ABSTRACT. In 2021, the maritime sector’s energy consumption relied on 99.9% fossil fuels, generating an estimated global well-to-wake emission exceeding one billion tonnes of CO₂e. Despite a decade of strong governmental and industry focus on decarbonization, the maritime energy transition has barely begun in practice. A few pioneering projects have demonstrated the technical feasibility of switching to green alternatives, but high costs and risks currently deter most shipowners. While regulations and carbon pricing could accelerate the adoption of alternative energy carriers, governing a global sector without triggering unintended shifts in trade patterns and value chains remains challenging. Recently, the EU and the International Maritime Organization (IMO) have introduced important regulatory frameworks that are expected to drive future uptake. Nevertheless, the IMO’s 2030 target calls for a 40% reduction in emissions, while the projected adoption of green energy by that date remains limited to just 5–10%. This gap highlights the urgent need to reduce energy consumption—through measures such as improved operational planning—alongside the development of green energy value chains to enable a true maritime energy transition.

Given the diversity of shipping segments, there is no universal pathway to decarbonization. This presentation focuses on a specialized yet significant segment within offshore oil and gas logistics: Platform Supply Vessels (PSVs), which transport essential supplies to offshore installations—such as those operating on the Norwegian continental shelf. Using optimization models and methods, we first analyze and demonstrate how improved operational planning—such as weather-dependent routing, speed optimization, and enhanced industry collaboration—can reduce energy consumption and costs in this segment by approximately 30%. We then present a phased fleet renewal strategy incorporating new fuels and technologies, along with an assessment of the associated costs.

ABSTRACT. Container drayage (i.e., the short-distance transport of containers between ports, depots, and customer sites) plays a significant role in maritime and intermodal logistics. Despite covering a limited geographical range, it often accounts for up to 40% of total transport costs. Conventional models for container drayage rely on full-truckload pickup and delivery assumptions, resulting in inefficient truck utilization and a high proportion of empty trips.

This work introduces the Container Drayage Problem with Fractional Loads (CDPFL), a novel extension of the Vehicle Routing Problem, which incorporates time windows, backhauling, multi-trip scheduling, clustered customer demands, and the possibility of sharing container capacity across multiple orders. These additions allow for more flexible and efficient use of truck and container resources and align with recent efforts to reduce congestion around ports and promote more sustainable use of transport assets. The goal is to minimize total travel costs while optimizing truck capacity, reducing empty movements, and satisfying customer requests on time.

We formulate the problem as MILP and, due to its complexity, we propose a constructive heuristic for fast initial solutions and a metaheuristic to improve solution quality, particularly under shared load arrangements. Numerical experiments on scenarios considering different shared-load configurations show that incorporating fractional load with multi-trip routing significantly reduces travel costs and empty truck movements, and simplifies computation. This is beneficial for port and hinterland operators aiming for efficiency. Though regulations are pending (e.g. liability, coordination), it supports ICCL’s focus on collaborative and sustainable logistics by exploring new operational modalities, tackling inefficiencies in container transport, and forming a basis for more integrated and responsive drayage operations in maritime supply chains.

ABSTRACT. Container terminals play an important role in the global logistic networks working as intermodal interfaces for both import and export containers that are transferred from the vessels to the hinterlands thanks to trains and trucks and vice versa. Due to the increasing throughputs in container terminals, congestion must be reduced to keep promising efficiency. Many works have focused on the congestion of material handling equipment during the processes in the seaside or yard area of container terminals, but have paid less attention to the congestion appeared in the landside area caused by heavy flows of trucks. To mitigate the long queues in the peak hours and avoid congestion outside and inside the terminal, we introduce a truck appointment system (TAS) ([1], [2]), together with the possibility to use a new infrastructure, known as a buffer area, outside the container terminal. The focus in this work is the evaluation of the different strategies for implementing the TAS, the slots and their capacity and different policies for truck delay management. We perform our analysis and evaluation by establishing a deterministic flow-based model with a variant of the Time-Space Network, called the Operation-Time-Space Network (OTSN) [3]. We implemented the OTSN since it enables the application of capacity constraints that can apply to a single activity, multiple activities, or the entire network, as well as more specific temporal constraints, such as exact times or time windows for the start and/or end of an activity, or maximum dwell time for trucks/containers (i.e., trucks/containers cannot remain in a specific area or node for longer than a specified limit). The innovative aspect of this study lies in the integration of the TAS with the reorganization of the intermodal network connecting the hinterland to the terminal. Thanks to the OTSN, we are able to represent a portion of the intermodal network inside and outside the terminal, permitting us to evaluate how different management strategies adopted at terminal level impact the whole network. Moreover, the OTSN can also be used for monitoring the effects of changes in the network, a new infrastructure, a different capacity of an existing one, are some examples of possible scenarios. The main aim is to optimize the flows, by minimizing the dwell time, by assuring low environmental impacts, by maximizing the service level. These analyses are based on a network that involves a port area in the Ligurian region, Italy. We will present extensive computational experiments for evaluating different scenarios. Real instances derived from the port area under investigation have been analyzed.

References: [1] Xu B, Liu X, Yang Y, et al. Optimization for a multi-constraint truck appointment system considering morning and evening peak congestion[J]. Sustainability, 2021, 13(3): 1181. [2] Sun S, Zheng Y, Dong Y, et al. Reducing external container trucks’ turnaround time in ports: a data-driven approach under truck appointment systems[J]. Computers & Industrial Engineering, 2022, 174: 108787. [3] D. Ambrosino, V. Asta. (2021) An innovative operation-time-space net- work for solving different logistic problems with capacity and time constraints. Networks, 78 (3), 350-367.

Funding: This work has been partially supported by the PNRR project Ecosystem RAISE (Robotics and AI for Socio-economic Empowerment)—CUPD33C22000970006—UNIGE: SPOKE 4—Sustainable Ports.

