Two-Stage Decomposition Algorithms for Single Product Maritime Inventory Routing

We review recent literature pertaining to the maritime inventory routing problem (MIRP), a stimulating, albeit niche, subclass of vendor‐managed inventory problems. MIRPs deal with optimally distributing products with a (typically heterogeneous) vessel fleet between production and consumption ports with inventory tracking and inventory limits. We present two mixed‐integer linear programming models for the MIRP—one based on discrete time, the other based on continuous time—and we discuss the advantages and disadvantages of each of the two modeling approaches. In surveying more than 50 papers spanning the decade 2013–2023, we investigate MIRP variants from many different applications and discuss how these have been modeled and solved. Our purpose is to provide a comprehensive overview of state‐of‐the‐art MIRP research published in this period, collated along multiple dimensions. In addition to providing information about available test instances, we highlight recent trends and interesting avenues for future research. As such, we believe this survey will be useful to students, researchers, and practitioners in this domain.

A single‐product maritime inventory routing problem (MIRP) is studied in which the production and consumption rates vary over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Two discrete time formulations are developed: an original model and a reformulated model that is a pure fixed charge network flow (FCNF) model with side constraints. Mixed integer sets arising from the decomposition of the formulations are identified. In particular, several lot‐sizing relaxations are derived for the formulations and used to establish valid inequalities to strengthen the proposed formulations. Until now, the derivation of models and valid inequalities for MIRPs has mainly been inspired by the developments in the routing community. Here, we have developed a new model leading to new valid inequalities for MIRPs obtained by generalizing valid inequalities from the recent lot‐sizing literature. Considering a set of instances based on real data, a computational study is conducted to test the formulations and the effectiveness of the valid inequalities. The FCNF formulation is generally much stronger than the original formulation. The developed valid inequalities reduce the integrality gap significantly for both formulations. By using a branch‐and‐bound scheme based on the strengthened FCNF formulation, most of our test instances are solved to optimality. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 62(4), 297–314 2013

We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet and multiple production and consumption ports with limited storage capacity. Maritime transportation is characterized by high levels of uncertainty, and sailing times can be severely influenced by varying and unpredictable weather conditions. To deal with the uncertainty, this paper investigates the use of adaptable robust optimization where the sailing times are assumed to belong to the well-known budget polytope uncertainty set. In the recourse model, the routing, the order of port visits, and the quantities to load and unload are fixed before the uncertainty is revealed, while the visit time to ports and the stock levels can be adjusted to the scenario. We propose a decomposition algorithm that iterates between a master problem that considers a subset of scenarios and an adversarial separation problem that searches for scenarios that make the solution from the master problem infeasible. Several improvement strategies are proposed aiming at reducing the running time of the master problem and reducing the number of iterations of the decomposition algorithm. An iterated local search heuristic is also introduced to improve the decomposition algorithm. A computational study is reported based on a set of real instances.

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, present new opportunities for hybrid-optimization algorithms that are hardware accelerated by these devices. In this work, we propose the idea of an Ising processing unit as a computational abstraction for reasoning about these emerging devices. The challenges involved in using and benchmarking these devices are presented and commercial mixed integer programming solvers are proposed as a valuable tool for the validation of these disparate hardware platforms. The proposed validation methodology is demonstrated on a D-Wave 2X adiabatic quantum computer, one example of an Ising processing unit. The computational results demonstrate that the D-Wave hardware consistently produces high-quality solutions and suggests that as IPU technology matures it could become a valuable co-processor in hybrid-optimization algorithms.

A Benders Decomposition-Based Matheuristic for the Cardinality Constrained Shift Design Problem

