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

A survey on metaheuristics for stochastic combinatorial optimization

Metaheuristics are general algorithmic frameworks, often nature-inspired, designed to solve complex optimization problems, and they are a growing research area since a few decades. In recent years, metaheuristics are emerging as successful alternatives to more classical approaches also for solving optimization problems that include in their mathematical formulation uncertain, stochastic, and dynamic information. In this paper metaheuristics such as Ant Colony Optimization, Evolutionary Computation, Simulated Annealing, Tabu Search and others are introduced, and their applications to the class of Stochastic Combinatorial Optimization Problems (SCOPs) is thoroughly reviewed. Issues common to all metaheuristics, open problems, and possible directions of research are proposed and discussed. In this survey, the reader familiar to metaheuristics finds also pointers to classical algorithmic approaches to optimization under uncertainty, and useful informations to start working on this problem domain, while the reader new to metaheuristics should find a good tutorial in those metaheuristics that are currently being applied to optimization under uncertainty, and motivations for interest in this fiel

A Progressive Hedging Method for the Optimization of Social Engagement and Opportunistic IoT Problems

Due to the spread of the social engagement paradigm, several companies are asking people to perform tasks in exchange for a reward. The advantages of this business model are savings in economic and environmental terms. In previous works, it has been proved that the problem of finding the minimum amount of reward such that all tasks are performed is difficult to solve, even for medium-size realistic instances (if more than one type of person is considered). In this paper, we propose a customized version of the progressive hedging algorithm that is able to provide good solutions for large realistic instances. The proposed method reaches the goal of defining a procedure that can be used in real environments

The stochastic vehicle routing problem : a literature review, part II : solution methods

Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems. Keywords: vehicle routing (VRP), stochastic programmingm, SVRPpublishedVersio

Service network design problem with quality targets and stochastic travel time: new model and algorithm

Network design formulations in which time is explicitly taken as a stochastic parameter have been neglected in the service network design literature in favor of settings in which other stochastic parameters were taken into account (primarily demand). Nowadays, however, reliability is one of the major competitive dimensions of many firms. From a customer point of view, reliability - the on-time delivery of products - is a criterion that a firm must meet a priori, just to be considered as a possible supplier. From the point of view of carriers, reliability - the on-time occurrence of operations - is strictly related to the respect of an "ideal" or "imposed" schedule. This is particularly important, for consolidation-based transportation systems, where total system costs may also involve the costs raising from missing a proper sequencing of services for some commodities. In this work, we propose to study a service network design problem from a carrier point of view in which travel time is explicitly considered as a stochastic parameter in the decision process and in which the goal is to define a cost-efficient service network that satisfies given service quality targets consistently as close as possible in time. To the best of our knowledge, this is the first time such a problem has been investigated. The problem is modeled as a two-stage scenario-based stochastic programming model. In the first stage, planning decisions are made considering their future effects: the selection of the services and the routing of freight are determined with the objective of minimizing the fixed service-selection and variable demand-routing costs, plus the expected penalty costs following the application of the chosen plan to the observed realizations of travel times. The second stage addresses how to deal with delays for a given travel time realization and a chosen design. Network design problems are notoriously NP-Hard. A progressive hedging-based meta-heuristic algorithm able to provide good quality solutions to the problem is, also, proposed. The idea is to decompose the original scenario-based stochastic problem into single-scenario-sub-problems by relaxing first stage variables' non-anticipativity constraints. At each iteration, sub-problems are solved and non-anticipativity is gradually enforced trying to consolidate sub-problem solutions into a unique one, for the original problem. This is the first attempts to solve such a problem heuristically and, hence, to apply such a methodology to a SND problem with uncertainty in travel time. An extensive experimentation is reported to show the benefits in considering explicitly travel time stochasticity into the model rather having a deterministic time assumption, structural differences between stochastic and deterministic solutions and the performance of the proposed meta-heuristic algorithm. The scientific contribution of this thesis is four-fold: • to propose a new branch of research in the field of service network design problems by introducing uncertainty in time and the need of satisfying given service quality targets; • to provide an original two-stage stochastic linear mixed-integer programming formulation for the proposed SSND-SDT problem; • to show the attractiveness of the formulation and explore the role and importance of the various random parameters through an extensive numerical analysis; • to develop a progressive hedging-based meta-heuristic algorithm with a variable hierarchic approach able to efficiently find good quality solutions to the SSND-SDT

The probabilistic travelling salesman problem with crowdsourcing

We study a variant of the Probabilistic Travelling Salesman Problem arising when retailers crowdsource last-mile deliveries to their own customers, who can refuse or accept in exchange for a reward. A planner must identify which deliveries to offer, knowing that all deliveries need fulfilment, either via crowdsourcing or using the retailer’s own vehicle. We formalise the problem and position it in both the literature about crowdsourcing and among routing problems in which not all customers need a visit. We show that to evaluate the objective function of this stochastic problem for even one solution, one needs to solve an exponential number of Travelling Salesman Problems. To address this complexity, we propose Machine Learning and Monte Carlo simulation methods to approximate the objective function, and both a branch-and-bound algorithm and heuristics to reduce the number of evaluations. We show that these approaches work well on small size instances and derive managerial insights on the economic and environmental benefits of crowdsourcing to customers.info:eu-repo/semantics/publishedVersio

Dynamic Route Planning for Last-Mile Delivery

There has never been a time with more demand than now for e-retailing and as a consequence last-mile services. The growth in demand is also bringing significant challenges. With the abundance of options, customers are ever more demanding and expecting more control. With the existing strategies, matching customers' foregoing expectations causes significant economic burdens and ecological disturbances. As a result, e-retailers need to define efficient routing strategies for their last-mile services. This thesis is motivated by identifying efficient routing strategies, in terms of environmental impacts, service time and cost, for last-mile delivery services. We investigate different routing strategies for the last-mile delivery problems, with a focus on same-day services. The corresponding problem is known as the last-mile same-day delivery problem and is dynamic due to the nature of service requests. In the first part, we investigate vehicle and drone integrated delivery systems. We consider an alternative way to integrate drones into conventional vehicle delivery systems, such that drones resupply vehicles with the future orders of customers while vehicles deliver available orders to customers. We evaluate the impact of the drone resupply system based on a case of the problem in which a single vehicle and a single drone are dedicated to the service area. We introduce a mixed-integer programming model for the delivery problem with known requests. For the dynamic problem in which the requests reveal dynamically throughout the horizon, we propose a periodic reoptimization algorithm as a solution approach. We compare the performance of the drone resupply system to the conventional vehicle only delivery systems over several practical instances that differ in terms of customer preferences and system settings. Through computational experiments, we showed that the drone resupply system outperforms the conventional system with respect to operational time, cost and carbon emissions levels. In the second part of the thesis, we evaluate the impact of outsourcing strategy in a multi-period delivery problem. Given the relevance of the problem in practice, we suggest that exploitable stochastic information might be gathered for the dynamically revealed information. To the best of our knowledge, we are the first to introduce outsourcing in the literature of dynamic multi-period vehicle routing problems with probabilistic information. We model the corresponding problem as a Markov decision process. We propose a multi-stage programming model and a progressive hedging algorithm to solve the decision problems. We evaluate several planning strategies to evaluate the impact of postponement and outsourcing decisions. Based on the computational experiments, we determined the best delivery strategy in terms of cost over different practical settings

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