ABSTRACT. One aim of efficient operations planning for shipping terminals is to keep vessel turnaround time to a minimum. This study focuses on the case of roll-on roll-off (RoRo) shipping. RoRo terminals and their heterogeneous cargo have unique complexities compared to container terminals, but they have been largely overlooked in past research. However, this study’s methodology can also be transferred to any other type of terminal. Vessel turnaround time depends on several sub-processes running in series or parallel, including stevedoring, i.e., the unloading and loading of goods. This determines the vessel service time (VST) at the berth. If the service is delayed and turnaround time grows, the vessel must increase its sailing speed to still reach its destination on time, resulting in higher emissions. Hence, terminal operators and researchers may aim to minimize the VST by optimizing the stevedoring process. Terminal operators are also interested in real-time information on the remaining service time, which primarily determines the estimated time of departure (ETD). Correctly anticipating the ETD facilitates efficient online berth planning, thereby avoiding congestion within the terminal and at the shore. Reliable ETDs also support planning activities related to shore power systems: In preparation for sailing, the vessel’s engines must be pre-heated before departure. Starting them too late results in unnecessary stay time at the berth. In contrast, starting them too early leads to vessel engine running times at the berth, resulting in increased fuel consumption and emissions. Predicting a reliable ETD is, therefore, a critical task in terminal operations management that is becoming increasingly relevant. However, existing research on methods to predict the ETD using real-time information on terminal operations is scarce. This study tackles both aspects of terminal operations by (i) (re-)planning the stevedoring process online and (ii) predicting the ETD using real-time information. For this, it considers a roll-on roll-off (RoRo) terminal that is controlled by a digital twin (DT), which mirrors the (pseudo-)analog system in real-time. The effectiveness of planning, forecasting, and decision-making through a DT hinges on factors such as the cost-intensive quality of data and software. This study conducts a sensitivity analysis to address the practically motivated question of how much validity and granularity a DT requires in practice. To explore this, it systematically manipulates the DT’s assumptions about the analog stevedoring process and the DT’s updating and replanning of stevedoring frequencies.

ABSTRACT. Seaports, as major energy consumers, are increasingly adopting energy management systems to address rising energy costs and meet sustainability goals. Many ports are transitioning from carbon-intensive fuels to electricity and alternative energy sources. This paper proposes a mixed-integer linear programming model and an exact algorithm to support integrated planning and energy management for seaports operating with a multi-energy port microgrid. The planning component of the model determines equipment allocation and schedules ship berthing times, directly influencing the port’s hourly energy demand. The energy management component optimises the balance between energy supply and demand by considering different pricing schemes, bidirectional energy trading between the utility grid and multiple energy sources, and the use of energy storage systems. The results demonstrate that implementing smart grid technologies through port microgrids can lead to significant cost savings.

ABSTRACT. Accurate estimation of order fulfillment time is critical for e-commerce logistics, yet traditional rule-based approaches often fail to capture the inherent uncertainties in delivery operations. This paper introduces a novel framework for distributional forecasting of order fulfillment time, leveraging Conformal Predictive Systems and Cross Venn-Abers Predictors---model-agnostic techniques that provide rigorous coverage or validity guarantees. The proposed machine learning methods integrate granular spatiotemporal features, capturing fulfillment location and carrier performance dynamics to enhance predictive accuracy. Additionally, a cost-sensitive decision rule is developed to convert probabilistic forecasts into reliable point predictions. Experimental evaluation on a large-scale industrial dataset demonstrates that the proposed methods generate competitive distributional forecasts, while machine learning-based point predictions significantly outperform the existing rule-based system-achieving up to 14% higher prediction accuracy and up to 75% improvement in identifying late deliveries.

ABSTRACT. Accurately estimating the impact of road maintenance schedules on traffic conditions is important because maintenance operations can substantially worsen congestion if not carefully planned. Reliable estimates allow planners to avoid excessive delays during periods of roadwork. Since the exact increase in congestion is difficult to predict analytically, traffic simulations are commonly used to assess the redistribution of the flow of traffic. However, when applied to long-term maintenance planning involving many overlapping projects and scheduling alternatives, these simulations must be run thousands of times, resulting in a significant computational burden. This paper investigates the use of machine learning-based surrogate models to predict network-wide congestion caused by simultaneous road renovations. We frame the problem as a supervised learning task, using one-hot encodings, engineered traffic features, and heuristic approximations. A range of linear, ensemble-based, probabilistic, and neural regression models is evaluated under an online learning framework in which data progressively becomes available. The experimental results show that the Costliest Subset Heuristic provides a reasonable approximation when limited training data is available, and that most regression models fail to outperform it, with the exception of XGBoost, which achieves substantially better accuracy. In overall performance, XGBoost significantly outperforms alternatives in a range of metrics, most strikingly Mean Absolute Percentage Error (MAPE) and Pinball loss, where it achieves a MAPE of 11% and outperforms the next-best model by 20% and 38% respectively. This modeling approach has the potential to reduce the computational burden of large-scale traffic assignment problems in maintenance planning.

ABSTRACT. In order to address the increasing regulatory pressure on reducing environmental impact and transport emissions, the truck-based freight transport sector must shift its focus from conventional diesel-powered trucks to battery-electric trucks. This introduces challenges for planners, who must now account for battery limitations and strategically schedule recharging stops within delivery routes. In this research, we develop an anticipative decision-making strategy for simultaneous routing and charging of electric trucks in a realistic variant of the dynamic stochastic electric vehicle routing problem. Using real-world data on stochastic travel speeds, electric truck energy consumption and fluctuating energy prices, we create an accurate representation of modern logistics operations. To navigate the complex interdependencies of the problem, we propose a heuristic that leverages the approximating capabilities of a neural network within an approximate dynamic programming framework (ADP-NN) for solving the problem. While the current ADP-NN implementation does not yet outperform simpler greedy methods, numerical analyses show that it is both scalable and responsive to development, indicating strong potential for further improvement.

ABSTRACT. Online Delivery Platforms (ODPs) have reshaped the food delivery landscape by enabling real-time, large-scale logistics coordination. A central operational challenge in ODPs is accurately forecasting short-term customer demand, which is essential for efficient driver dispatching and service quality. This study investigates the effectiveness of various machine learning models—Random Forest, XGBoost, LightGBM, and LSTM—at forecasting food delivery demand across 15-minute, 1-hour, and 6-hour intervals. Using real-world order data enriched with weather and calendar features. Exploratory analysis reveals strong temporal patterns in demand, highlighting the importance of time-aware and feature-rich forecasting methods. The results offer actionable insights for improving operational responsiveness in dynamic delivery environments.

ABSTRACT. Efficient freight transportation planning is crucial for large-scale logistics operations, where demand fluctuations and fleet constraints require sophisticated optimization strategies. This study presents a real-world routing application designed to optimize the distribution network of a major logistics company handling 33,000 sales points across five workdays. The problem is formulated as a Large-Scale Heterogeneous Fleet Balanced Vehicle Routing Problem with Time Windows.

The logistics company operates between 105 and 140 trucks (6200 kg capacity) and up to 15 vans (1500 kg capacity) per day, dynamically adapting to fluctuating daily demand levels ranging from 300,000 kg to 1.5 million kg. The company needs to operate its fleet in two different ways: for both low-load and high-load scenarios. On low-load days, trucks complete one trip per shift, while vans operate up to two trips per shift. On high-load days, trucks can do two trips per shift, and vans up to three, with an added objective of minimizing second trips.

