Bin Packing Problem with uncertainty on item availability: an application to Capacity Planning in Logistics

Most modern companies are part of international economic networks, where goods are produced under different strategies, then transported over long distances and stored for variable periods of time at different locations along the considered network. These activities are often performed by first consolidating goods in appropriate bins, which are then stored at warehouses and shipped using multiple vehicles through various transportation modes. Companies thus face the problem of planning for sufficient capacity, e.g., negotiating it with third party logistic firms (3PLs) that specify both the capacity to be used and the logistical services to be performed. Given the time lag that usually exists between the capacity-planning decisions and the operational decisions that define how the planned capacity is used, the common assumption that all information concerning the parameters of the model is known is unlikely to be observed. We therefore propose a new stochastic problem, named the Variable Cost and Size Bin Packing Problem with Stochastic Items. The problem considers a company making a tactical capacity plan by choosing a set of appropriate bins, which are defined according to their specific volume and fixed cost. Bins included in the capacity plan are chosen in advance without the exact knowledge of what items will be available for the dispatching. When, during the operational phase, the planned capacity is not sufficient, extra capacity must be purchased. An extensive experimental plan is used to analyze the impact that diversity in instance structure has on the capacity planning and the effect of considering different levels of variability and correlation of the stochastic parameters related to items

The Generalized Bin Packing Problem

In the Generalized Bin Packing Problem a set of items characterized by volume and profit and a set of bins of different types characterized by volume and cost are given. The goal consists in selecting those items and bins which optimize an objective function which combines the cost of the used bins and the profit of the selected items. We propose two methods to tackle the problem: branch-and-price as an exact method and beam search as a heuristics, derived from the branch-and-price. Our branch-and-price method is characterized by a two level branching strategy. At the first level the branching is performed on the number of available bins for each bin type. At the second level it consists on pairs of items which can or cannot be loaded together. Exploiting the branch-and-price skeleton, we then present a variegated beam search heuristics, characterized by different beam sizes. We finally present extensive computational results which show a high accuracy of the exact method and a very good efficiency of the proposed heuristics

Urban Logistics in Amsterdam: A Modal Shift from Roadways to Waterway

The efficiency of urban logistics is vital for economic prosperity and quality of life in cities. However, rapid urbanization poses significant challenges, such as congestion, emissions, and strained infrastructure. This paper addresses these challenges by proposing an optimal urban logistic network that integrates urban waterways and last-mile delivery in Amsterdam. The study highlights the untapped potential of inland waterways in addressing logistical challenges in the city center. The problem is formulated as a two-echelon location routing problem with time windows, and a hybrid solution approach is developed to solve it effectively. The proposed algorithm consistently outperforms existing approaches, demonstrating its effectiveness in solving existing benchmarks and newly developed instances. Through a comprehensive case study, the advantages of implementing a waterway-based distribution chain are assessed, revealing substantial cost savings (approximately 28%) and reductions in vehicle weight (about 43%) and travel distances (roughly 80%) within the city center. The incorporation of electric vehicles further contributes to environmental sustainability. Sensitivity analysis underscores the importance of managing transshipment location establishment costs as a key strategy for cost efficiencies and reducing reliance on delivery vehicles and road traffic congestion. This study provides valuable insights and practical guidance for managers seeking to enhance operational efficiency, reduce costs, and promote sustainable transportation practices. Further analysis is warranted to fully evaluate the feasibility and potential benefits, considering infrastructural limitations and canal characteristics

Capacity Planning with Uncertainty on Contract Fulfillment

This paper focuses on the tactical planning problem faced by a shipper which seeks to secure transportation and warehousing capacity, such as containers, vehicles or space in a warehouse, of different sizes, costs, and characteristics, from a carrier or logistics provider, while facing different sources of uncertainty. The uncertainty can be related to the loads to be transported or stored, the cost and availability of ad-hoc capacity on the spot market in the future, and the availability of the contracted capacity in the future when the shipper needs it. This last source of uncertainty on the capacity loss on the contracted capacity is particularly important in both long-haul transportation and urban distribution applications, but no optimization methodology has been proposed so far. We introduce the Stochastic Variable Cost and Size Bin Packing with Capacity Loss problem and model that directly address this issue, together with a metaheuristic to efficiently address it. We perform a set of extensive numerical experiments on instances related to long-haul transportation and urban distribution contexts and derive managerial insights on how such capacity planning should be performed

Problema generalizado del empaquetamiento de contenedores: una comparación entre diferentes métodos de solución

Objetivos y método de estudio: ´ El objetivo general de esta tesis es analizar modelos de propagación de restricciones para el problema generalizado del empaquetamiento de contenedores. El problema generalizado de empaquetamiento de contenedores consta de dos clases de objetos que deben ser empacados, los obligatorios y los no obligatorios. Cada objeto tiene un beneficio por ser empaquetado y un volumen. Los contenedores tienen un costo por uso y una capacidad que no debe ser excedida. El modelo de flujo en redes es uno de los mejores métodos resolviendo los problemas Bin Packing. Por ello utilizaremos este modelo para evaluar el desempeño de los modelos a ser resueltos por propagación de restricciones

Diseño de tamaño de empaque y embalaje óptimo de productos de consumo masivo, por medio de algoritmos genéticos, teniendo en cuenta los costos logísticos de salida: caso de una empresa colombiana

Diseño del tamaño del empaque y embalaje para una línea de productos de características homogéneas, a fin de minimizar los costos logísticos de salida. Se realizaron dos métodos de solución: un modelo matemático y una herramienta metaheuristica. El modelo matemático nos arrojo una solución relajada, por medio del software Lp-Solve, lo cual da una aproximación a la situación actual de la empresa. Por otro lado, el modelo metaheuristico, nos arroja una solución optima para resolver el problema que presenta la empresa ABC, ya que el software utilizado, Microsoft Excel, permitió resolver el problema a gran escala, mientras que el software Lp-Solve, permitió una solución con un numero mínimo de candidatos (inner y outer packs) y con una respuesta ineficienteIngeniero (a) IndustrialPregrad

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