significantly impact availability and price of electrical energy are also developed. The techniques introduced and developed through this work are tested using 2005 data, and special effort is devoted to the modeling and study of the effects of hurricanes Katrina and Rita in the energy system. In summary, this research is a step forward in the direction of an integrated analysis of the electric subsystem and the fossil fuel production and transportation networks, by presenting a set of tools for a more comprehensive assessment of congestion, reliability, and the effects of disruptions in the U.S. energy grid

Supply Chain

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications

Sequence-Based Simulation-Optimization Framework With Application to Port Operations at Multimodal Container Terminals

It is evident in previous works that operations research and mathematical algorithms can provide optimal or near-optimal solutions, whereas simulation models can aid in predicting and studying the behavior of systems over time and monitor performance under stochastic and uncertain circumstances. Given the intensive computational effort that simulation optimization methods impose, especially for large and complex systems like container terminals, a favorable approach is to reduce the search space to decrease the amount of computation. A maritime port can consist of multiple terminals with specific functionalities and specialized equipment. A container terminal is one of several facilities in a port that involves numerous resources and entities. It is also where containers are stored and transported, making the container terminal a complex system. Problems such as berth allocation, quay and yard crane scheduling and assignment, storage yard layout configuration, container re-handling, customs and security, and risk analysis become particularly challenging. Discrete-event simulation (DES) models are typically developed for complex and stochastic systems such as container terminals to study their behavior under different scenarios and circumstances. Simulation-optimization methods have emerged as an approach to find optimal values for input variables that maximize certain output metric(s) of the simulation. Various traditional and nontraditional approaches of simulation-optimization continue to be used to aid in decision making. In this dissertation, a novel framework for simulation-optimization is developed, implemented, and validated to study the influence of using a sequence (ordering) of decision variables (resource levels) for simulation-based optimization in resource allocation problems. This approach aims to reduce the computational effort of optimizing large simulations by breaking the simulation-optimization problem into stages. Since container terminals are complex stochastic systems consisting of different areas with detailed and critical functions that may affect the output, a platform that accurately simulates such a system can be of significant analytical benefit. To implement and validate the developed framework, a large-scale complex container terminal discrete-event simulation model was developed and validated based on a real system and then used as a testing platform for various hypothesized algorithms studied in this work

Liner ship fleet planning with uncertain container shipment demand

Ph.DDOCTOR OF PHILOSOPH

Stochastic Service Network Design for Intermodal Freight Transportation

In view of the accelerating climate change, greenhouse gas emissions from freight transportation must be significantly reduced over the next decades. Intermodal transportation can make a significant contribution here. During the transportation process, different modes of transportation are combined, enabling a modal shift to environmentally friendly alternatives such as rail and inland waterway transportation. However, at the same time, the organization of several modes is more complex compared to the unimodal case (where, for example, only trucks are employed). In particular, an efficient management of uncertainties, such as fluctuating transportation demand volumes or delays, is required to realize low costs and transportation times, thereby ensuring the attractiveness of intermodal transportation for a further modal shift. Stochastic service network design can explicitly consider such uncertainities in the planning in order to increase the performance of intermodal transportation. Decisions for the network design as well as for the mode choice are defined by mathematical optimization models, which originate from operations research and include relevant uncertainities by stochastic parameters. As central research gap, this dissertation addresses important operational constraints and decision variables of real-life intermodal networks, which have not been considered in these models so far and, in consequence, strongly limit their application in everyday operations. The resulting research contribution are two new variants of stochastic service network design models: The "stochastic service network design with integrated vehicle routing problem" integrates corresponding routing problems for road vehicles into the planning of intermodal networks. This new variant ensures a cost- and delay-minimal mode choice in the case of uncertain transportation times. The "stochastic service network design with short-term schedule modifications" deals with modifications of intermodal transportation schedules in order to adapt them to fluctuating demand as best as possible. For both new model variants, heuristic solution methods are presented which can efficiently solve even large network instances. Extensive case studies with real-world data demonstrate significant savings potentials compared to deterministic models as well as (simplified) stochastic models that already exist in literature

Reliable multi-product multi-vehicle multi-type link logistics network design: A hybrid heuristic algorithm

Abstract This paper considers the reliable multi-product multi-vehicle multi-type link logistics network design problem (RMLNDP) with system disruptions, which is concerned with facilities locating, transshipment links constructing, and also allocating them to the customers in order to satisfy their demand with minimum expected total cost (including locating costs, link constructing costs, and also expected transshipment costs in normal and disruption conditions). The motivating application of this class of problem is in multi-product, multi-vehicle, and multitype link logistics network design regarding to system disruptions simultaneously. In fact, the decision makers in this area are not only concerned with the facility locating costs, link constructing costs, and logistical costs of the system but also by focusing on the several system disruption states in order to be able to provide a reliable sustainable multi configuration logistic network system. All facility location plans, link construction plans and also link transshipment plans of demands in the problem must be efficiently determined while considering the several system disruptions. The problem is modeled as a mixed integer programming (MIP) model. Also, a hybrid heuristic, based on linear programming (LP) relaxation approach, is proposed. Computational experiments illustrate that the provided algorithm will be able to substantially outperform the proposed integer programming model in terms of both finding and verifying the efficient optimal (or near optimal) solution at a reasonable processing time

Mathematical Optimization for Routing and Logistic Problems

In this thesis, we focus on mathematical optimization models and algorithms for solving routing and logistic problems. The first contribution regards a path and mission planning problem, called Carrier-Vehicle Traveling Salesman Problem (CVTSP), for a system of heterogeneous vehicles. A Mixed-Integer Second Order Conic Programming (MISOCP) model and a Benders-like enumeration algorithm are presented for solving CVTSP. The second work concerns a class of routing problems, referred to as Interceptor Vehicle Routing Problems (IVRPs). They generalize VRPs in the sense that target points are allowed to move from their initial location according to a known motion. We present a novel MISOCP formulation and a Branch-and-Price algorithm based on a Lagrangian Relaxation of the vehicle-assignment constraints. Other two contributions focus on waste flow management problems: the former considers a deterministic setting in which a Mixed-Integer Linear Programming (MILP) formulation is used as a Decision Support System for a real-world waste operator, whereas the latter deals with the uncertainty of the waste generation amounts by means of Two-Stage Multiperiod Stochastic Mixed-Integer Programming formulations. Finally, we give an overview on the optimization challenges arising in electric car-sharing systems, both at strategic and tactical planning level