Our model integrates multiple constraints: vehicle capacities, TW, delivery zone; and optimizes several objective functions in a hierarchical manner: (i) total traveled distance minimization, (ii) reduction of overlapping routes, (iii) minimization of visited delivery zones, and (iv) load balancing across the fleet (but only for low-load demands).

Computational results indicate significant improvements with respect to historical manual plannings in route efficiency (reductions in total traveled distance, balanced vehicle usage, overlapping…). The algorithm's effectiveness is validated under both low-load and high-load conditions, showcasing its robustness in managing complex transportation demands. This work contributes to the practical application of VRP heuristics by bridging theoretical approaches with real-world logistics challenges. The proposed methodology offers a scalable solution for large-scale transportation networks, providing insights into optimizing fleet allocation, reducing operational costs, and enhancing service reliability.

References: 1. Cavaliere, F., Accorsi, L., Laganà, D., Musmanno, R., & Vigo, D. (2024). An efficient heuristic for very large-scale vehicle routing problems with simultaneous pickup and delivery. Transportation Research Part E: Logistics and Transportation Review, 186, 103550. 2. Accorsi, L., & Vigo, D. (2021). A fast and scalable heuristic for the solution of large-scale capacitated vehicle routing problems. Transportation Science, 55(4), 832-856. 3. Zhang, J., Luo, K., Florio, A. M., & Van Woensel, T. (2023). Solving large-scale dynamic vehicle routing problems with stochastic requests. European Journal of Operational Research, 306(2), 596-614. 4. Tiwari, K. V., & Sharma, S. K. (2023). An optimization model for vehicle routing problem in last-mile delivery. Expert Systems with Applications, 222, 119789.

ABSTRACT. Urban freight transportation contributes substantially to congestion, pollution, and inefficiencies in urban mobility systems. To mitigate these adverse effects, policymakers are increasingly exploring incentive-based mechanisms that promote the adoption of sustainable transportation modes, such as inland waterways and rail-based scheduled services. The effectiveness of such policies critically depends on the strategic interactions among multiple decision-making agencies.

This study proposes a multi-agency game-theoretic framework to analyze incentive-based urban freight policies involving three key agencies: transportation authorities, logistics service providers (LSPs), and end customers. The model captures the interdependence among regulatory interventions, LSP logistics and pricing decisions, and customer choice behavior. Specifically, we consider an urban context where the transportation authority levies road usage taxes and subsidizes scheduled modes to alleviate congestion and emissions. LSPs respond by optimizing routing and pricing strategies, while customers make service selections based on a utility-maximizing logit model that accounts for price, frequency, mode preferences, and reliability.

We develop a bilevel game-theoretic structure: the upper-level models the authority’s decision problem—setting road tax rates and scheduled service subsidies under a limited budget—while the lower-level captures market equilibrium among LSPs and customers. LSPs maximize profit by selecting transportation modes and setting prices; customers respond via a discrete choice model. We consider both cooperative and competitive interactions among LSPs, exploring outcomes under different market structures such as Nash and Stackelberg equilibria.

The objective of this research is to develop a comprehensive game-theoretic framework that jointly models the strategic behavior of transportation authorities, LSPs, and customers. The transportation authority aims to minimize congestion and emissions by setting a per-unit road tax and subsidizing scheduled services through a subsidy rate, constrained by a total available budget. Additional subsidies must be financed by revenue generated from road access taxes. LSPs aim to maximize profits by choosing transportation modes (road vs. scheduled services) and determining pricing strategies, considering both regulatory signals and market competition. Customers select among competing LSPs or opt out of the service, based on a utility function incorporating price, frequency, delivery time windows, reliability, and mode preferences, etc.

The proposed multi-agency game-theoretic model provides a structured approach to analyze the impacts of incentive-based logistics policies in urban freight systems. By capturing the interactions between authorities, LSPs, and customers, the model offers insights into how regulatory mechanisms can be aligned with market behavior to achieve sustainable and efficient urban logistics.

ABSTRACT. Two echelon logistics systems support sustainable urban freight by integrating heterogeneous modes such as inland waterways and land vehicles. Integrated water- and land-based transportation (IWLT) systems employ vessels for bulk transport and light electric freight vehicles (LEFVs) for last-mile delivery, thereby enhancing cost efficiency, reducing environmental externalities, and alleviating urban congestion.

However, to remain competitive, such multimodal systems require precise spatiotemporal synchronization across echelons at transshipment points (such as satellites), especially when no storage is available to buffer cargo. Additionally, uncertainty in transshipment operations at satellites, resulting from factors such as regional traffic or variable transshipment processing times, can cause delays that propagate through downstream operations, thereby undermining the reliability of a transportation plan.

Although the literature has addressed uncertainties in single-echelon routing, including stochastic travel times, cost variability, and delays, stochasticity in the two-echelon multi-trip vehicle routing problem with satellite synchronization (2E-MVRP-SS) remains underexplored, especially in storage-constrained urban settings.

In this study, we address transshipment time uncertainty within the context of city logistics to improve service reliability through a two-echelon modeling framework. We extend a deterministic IWLT model from the literature, which assumes constant transshipment times and minimizes total operational costs at both echelons, by adding an objective to reduce customer inconvenience, modeled as resulting from upstream delays.

We model the routing problem as a two-stage stochastic optimization program with mixed integer recourse and solve it using an L-shaped algorithm with Bender's logical cuts to accelerate convergence. In the first stage, we solve a multi-depot, multi-trip vehicle routing problem with time windows (MDMVRPTW) at pickup points to determine LEFV routes and assign adequate transfers. In the second stage, we solve a VRPTW on the waterway network, where vessels synchronize transfers with LEFVs under probabilistic (scenario-based) transshipment delays. The algorithm alternates between these two stages, adding logical cuts to the master problem after each recourse solution until convergence is achieved.

We assess the model on instances with four satellites and ten pickup locations in clustered, random, or randomly clustered patterns. Delay scenarios sample stochastic transshipment-time variability and show decreasing variance as the sample size grows. Across all instances, the stochastic model reduces expected total cost by 37% compared to the deterministic baseline.

ABSTRACT. In this work, we propose a restless bandit framework for modeling stochastic stock replenishments commonly encountered in vendor-managed inventory systems, with the objective of minimizing the expected discounted costs over an infinite horizon. Mathematical expressions for the expected one-period costs and transition probabilities are derived, considering different types of stocking units. Motivated by extensive evidence on the near-optimality of index policies, we focus on computing the Whittle index for large-scale inventory systems by implementing two different algorithms from the literature, one is a tailored algorithm for inventory replenishments and the other is a general-purpose algorithm. To rigorously assess their viability in practical applications, we conduct a suite of exhaustive numerical experiments that benchmark both algorithms in terms of their runtime and memory requirements. The experimental findings highlight the trade-offs between computational performance and implementation flexibility, offering critical insights into the selection of an appropriate algorithm for real-world inventory management. In addition, we compare Whittle’s index policy with off-the-shelf heuristic policy based on linear programming in terms of both computational and cost performance.

