Non-Markovian (renewal) epidemic simulation on multi-million-node contact networks is essential for realistic forecasting under general age-dependent holding-time distributions (log-normal, Weibull, Erlang, and similar), but the age-dependent hazard forces dense per-step updates that render the sparse event-queue strategies of standard CPU methods ineffective. We present FlashSpread, a GPU framework that consolidates the per-step renewal pipeline (CSR traversal, numerically stable erfcx-based hazard evaluation, Bernoulli tau-leaping, state transition, and next-step infectivity write-back) into a single fused Triton kernel whose intermediates never leave streaming-multiprocessor registers, with block-scalar skips that preserve CUDA Graph capture and a degree-aware CSR dispatch (thread / warp / edge-merge) that keeps the peak throughput on scale-free graphs. On an NVIDIA A100 the fused CUDA-Graph engine reaches 8.09 Giga-NUPS at N = 10^6 on a uniform-degree graph, a 217x strict hardware speedup over optimised CPU tau-leaping at the same N; on a Barabasi-Albert graph of the same size the merge-based dispatch recovers 4.5x (0.45 to 2.0 Giga-NUPS) over the default kernel, and the framework scales to N = 10^8 on a single A100 (40 GB), with a mixed-precision storage path that extends the L2-reachable scale by roughly 3x and delivers a 1.15x throughput lift at the far bandwidth-bound end. Validation against an exact non-Markovian Gillespie reference shows a structural-bias floor of approximately 6

Firms increasingly rely on both price discounts and advertising campaigns to shape product diffusion in socially connected markets, yet existing models rarely treat these levers jointly or account for network heterogeneity. This study develops an integrated, network-aware framework for dynamic pricing and advertising control. A stochastic compartmental model of the consumer decision-making model (CDM) is formulated on a social graph, with transition intensities modulated by price, advertising spend, and peer influence. A deterministic mean-field approximation yields closed-form expressions for a trade-free equilibrium (TFE) and a reproduction number threshold that delineates when adoption dies out versus persists. Building on this analytical core, the paper introduces twin delayed deep deterministic policy gradient with encoded state (TD3ES), a reinforcement learning (RL) controller that couples an actor-critic architecture with a graph-convolutional autoencoder, thereby compressing high-dimensional network states into a tractable latent representation. A custom GPU-accelerated simulator facilitates large-scale training. Numerical experiments on Erd & odblac;s-R & eacute;nyi and heavy-tailed exponential networks show that twin delayed deep deterministic policy gradient with encoded state (TD3ES) swiftly converges to profit-maximizing joint policies and, on heterogeneous graphs, outperforms a TD3 baseline that lacks network-structural information. Error analysis reveals that the autoencoder naturally prioritizes high-degree hubs in dominant CDM compartments, explaining its superior performance. Managerially, the results demonstrate that ignoring topology can forfeit substantial revenue and that adaptive, network-aware coordination of price and advertising is both feasible and valuable. The framework thus unites rigorous diffusion theory with scalable learning, offering a practical tool for data-driven marketing in connected consumer ecosystems.

The second smallest eigenvalue of the Laplacian matrix, known as algebraic connectivity, determines many network properties. This paper investigates the optimal design of interconnections that maximizes algebraic connectivity in multilayer networks. We identify an upper bound for maximum algebraic connectivity for total weight below a threshold, independent of interconnections pattern, and only attainable with a particular regularity condition. For efficient numerical approaches in regions of no analytical solution, we cast the problem into a convex framework and an equivalent graph embedding problem associated with the optimum diffusion phases in the multilayer. Allowing more general settings for interconnections entails regions of multiple transitions, giving more diverse diffusion phases than the more studied one-toone interconnection case. When there is no restriction on the interconnection pattern, we derive several analytical results characterizing the optimal weights using individual Fiedler vectors. We use the ratio of algebraic connectivity and layer sizes to explain the results. Finally, we study the placement of a limited number of interlinks heuristically, guided by each layer's Fiedler vector components.

This manuscript introduces an innovative approach to optimizing the distribution of a limited vaccine resource within a population modeled as a contact network, aiming to mitigate the spread of infectious diseases. The study develops a novel methodology that combines reinforcement learning and graph neural networks. To understand the dynamics of disease propagation, the study constructs an analytical model that outlines conditions for disease eradication or endemic states. This model supports a series of simulation experiments across various scenarios, demonstrating the proposed method’s superiority over random and centrality-based approaches in reducing the average number of infections per individual during an outbreak. The adaptability of the proposed method is further emphasized by its robust performance across networks of diverse sizes and configurations, highlighting its real-world applicability. The findings of this study have significant implications for public health policy and resource allocation, offering a promising framework for managing infectious disease outbreaks in complex and dynamic environments.