Given a graph with a weight associated with each vertex , the maximum weighted induced forest problem (MWIF) consists of encountering a maximum weighted subset of the vertices such that induces a forest. This NP‐hard problem is known to be equivalent to the minimum weighted feedback vertex set problem, which has applicability in a variety of domains. The closely related maximum weighted induced tree problem (MWIT), on the other hand, requires that the subset induces a tree. We propose two new integer programming formulations with an exponential number of constraints and branch‐and‐cut procedures for MWIF. Computational experiments using benchmark instances are performed comparing several formulations, including the newly proposed approaches and those available in the literature, when solved by a standard commercial mixed integer programming solver. More specifically, five formulations are compared, two compact ones (i.e., with a polynomial number of variables and constraints) and the three others with an exponential number of constraints. The experiments show that a new formulation for the problem based on directed cutset inequalities for eliminating cycles (DCUT) offers stronger linear relaxation bounds earlier in the search process. The results also indicate that the other new formulation, denoted tree with cycle elimination (TCYC), outperforms those available in the literature when it comes to the average times for proving optimality for the benchmark instances with up to 81 vertices. Additionally, this formulation can achieve much lower average times for solving the larger random instances that can be optimally solved. Furthermore, we show how the formulations for MWIF can be easily extended for MWIT. Such extension allowed us to analyze the difference between the optimal solution values of the two problems when considering different classes of graphs.

We consider an inventory routing problem (IRP) in the liquefied natural gas (LNG) supply chain, called the LNG-IRP. Here, an actor is responsible for the LNG production and inventory management at the liquefaction plants, the routing and scheduling of a heterogeneous fleet of LNG ships, as well as the inventories and sales at the regasification terminals. Furthermore, all ports have a limited number of berths available for loading and unloading. The LNG-IRP is more complicated than many other maritime inventory routing problems because a constant rate of the cargo evaporates in the tanks each day and is used as fuel during transportation. In addition, a variable number of tanks are unloaded at the regasification terminals. We introduce a new path flow formulation for this problem arising from a novel decomposition scheme based on parts of a ship schedule, called duties. A ship schedule for the entire planning horizon can be divided into duties consisting of a visit to a liquefaction plant, then one or two visits to a regasification terminal before ending in a liquefaction plant. The solution method suggested is based on a priori generation of duties, and the formulation is strengthened by valid inequalities. The same problem was previously solved by a branch-price-and-cut algorithm for a schedule-based formulation. Computational results show that the new formulation provides tighter bounds than the previous schedule-based formulation. Furthermore, on a set of 27 benchmark instances, the proposed algorithm clearly outperforms the previous branch-price-and-cut algorithm both with regard to computational time and the number of problems solved within a 10-h time limit.

In the k-terminal cut problem, we are given a graph with edge weights and k distinct vertices called “terminals.” The goal is to remove a minimum weight collection of edges from the graph such that there is no path between any pair of terminals. The k-terminal cut problem is NP-hard. The k-terminal cut problem has been extensively studied and a number of algorithms have been devised for it. Most are approximation algorithms. There are also fixed-parameter tractable algorithms, but none have been shown empirically practical. It is also possible to apply implicit enumeration using any integer programming formulation of the problem and solve it with a branch-and-bound algorithm. Here, we present a branch-and-bound algorithm for the k-terminal cut problem which does not rely on an integer programming formulation. Our algorithm employs “minimum isolating cuts” and, for this reason, we call our branch-and-bound algorithm Isolation Branching. In an empirical experiment, we compare the performance of Isolation Branching to that of a branch-and-bound applied to the strongest known integer programming formulation of k-terminal cut. The integer programming branch-and-bound procedure is implemented with Gurobi, a commercial mixed-integer programming solver. We compare the performance of the two approaches for real-world instances and simulated data. The results on real data indicate that Isolation Branching, coded in Python, runs an order of magnitude faster than Gurobi for problems of sizes of up to tens of thousands of vertices and hundreds of thousands of edges. Our results on simulated data also indicate that Isolation Branching scales more effectively. Though we primarily focus on creating a practical tool for k-terminal cut, as a byproduct of our algorithm we prove that the complexity of Isolation Branching is fixed-parameter tractable with respect to the size of the optimal solution, thus providing an alternative, constructive, and somewhat simpler, proof of this fact.