ABSTRACT. Onshore power supply (OPS) is a critical measure for achieving port decarbonization, especially under regulatory mandates requiring container and passenger vessels to connect to onshore electricity while at berth by 2030. However, existing OPS demand estimation approaches often lack hourly resolution and fail to incorporate interpretable operational features. This study proposes a regression-based framework for predicting hourly OPS energy demand using port call data and other ship characteristics. By segmenting each vessel’s port stay into operational phases, such as pre-handling, cargo operations, and post-handling periods, we estimate hourly OPS demand under realistic consumption rules. The study designs two input feature settings: a Full-Insight set using full information obtained from historical data and an Operational-Planning set simulating real-time pre-arrival information. We train Random Forest and XGBoost models to predict hourly OPS demand profiles and assess their performance using MAE, RMSE, and R^2 scores. The two models demonstrate strong predictive capability, particularly when comprehensive features are available. On the test set, the best XGBoost model achieved an MAE of 113.36 kWh, RMSE of 484.25 kWh and an R2 of 0.96. Feature importance analysis using SHAP highlights auxiliary engine power, and handling durations as dominant contributors to OPS demand. The proposed approach provides an interpretable tool for forecasting OPS load profiles and supports OPS deployment and port energy management.

ABSTRACT. Improved coordination between shipping lines and terminals through speed optimization is a candidate measure to reduce fuel emissions in the international shipping industry, according to the International Maritime Organization. To quantify the potential benefits of this instrument, we integrate speed optimization in the berth allocation problem in a dynamic, rolling-horizon setting. Before our simulation runs, we determine a tactical-level baseline schedule, in which each vessel is assigned a time slot and berthing location. We propose two variants of speed optimization: one where the baseline order of service and berthing locations are unchangeable and one where they can be changed. If speeds can be adjusted during the last 1,500 nautical miles of sailing, we find that speed optimization can result in a 4% to 6% reduction in total cost. However, while deadline violation cost is reduced, fuel usage increases. Besides quantifying the benefits, we introduce a system of sanctions and compensation through which the cost savings are distributed fairly across vessels and which ensures that both the terminal and ships profit.

ABSTRACT. Efficient and timely vessel arrival planning is crucial for smooth operations in maritime transportation networks, ensuring optimal resource utilization and minimizing operational costs. When proforma schedules are disturbed by arrival deviations of vessels, waiting time and unnecessary fuel consumption become problems that shipping lines are faced with. Using a simulation model of a single-berth terminal, we test speed selection strategies for vessels that aim to minimize fuel, sailing, and waiting costs under varying availability of information. In different scenarios, we find optimality gaps ranging from 0.1% to 19.6% and show that knowing and communicating service end-time to the vessel calling next could be valuable to integrated shipping lines and terminals.

ABSTRACT. Ports are pivotal to global supply chains. However, they are confronted with numerous challenges related to increased vessel sizes and numbers, uncertain weather conditions, and congestion. This leads to significant waiting times as well as related costs and emissions of vessels calling ports, highlighting the importance of optimizing port calls in collaboration with all involved parties. In this work, we use a literature review and semi-structured interviews with experts from 20 ports around the world, to frame the adoption of collaborative port call optimization (PCO) measures. We extend the Technology-Organization-Environment (TOE) framework to include the dimension of inter-organizational arrangements. We identify and categorize preconditions for collaborative PCO adoption into technology, organizational, external environment, and inter-organizational aspects. This framework recognizes the complexity of collaborative PCO adoption by diverse stakeholders within the port call ecosystem. The extended framework allows inter-organizational innovations to be addressed explicitly and can be used to support PCO processes in strategic port management practice.

ABSTRACT. Many logistics platforms enable collaboration between agents to reduce costs, but determining fair pricing remains challenging when agents have pre-existing partnerships. This paper introduces a cooperative game theory framework to model platform-mediated collaboration, modeling the platform as an additional player. We present a novel characteristic function that distinguishes between partial collaborations (existing relationships) and full collaborations (platform-enabled). Using Shapley value, we derive fair cost allocations and platform charges that reflect each participant's contribution. We address stability concerns through an optimization model that minimizes platform subsidies while preventing profitable deviations. The framework is demonstrated through an application in freight forwarding for Less-than-Container Load(LCL) consolidation, showing how it balances participant incentives with platform revenue across varying collaboration structures and network sizes.

ABSTRACT. This paper addresses a collaborative version of the Truck Dispatching Problem for a consortium of logistic service providers. A key challenge in this domain is reducing the prevalence of empty truck trips, avoiding wasted mileage and energy. While collaboration among service providers can significantly reduce such inefficiencies, it is hindered by the need to protect commercially sensitive data. To overcome this, we propose a secure method using Secure Multi-Party Computation that enables multiple service providers to jointly optimize truck dispatching without revealing proprietary information. Our approach consists of three main steps: a secure computation of a cost matrix for all possible pickup and delivery combinations; a novel secure adaptation of the Hungarian algorithm to combine pickups and deliveries into trips efficiently; and an efficient distribution of these trips to trucks. We demonstrate that our modified Hungarian algorithm significantly reduces the number of costly cryptographic operations. We implement the 3-step approach into a single pipeline, and briefly evaluate the results.

ABSTRACT. Synchromodal transportation is a resilient freight paradigm that dynamically selects and switches among road, rail, and inland waterway transport modes in response to real-time operational conditions, thereby improving service reliability and reducing total system cost. Implementing such flexibility requires stitching together the heterogeneous networks of multiple operators to form a door-to-door transport plan. However, two key challenges arise. First, operators manage their own networks and safeguard commercially sensitive information such as capacity and cost, limiting the platform’s access to critical data. This information asymmetry makes it difficult for the platform to construct a globally optimal transport plan. Second, the platform coordinator and the operators, although both aiming to maximize profit, face misaligned economic objectives due to differences in cost responsibility. We consider a scenario in which the platform commits to a delivery-time guarantee for every request, while operators bill the platform a standard rate that depends only on the origin–destination pair. Under this assumption, the platform bears the cost of delivery delays and therefore prefers more reliable or faster transport modes. Operators, by contrast, face no delay penalties and thus seek to minimize their own transport costs—even at the risk of lateness. To align these divergent interest, the platform must introduce explicit economic levers—targetted subsidies—that coax operators toward routes that remain profitable for them yet sufficiently punctual for the platform.

We study this transport planning problem from the platform’s perspective under decentralized setting and incomplete information, in which the platform decomposes door-to-door container shipments into individual legs and subcontracts each leg to an autonomous multimodal operator. The platform also offers targetted monetary subsidies that nudge operators toward decisions that better align with platform objectives.

In the literature, existing multimodal transportation planning problems mostly assume a centralized, omniscient planner—despite substantial evidence that full network visibility is rarely feasible. Some studies assume a decentralized platform and propose algorithms to coordinate the involved parties without requiring the exchange of commercially sensitive information. However, these approaches lack explicit economic incentives to align all participants, making them less feasible in practice. To address this gap, we are the first to propose the Incentive-Based Decentralized Synchromodal Transport Planning Problem, formulated as a Bi-level mixed-integer program that embeds a one-shot, request- and service-specific subsidy into standard freight subcontracts. The upper level (platform) decides on order acceptance, leg-to-operator assignments, and subsidies to maximize its expected profit. The lower level (each operator), acting independently, selects routing plans to minimize its own cost. This mechanism steers self-interested operators toward platform-beneficial decisions without requiring disclosure of commercially sensitive information.

ABSTRACT. All nations in the world were under tremendous economic and logistical strain as a result of the advent of COVID-19. Early in the pandemic, distributing antiviral treatments such as Paxlovid posed a significant challenge. Further complicating this effort were logistical difficulties stemming from restricted transportation infrastructure and disruptions in international supply chains. In the face of such obstacles, it is critical to prioritize patients’ needs to ensure equitable access to treatment. This work aims to develop a mathematical model that optimizes the distribution of Paxlovid by focusing on mobile delivery routes and resource allocation. The model addresses constraints such as limited supplies, geographic clustering of patient populations, and treatment capacity limitations. It strives to maximize patient outcomes while minimizing the number of untreated high-risk individuals. This study introduces an equitable classification system that categorizes patients into “standard” and “risky” groups based on their clinical backgrounds. Geographic clustering is applied based on factors such as average age and contact rate to better tailor distribution efforts. A comparative analysis between quarantine and non-quarantine scenarios is also incorporated to capture different logistical conditions.

ABSTRACT. Terminals and intermodal carriers run the vast majority of import and export transportation in the world. Due to the involvement of multiple stakeholders, interactions among them trigger a series of chain reactions. Delays in pick-up and delivery by carriers may disrupt the loading and unloading process of vessels at terminals. Meanwhile, delays in vessels arrival and departure at terminals may impact the pick-up and delivery schedules of carriers. Currently, most studies emphasize vertical collaboration across stakeholders within interconnecting transport networks and the horizontal collaboration among carriers through auctions is studied. However, few studies solve the problem involving both horizontal collaborative planning among carriers and vertical collaborative planning between terminals and carriers, which is essential for the coordination between stakeholders in practice. To address the challenges of coordination in intermodal transport, this paper proposes a multi-agent auction-based planning framework that facilitates both horizontal and vertical collaboration. Within the proposed framework, the planning process includes several iterative rounds of interaction between terminal operators and carriers. In each round, the terminal operator first develops a berth and crane allocation plan for arriving vessels. Based on this plan, transportation requests—such as container pick-up and delivery time windows and locations—are generated and forwarded to the hinterland intermodal transport carriers. These carriers participate in an auction process to bid for the transportation tasks. This bidding process fosters horizontal collaboration among carriers, as each evaluates their operational schedules and submits bids reflecting their estimated pick-up times and associated costs. The terminal coordinator collects these bids and sends them back to the terminal operator. If the bids indicate significant deviations from the terminal’s original plan (e.g., high costs or timing conflicts), the terminal may adjust the vessel allocation to better align with hinterland capacity and carrier availability. This forms an iterative feedback loop in which the terminal may revise its resource allocation based on predefined criteria, such as cost thresholds, berth flexibility, or service level requirements, thus achieving vertical coordination across the terminal-hinterland interface. Compared to conventional approaches that consider only horizontal coordination among carriers, the proposed framework significantly mitigates scheduling mismatches and improves end-to-end service fulfillment. Furthermore, we evaluate the system under various decision-making scenarios, demonstrating its adaptability and robustness. The managerial insights derived from our numerical experiments offer practical guidance for real-world implementation, highlighting the value of integrated, multi-agent collaborative planning in complex transport systems.

ABSTRACT. This study addresses the tactical decision-making challenges faced by logistics service providers (LSPs) that periodically supply business customers (e.g., restaurants, hotels, cafes). Customers show distinct preferences for delivery service characteristics, such as price, visit frequency, time of day, and time window length. Leveraging customer preference at a disaggregated level improves the accuracy of service customization and pricing strategies. To this end, we propose a Choice-Based optimization framework that integrates advanced discrete choice models into the Periodic Vehicle Routing and Pricing problem (CB-PVRP).

We formulate the problem as a stochastic bi-level model to optimize the system across multiple objectives. At the upper level, the LSP aims to maximize the total expected profit by strategically setting prices for service options and making personalized recommendations to attract customers. In response, customers at the lower level make choices to accept or reject the recommendation to maximize individual utility. To handle the random term in the utility function, we apply a sample average approximation (SAA) and reformulate the problem as a single-level mixed-integer program. Experimental results show that explicitly incorporating disaggregated customer choice behavior avoids profit overestimation, increases the customer choice probabilities, and improves the estimated total profit.

ABSTRACT. Automated pipe routing is essential in the design of complex piping systems in industries such as shipbuilding, chemical plants, and aerospace engineering. Despite decades of research, the field lacks a standardized set of benchmark instances, with each study relying on its own problem formulations and test cases. This absence of standardized benchmark problems and their formulation makes it challenging to thoroughly compare solution approaches and assess algorithmic performance objectively. In this paper, a structured library of benchmark test problems for automated pipe routing with variable obstacle and search space dimensions is introduced. The library consists of a collection of existing test problems from literature, an automated pipe routing problem generator in which the levels of complexity can be varied, and a general automated pipe routing algorithm. The test instances in the benchmark cover key challenges in pipe routing, including multi-pipe routing. By offering a diverse set of well-defined problem instances, the presented benchmark suite enables systematic evaluation and fosters progress toward more robust and generalizable automated pipe routing methodologies. This work aims to establish a foundation for future research, facilitating meaningful comparisons and accelerating advancements in automated pipe routing.