The choice of a suitable time representation plays a major role in designing a computationally efficient planning/scheduling framework. For the time representation to be effective, it needs to capture the nuances of the actual process, while ensuring that the resultant model is tractable and computationally efficient. In this paper, a novel time representation scheme, titled hybrid time discretization, which combines both continuous- and discrete-time representations in a single framework, is proposed and used to solve a complex multiproduct maritime inventory routing problem (MIRP) with undedicated compartments. Several continuous- and discrete-time-based frameworks have been proposed to solve the MIRP over the years. While single-/multigrid discretized frameworks do efficiently capture the time-sensitive nuances of the problem (such as active/inactive jetty hours and hourly/daily variations in the demands), they struggle to solve larger problem instances to the required optimality gap in a reasonable time. This is primarily due to the large disparities among the timings of different task components in the model. On the other hand, continuous-time representation can significantly reduce the problem size and computational effort; however, modeling the entire problem using the continuous-time-based framework could have problems in representing some time-sensitive intricacies in the demands and jetty/port activities. To allay the above-mentioned drawbacks, in this paper, a novel hybrid time representation is proposed, which combines a continuous-time representation with a multigrid discrete-time framework. The proposed novel framework is cast in a rolling horizon strategy and tested on various scenarios generated for the above-mentioned maritime transportation problem, which are shown to be significantly more complex than those presented in the literature. The proposed MILP framework is able to solve most of the test cases to the required optimality in a reasonable time without the need for heuristic or meta-heuristic assists. The proposed hybrid time representation could find significant utility in other lateral applications such as batch scheduling and inventory routing problems.

In This Issue

The problem we consider is short‐term harvesting planning for a total planning period of 4–6 weeks where we want to decide the harvest sequences or schedules for harvest crews. A schedule is an order or sequence of harvest areas assigned to each crew. The harvesting of areas is planned in order to meet industrial demand. The total cost includes harvesting, transportation, and storage. One considerable cost is due to the quality reduction of logs stored at harvest areas. There are a number of restrictions to be considered. Areas are of varying size and the composition of assortments in each area is different. Each harvest team has different skills, a different home base, and different production capacity. Another aspect is the road network. There is a cost related to road opening (restoring, snow removal). In this paper, we develop a mixed integer programming (MIP) model for the problem. The schedules are represented by 0/1 variables. With a limited number of schedules, the problem can be solved by a commercial MIP solver. We have also developed a heuristic solution approach that provides high‐quality integer solutions within a distinct time limit to be used when more schedules are used. Computational results from a major Swedish forest company are presented.

Multi-supply multi-capacitated p-median location optimization via a hybrid bi-level intelligent algorithm

The standard traffic assignment problem (TAP) is often augmented with additional constraints to address non-standard applications. These models are called TAP with side constraints (TAPSC). Despite the rising significance of TAPSC models, the ability to efficiently solve them to satisfactory precision remains limited in real-world applications. The purpose of this paper is to fill this gap by integrating a recently developed high performance TAP solver, known as the path-based Greedy algorithm, with the augmented Lagrangian multiplier (ALM) method. This paper examines how precisely the subproblems in the ALM method should be solved to optimize the overall convergence performance. It is found that insufficiently converged subproblem solutions sometimes lead to catastrophic failures, although pursuing extremely high precision could also be counterproductive. Accordingly, it is proposed to adjust the precision required to solve the subproblems based on an approximate gap measured by the augmented Lagrangian. Results of numerical experiments show that adaptively adjusting the subproblem precision limit produces a 25% speed-up compared with the algorithm with a fixed limit.