ABSTRACT. The adoption of sustainable transportation systems is not only an environmental concern but also an economic one, as it reduces energy consumption and maintenance costs, and a social one, as it improves public health and enhances quality of life. Therefore, the rapid proliferation of Electric Vehicles (EVs) among both practitioners and researchers is not a surprising phenomenon. In this paper, we introduce a novel problem called the Speed and Load Dependent Multi-Depot Electric Vehicle Routing Problem with Half-Open Rotations (SLD-MDEVRP-HOR), which considers two conflicting objective functions: minimizing total CO2 emissions and minimizing total tardiness. Distribution operations are performed by a homogeneous fleet of EVs, which can execute multiple routes (rotations) and may return to a depot different from the one they departed from (half-open rotations). We also propose an energy consumption model where consumption depends on both the speed and the load of the EVs. Accordingly, we present a bi-objective mixed-integer linear programming (MILP) formulation and apply the Augmented ε-Constraint (Augmecon) method to generate Pareto-optimal solutions. Experimental studies are conducted using a modified version of a small-sized benchmark dataset from the existing literature, and performance is evaluated using several well-known metrics. Additionally, we carry out a comparative computational experiment that demonstrates the clear superiority of our five-speed-mode configuration over alternative setups with only one or three speed modes.

ABSTRACT. In Japanese logistics, many distributors divide the service area into driver territories. In addition, drivers divide their territories into several subterritories when there is a multiday delivery window. In this study, we analyze how the shape of the territory and the number of territories affect the total delivery distance using a continuous approximation model. We assume that the rectangular service area is divided into rectangular territories by a two-stage guillotine cut and that the same given number of customers is generated uniformly and randomly in each territory. After establishing a routing distance formula, we first calculate the total routing distance according to the length‒width ratio of the territories and the number of customers. As a result, we find that the length‒width ratio of the territory has no significant effect on the routing distance if there are many customers. We also calculate the optimal number of subterritories for drivers. In the actual case, three to five sub-territories are appropriate, but the optimal number of subterritories depends on the time spent at the customer, the average visit cycle, and the number of customers.

ABSTRACT. A classical problem in port operations is the Berth Allocation Problem (BAP). It aims at assigning berth positions and service times to calling ships at a container terminal. Several variants of the problem may be considered depending on the nature of the berths or the information available on ship arrival times.

It is very common for ships to moor in ports on a regular basis. Due to port capacity constraints, multiple decisions need to be made. The Strategic Berth Template Problem (SBTP) combines strategic with operational decisions. The former regard the ships that should be served; the latter regard timing and berthing positions for the service to be provided. This is done for a given set of cyclically calling ships, which provides a template that will be applied in a cyclic fashion in the considered planning horizon. Furthermore, we often find strong transshipment relations between some large mother ships and some smaller feeder ships, which are contractually linked to each other. For this reason, we assume that all the ships within each group must be handled similarly, in the sense that all of them are either served or rejected.

Usually, the arrival time of a ship to a port is not known exactly at planning time. Ignoring this aspect may lead to infeasible plans, which highlights the relevance of integrating uncertainty in the models. The main objective of this work is to extend the results for the SBTP in [1] by considering uncertainty in arrival times. The BAP with uncertainty in arrival time will be called the Robust Berth Template (RSBTP).

The formulation of RBTP in [1] is considered here as the starting point. As a first step, that formulation is extended for a worst-case analysis, thereby providing our first formulation for SSBTP. As usual, this approach leads to very conservative solutions. A less conservative approach can be considered by embedding budget uncertainty as discussed in [2]. The idea is to limit the amount of uncertainty that must be tolerated by a solution. In our work, this is expressed as a set of inequalities, which can be integrated into the main formulation, and can be derived by applying dualization techniques to an auxiliary subproblem.

The instance problems introduced in [3] are extended to include uncertainty to our problem. Extensive computational tests were conducted. The results show the usefulness of our modeling framework. The cost of including uncertainty in the model is analyzed by showing the relationship between the budget uncertainty parameter and waiting times in the case-based analysis.

[1] Fernández, E. and Munoz-Marquez, M. (2022). New formulations and solutions for the strategic berth template problem. European Journal of Operational Research, 298(1):99–117.

[2] Bertsimas, D. and Sim, M. (2004). The price of robustness. Operations Research, 52(1):35–53.

[3] Iris, Ç., Lalla-Ruiz, E., Lam, J., and Voss, S. (2018). Mathematical programming formulations for the strategic berth template problem. Computers & Industrial Engineering, 124:167–179

ABSTRACT. We introduce a problem that extends the scope of berth allocation and quay crane assignment decisions at a container terminal by taking transshipments into consideration. A transshipment is an operation that occurs when one or multiple containers need to be transferred from one vessel to another, which requires the coordination of their berthing times. When a transshipment between two vessels is at risk of being missed due to a delay, two alternatives can be considered: disrupting the vessels' schedules, or transferring the containers to another vessel. The problem is referred to as the Berth Allocation and Quay Crane Assignment Problem with Transshipment Handling (BACAP-TH). A MIP model is formulated, and a matheuristic algorithm is proposed to find feasible solutions. The model and the matheuristic are tested on a novel set of benchmark instances, with runtimes of 10 minutes. Although the MIP model shows superior performance for small instances, it mostly fails at finding feasible solutions to large ones, and when it does not, it is outperformed by the matheuristic in the majority of cases.

ABSTRACT. Maritime trade has undergone serious changes in recent years, which has affected shipping and port operations. Geopolitical tensions and sanctions gave container terminal operators little time to react, pushing them to adjust their operations with the means at hand and to adapt automated processes in the IT systems that run the container terminal. Such a Terminal Operating System (TOS) typically leaves some space for improvement by manually fine-tuning its configuration. The present study explores the potential of fine-tuning such a configuration, focusing on a parameterized container slot allocation heuristic in a simulated environment. In total, nine cases are tested. Traffic profiles are generated based on data from three actual container terminals. For each set of traffic profiles, three layout variants are tested. The results show that in each case, a different configuration has performed best in terms of the average waiting time of terminal trucks at Rubber-Tired Gantry (RTG) cranes, a metric that is nearly perfectly correlated with the average productivity of ship-to-shore cranes in this study. This shows that there is no single optimum in the fine-tuning process of yard operations. In this study, using the best respective configuration of the container slot allocation heuristic, more than 5 percent of waiting times at RTGs are saved compared to the case-specific average, in some instances even more than 10 percent. These findings highlight the importance of fine-tuning parameterized container slot allocation heuristics to the given situation.

ABSTRACT. Berth Allocation Problems (BAP) play an important role in optimizing terminal operations, directly impacting port efficiency, vessel turnaround times, and resource utilization. This study extends the classical BAP by integrating equipment assignment and dual-berthing for cruise vessels into a Mixed-Integer Linear Programming (MILP) model for multi-purpose terminals. Four model variants are developed: a base model, an equipment assignment extension, a cruise berthing extension, and a combined model. The novelty lies in the integration of equipment sequencing and cruise dual-berthing within an integrated MILP framework. A comprehensive computational study is conducted across 54 artificially generated instances, varying numbers of vessels, type compositions, berth capacities, and equipment availability. The results demonstrate that equipment sequencing and cruise berthing significantly increase computational complexity. Equipment assignment introduces challenging sequencing constraints, while cruise berthing affects vessel waiting time more directly. Although the combined model remains computationally feasible across all instances, it struggles to close the optimality gap as the problem size grows.

ABSTRACT. Disruptive events challenge airline operations due to tightly optimized schedules, requiring rapid operational adjustments. Traditional disruption management methods are typically reactive and static. Reactive approaches often lead to suboptimal decisions, as airlines have limited time to respond. In turn, relying on the same static responses may not be effective, as a one-size-fits-all solution rarely suits every disruption. This study proposes a model-based reinforcement learning (RL) approach for aircraft recovery given information on the probability of future disruptions. The aircraft recovery problem is modeled as a Markov decision process, and a solution framework is developed using approximate dynamic programming with value function approximation. Disruptions are represented as aircraft unavailabilities occurring with a fixed probability. The objective is to minimize delays and cancellations while leveraging stochastic information about potential disruptions. This method is evaluated across multiple scenarios with varying disruption levels and operational objectives, and benchmarked against an exact optimization algorithm. Results show that the RL-based proactive strategy outperforms reactive models, particularly in high-utilization, high-disruption settings, and achieves near-optimal solutions with fewer corrective actions. The proposed framework serves as a decision support tool, enabling airline operators to improve resilience by integrating probabilistic forecasts into recovery planning.

ABSTRACT. The Berth Allocation Problem (BAP) has been extensively studied in the elds of operations research and maritime logistics. A major emerging challenge is handling disruptionsparticularly adverse weather conditionsthat signicantly aect the eciency of container terminals. Despite its practical relevance, the impact of weather-related disruptions on the BAP has received limited attention. Moreover, while real-time optimization methods are increasingly applied in port operations, their use under weather-induced uncertainty, especially across dierent sea environments (restricted waters, coastal waters, and open sea), remains underexplored. This paper introduces a novel model and applies Q-Learning, a Reinforcement Learning technique, to solve the BAP under varying weather conditions that influence vessel handling times. Preliminary computational tests show that Q-Learning matches MILP in small instances (avg. waiting time difference < 0.2 hours), but exhibits higher delays in larger cases. Still, the Q-Learning approach executes 20-30 times faster and can support real-time operations.

ABSTRACT. Operation and Maintenance (O&M) of offshore wind farms is challenged by harsh environmental conditions, logistical constraints, and unpredictable component failures. This paper presents a novel framework that formulates O&M planning as a Partially Observable Markov Decision Process (POMDP) and optimizes maintenance decisions using Deep Reinforcement Learning (DRL). The key novelty of this study is the integration of multi-level maintenance actions such as minor, major repairs, and component replacements, informed by probabilistic Remaining Useful Life (RUL) predictions to acknowledge the uncertainty inherent in health monitoring. A Proximal Policy Optimization (PPO) agent is employed to learn an optimal maintenance policy that minimizes overall costs by balancing maintenance expenditures with downtime losses. Simulation results on a 3 turbine offshore wind farm demonstrate that the DRL approach outperforms traditional corrective, age-based, and random maintenance strategies, achieving lower total costs, fewer unexpected failures, and more consistent operational performance.

ABSTRACT. In today’s complex and rapidly evolving supply chains — marked by globalised sourcing, fluctuating transportation conditions, and diverse vendor ecosystems — selecting the appropriate International Commercial Term (Incoterm) for each shipment is a critical decision that influences delivery timelines, cost structures, and supplier accountability. Traditional selection methods often rely on either (1) fixed business rules, typically embedded in procurement policies or contractual norms, or (2) historical shipment patterns. While these approaches offer consistency, they are often ill-suited to dynamic operational contexts shaped by changing vendor performance, geopolitical volatility, and regional infrastructure variability.

Humanitarian supply chains, in particular, demand rapid responsiveness, equitable resource allocation, and contextual sensitivity — needs that traditional models fail to address, especially in regions with poor infrastructure, unreliable vendors, or shifting geopolitical risks.

To overcome these limitations, our research introduces a novel reinforcement learning (RL) framework that learns to select the most suitable Incoterm for each shipment to maximise long-term supply chain performance.

Using a real-world dataset comprising over 38,000 shipment records from USAID's humanitarian supply chain operations, we define an RL environment where the agent observes key shipment attributes such as product type, destination country, vendor, transportation mode, and order volume as its state. The action space consists of discrete Incoterm options (e.g., EXW, FOB, CIF, DDP), while the reward function is designed to reflect downstream logistics success through a combination of metrics such as on-time delivery (OTD), in-full delivery (IFD), lead time, and cost efficiency. We simulate this environment using historical shipment outcomes and train an agent using Proximal Policy Optimisation (PPO), a state-of-the-art policy gradient method well-suited for discrete action spaces and high-dimensional observations. Our evaluation benchmarks PPO against both rule-based heuristics and supervised machine learning baselines, including XGBoost and Random Forest. Results show that PPO improves OTD by 8%, reduces average lead time by 18%, and cuts total cost by 13% compared to the best-performing baseline. To address ethical concerns, the RL policy is trained under constraints to avoid deprioritizing critical or remote shipments, ensuring that efficiency gains do not come at the expense of equity or humanitarian impact. This approach provides a foundation for decision-support systems that move beyond predictive analytics and toward adaptive logistics optimisation. Future directions include extending this framework to multi-agent settings, integrating real-time data sources (e.g., weather or conflict risk), and evaluating policy generalizability across different humanitarian networks and even commercial supply chains. The proposed RL framework demonstrates how AI can support humanitarian logistics planners, procurement officers, and supply chain managers in making more resilient, data-driven decisions under uncertainty, ultimately improving aid delivery efficiency and public health outcomes in resource-constrained environments.