On the technical side, both traditional, shallow feature-based methods (e.g., Support Vector Machines and Random Forest) and deep neural network models (e.g., LSTM and CNN types) have been utilized (Khare et al., 2024;Pepa et al., 2023). A key focus has been the development of multimodal systems that integrate diverse data sources, such as facial expressions, voice tone, dialogue sentiment, and physiological signals (Geetha et al., 2024). Multiple signals enable the aggregation of complementary information, leveraging the strengths of various measurement techniques to enhance robustness and accuracy.Technology is only effective with users; thus, beyond developing methods, fostering adoption among professionals and citizens is essential. Alongside technical advancements, researchers have explored psychological and social factors influencing the acceptance and trust of AI systems, particularly in healthcare and education. Trust has proven pivotal for AI adoption, with studies investigating how to build it and what system attributes ensure trustworthiness (Li et al., 2024). Key trust factors include explainability, transparency in processes and data usage, and the credibility of the institutions behind AI development.This Research Topic explores novel theories, methodologies, and applications of Emotion AI in healthcare and education. The published works address technical aspects, models, and AI acceptance and literacy. Burgess et al. (2023) evaluated automated facial coding software for parent-infant interactions across five studies with fathers and mothers. Automated detection rates were low (~25%) compared to manual coding in naturalistic settings but strongly correlated with manual assessments, particularly for positive expressions, when successful. Key challenges included poor lighting, facial occlusion, and rapid movements, highlighting the need for greater robustness in real-world conditions. Despite these limitations, the study demonstrated the potential of automated systems for analyzing authentic emotional expressions in parent-child interactions. 2023) introduced an innovative semi-supervised learning approach for stress monitoring. Using physiological data from 14 participants across five experiments, they achieved 77% accuracy with label propagation and 76% with deep autoencoders despite utilizing only 17% labeled data. Their method matched the performance of fully supervised approaches while substantially reducing annotation requirements, offering a practical solution for continuous stress monitoring in real-world healthcare applications. Žvanut and Mihelič (2024) identified four distinct attitudes among older adults toward domestic social robots: Cautious Optimists, Skeptical Traditionalists, Positive Optimists, and Technophiles. Through interviews with 24 participants, they highlighted the influence of factors like technology familiarity, privacy concerns, and perceived utility on AI acceptance. Their findings offer valuable insights for designing emotionally intelligent robotic assistants tailored to diverse user needs and concerns. Shen and Cui (2024) investigated the link between psychological needs satisfaction and AI literacy in 445 university students. Their findings revealed that technical and teacher support positively impacted students' autonomy and competence, subsequently improving AI literacy. Notably, satisfying psychological needs proved more critical than direct support in enhancing AI literacy. These insights offer valuable guidance for designing AI-enhanced educational environments that foster better learning and engagement. Gong et al. (2024) examined patients' trust in AI-powered pharmacy intravenous admixture services across five studies. They found that patients generally trusted AI PIVAS less than human services, primarily due to a limited subjective understanding of AI systems. However, informed consent significantly improved trust by enhancing patients' understanding. This study underscores the critical role of transparent communication and psychological factors in adopting AI in healthcare.The articles in this Research Topic advance methods for analyzing real-world datasets and explore how Emotion AI can be effectively integrated into healthcare and education, addressing challenges related to trust, privacy, and user acceptance. While Emotion AI shows promise, its use in these fields raises technical and ethical concerns, including data privacy, surveillance, and potential misuse of personal information. Clinical applications are further constrained by small sample sizes, lack of control groups, limited real-world testing, and methodological variability, which hinder reproducibility and reliability (Pepa et al., 2023). These studies tackle these challenges by developing novel model-training approaches for limited and noisy labeled data and identifying factors influencing AI acceptance and trust.Future research should prioritize enhancing the robustness of emotion recognition in naturalistic settings, developing efficient learning methods to reduce dependence on labeled data, and addressing ethical considerations to support user acceptance of AI. Emphasis on cross-cultural validation and long-term evaluation in real-world applications is crucial. Recent generative AI (GenAI) foundation models, such as GPT-4, offer significant potential for advancing Emotion AI due to their versatility (Cheng et al., 2023). GenAI has already shown promise in recognizing emotional indicators (Elyoseph et al., 2024) and could help alleviate data scarcity challenges that hinder specialized model development. Additionally, there is growing interest in the emotional analysis of groups and crowds, broadening the field's scope (Veltmeijer et al., 2023;Li et al. 2024).

We compare the capacity requirements of two new end-to-end (e2e) protection switching mechanisms: the self-protecting multipath (SPM) and several (multi-)path protection (PP) methods. Their structure consists of disjoint parallel e2e paths and the traffic is distributed over these paths according to a load balancing function. If one of the paths fails, the traffic is redistributed to the working paths according to a path failure specific load balancing function. The contribution of this work is the calculation of the path layout and the load balancing functions for both the PP and the SPM method. We use exact optimizations and simple heuristics for that objective and take a dimensioning approach to compare the capacity requirements of the different mechanisms. Our results illustrate, e.g., that the savings potential depends on the network topology and that 17% additional capacity can be sufficient for full resilience against all single router and link failures in well designed networks.