ABSTRACT. We study an integrated project and personnel scheduling problem (IPPSP) faced in the construction industry. Such companies have several ongoing projects simultaneously and often need to commence new projects while executing these projects to ensure enough revenue throughout the year. The relevance of this problem lies in its potential to help construction companies reduce reliance on costly external resources. A main challenge is to make schedules that efficiently utilise internal resources and balance the need for resources during the current scheduling with the need to keep internal resources available for future projects. Imbalances lead to bad utilisation of internal resources and the use of costly external resources. This involves both scheduling activities in one or more projects and allocating the personnel and transportable equipment required to complete the activities. The activities are multi-modal and discretely preemptive, meaning they can be executed in different modes, and interrupted and resumed later. This introduces flexibility in how and when activities are performed but also increases the complexity of the scheduling problem. Furthermore, precedence constraints between activities must be respected, making the coordination of resources and timing more critical.

In this study, we investigate how proactive and reactive strategies can improve the cost-efficiency of the schedule using seven generated instances which are solved with various mathematical programming formulations. These strategies are compared to a naïve scheduling strategy. Our experiments show that tightening the activity time windows after they are scheduled for the first time and including a makespan-related cost yield the best overall results.

ABSTRACT. Order picking is a critical factor influencing the efficiency of non-automated warehouse operations and has long been a focus of both academic and industrial research. However, most existing studies have concentrated on static demand environments, with limited empirical work offering structured and practical solutions for optimizing order picking. This research aims to develop an order picking optimization model that accounts for the interdependence between batching and routing decisions to minimize picker walking distance (or time). A clustering-based approach is proposed, featuring a modified Silhouette index to quantify the association among pick lists. Leveraging this index, a sequential batching and routing optimization model is implemented to reduce travel distance (or time) without increasing the warehouse's operational footprint or staffing requirements. An experimental design is employed to assess the impact of batch size and picking cart capacity on travel distance (or time) reduction. The results demonstrate that the proposed model yields significant improvements in operational efficiency.

ABSTRACT. Manual picking in warehouses remains a dominant and flexible approach in contemporary logistics. Human capabilities allow for particularly flexible and precise operations, but also pose significant ergonomic, physical, and psychological challenges. Most traditional optimization models totally neglect these human-centric issues, focusing primarily on minimizing total time or distance. In this work, we propose a novel modeling framework that integrates picker discomfort into the picker routing decisions. The proposed model is rather generic and can account for multiple dimensions of human discomfort, including fatigue, perceived exertion, and musculoskeletal disorders, under a single notion of instantaneous discomfort, which dynamically evolves over the course of a picking tour.

Precisely, our model assumes that each picking task is categorized with a given level of complexity, based on factors such as the item weight, the packaging, the shelf height, and the accessibility of the item. Performing a picking increases instantaneous discomfort depending on the level of complexity of the task, and the current discomfort level, resulting in non linear phenomena where the accumulation of discomfort generates more instantaneous discomfort. However, the model also allows for recovery, i.e. a decrease in the discomfort, when the picker is walking a reasonable distance between two consecutive pick locations.

To minimize the total accumulated discomfort under such a non-linear discomfort model, we propose a labeling algorithm that systematically explores feasible picking sequences and evaluates discomfort dynamically. Computational experiments on realistic warehouse layouts show that the accumulated discomfort can be significantly reduced over 40% on average with a limited (under 5%) increase in total picking time. The results also highlight the importance of sequencing tasks strategically and exploiting opportunities to not saturate a picker with several complicated tasks in a row and exploit recovery during travel.

ABSTRACT. This study proposes a branch-and-bound algorithm for the dynamic block relocation problem, which arises in container yards, slab yards, and warehouses. Unlike the ordinary block relocation problem that focuses on the efficient retrieval of already stacked blocks, this problem additionally accounts for the dynamic arrival of blocks. While the block relocation problem has been extensively studied, research on the dynamic block relocation problem [1-4] remains limited. In particular, no problem-specific exact algorithm has yet been developed, although several integer programming models have been proposed. To address this gap, we propose a branch-and-bound algorithm for the dynamic block relocation problem to minimize the total delay from scheduled arrival and retrieval times. The problem is formally defined as follows. The storage area (bay) consists of S stacks, each capable of holding up to H blocks. Initially, N0 blocks are stored in the bay, and N1 blocks arrive over time. A total of N=N0+N1 must be retrieved after their departure times. The arrival time and departure time of a block are known in advance and assumed to be distinct. We can perform at most one operation among loading, relocation, and retrieval in each period to load N0 blocks into and retrieve all N blocks from the bay. The loading (resp. retrieval) of blocks must be in ascending order of their arrival (resp. departure) times. Each block is given penalty coefficients for unit delays in loading and retrieval, respectively. The primary objective is to minimize the total delay penalty. As a secondary objective, the number of relocations is also minimized. To solve the dynamic block relocation problem, we develop a branch-and-bound algorithm that seeks an optimal sequence of operations. At each node in the search tree, we apply feasibility checking, dominance rules, and lower bounding to enable pruning and enhance computational efficiency. A beam search algorithm is employed to compute an initial upper bound for the branch-and-bound algorithm. Finally, we conduct numerical experiments to verify the effectiveness of the proposed algorithm.

[1] R.J. Rei and J.P. Pedroso, Heuristic search for the stacking problem, International Transactions in Operational Research, Vol. 19, (2012), pp. 379-395. [2] R.J. Rei and J.P. Pedroso, Tree search for the stacking problem, Annals of Operations Research, Vol. 203, (2013), pp. 371-388. [3] M.H. Akyüz and C.-Y. Lee, A mathematical formulation and efficient heuristics for the dynamic container relocation problem, Naval Research Logistics, Vol. 61, (2014), pp. 101-118. [4] C. Expósito-Izquierdo, E. Lalla-Ruiz, J. De Armas, B. Melián-Batista, J.M. Moreno-Vega, A heuristic algorithm based on an improvement strategy to exploit idle time periods for the stacking problem, Computers & Industrial Engineering, Vol. 87, (2015), pp. 410-424.

ABSTRACT. This paper tackles the challenge of scheduling phosphate pulp transportation through a straight pipeline while concurrently managing inventories to satisfy client demand and optimize water usage within a planning horizon. The problem is inspired by a real industrial case, which focuses on optimizing the transportation of phosphate pulp from mining sites to processing facilities while efficiently managing multiple storage locations. To tackle the scheduling challenge, we formulated a mathematical model grounded in Mixed Integer Linear Programming (MILP). The model adopts a discrete representation of both time and volume to enable precise batch scheduling of product flows through the pipeline. To manage computational complexity, particularly as the planning horizon extends, we incorporated a rolling horizon decomposition strategy. This layered approach allows for iterative decision-making over manageable sub-periods. Our formulation holistically integrates pipeline scheduling with inventory control, simultaneously coordinating the operations of upstream and downstream tank groups to ensure efficient and synchronized product transport. The approach was evaluated using real dataset instances, and the experimental results demonstrate its effectiveness in generating optimal solutions with rational water usage within a reasonable computation time.