This paper will study the pricing problem of two competitive products in a market characterized by local externalities. For this purpose, a stochastic model of sales propagation among consumers is developed. This model utilizes a compartmentalized schema denoted as a Markov Chain where the local network ef-fects impact transition rates. A key aspect of the proposed model is its multilayer structure, where prod-ucts' information streams through different layers. The equilibrium conditions and the optimal pricing strategies in a competitive market are examined. The pricing problem is investigated in two settings of homogeneous and heterogeneous (i.e., differential). It is shown that the existence and coexistence of in-dividual products in the equilibrium point depends on an epidemic parameter, called reproduction num-ber, that quantifies the speed by which a product's sales spread over the network. Moreover, it is found that the correlation between the network's layers impacts the equilibrium point. Specifically, a negative correlation between the network's layers allows a wider coexistence region than a positive correlation. Additionally, it is found that a negative correlation between the network's layers provides more flexibil-ity to firms for their pricing practices and yields a higher profit. Finally, different pricing strategies are characterized with respect to model parameters and the centrality measures of different networks. It is observed that while centrality measures and optimal prices are highly correlated, node centralities alone are not enough to determine optimal prices. & COPY; 2023 Elsevier B.V. All rights reserved.

Clustering is a widely used data mining technique with a diverse set of applications. Since clustering is an NP-hard problem, finding high-quality solutions for large-scale clustering problems can be an arduous and computationally expensive task. Therefore, many metaheuristics are utilized to solve these problems efficiently. In this paper, a modified unconscious search (US) and its k-means hybrid for data clustering are proposed with two main modifications: (1) generating initial population by combining solutions of k-means and random solutions, (2) replacing the usual local search step of the original US by an existing Heuristic Search method. Modified US is tested on the seven following well-known benchmarks from the UCI machine learning directory: Iris, Wine, Glass, Cancer, Vowel, CMC, and Ecoli. The results are then compared against metaheuristics, such as genetic algorithm, particle swarm optimization (PSO), black hole algorithm, hybrid of PSO k-means, and accelerated chaotic PSO. The results of experiments show that, on average, the quality of best solutions obtained by the proposed methods on all seven datasets is 0.176% better than the quality of the other six algorithms applied for experimentations.

The manufacturing environment for apparel is subject to a variety of constraints, stochasticity, and unforeseen events. In order to create an accurate scheduling-system for this environment, these complexities must be considered. This article presents the development and the application of a scheduling and rescheduling decision support system for an apparel manufacturer. Furthermore, the results of applying the proposed system are presented and discussed. The scheduling and rescheduling decision support system presented in this article takes advantage of a variable neighborhood search and Monte Carlo simulation in order to minimize tardiness in the presence of different release times, sequence-based setup times, blocking, and resource constraints. The results show that the quality of the schedules generated by the proposed scheduling and rescheduling decision support system is superior to the current firm’s scheduling practice, which is based on an earliest due date heuristic. Moreover, the percentage of the realized schedule and overall equipment effectiveness were improved.

The selective pickup and delivery problem addresses real-life issues in logistics and transportation. The aim is to optimally select some pickup locations to collect the required demands and unload commodities at delivery locations. Everyday, much of such logistics processes are outsourced to Third-Party Logistics (3PL) companies. However, decentrally truck scheduling by 3PLs specifically when there are only a limited number of warehouse loading docks and time slots will likely cause the random arrival of carriers at warehouses, capacity violation at loading docks, and consequently increased total costs. This study offers a promising approach to optimize the intricate problem of coordination in transportation logistics. We present an integrated time slot allocation and selective pickup and delivery problem while taking real-world variants and constraints, including mixed time windows and capacity, into consideration. To achieve this, we propose a mixed-integer linear programming formulation for the problem. To solve the model, we utilize some valid inequalities and constraints tightening method to strengthen its linear programming relaxation. In addition, a sensitivity analysis is performed on different problem features to validate the presented model. Computational results illustrate the effectiveness of the presented model and valid inequalities in providing faster and tighter results. With respect to the solution time and the number of nodes, the average of both measures drastically is reduced by approximately 90%, followed by tight lower bounds. Furthermore, the value of the integrated model is investigated on larger-sized instances, which shows the proposed model can achieve significant savings and gains compared to the decomposed subproblems of vehicle routing and time slot allocation.

This study proposes a two-echelon location routing framework for cash-in-transit. In order to mitigate the risk of robbery in cash transportation, a dynamic risk index is considered. The utilized risk function encompasses both the amount of cash carried by a vehicle and the travel time of a route, and it relaxes a pre-defined parameter of risk threshold in the literature. Multiple exact and metaheuristic methodologies are utilized and evaluated on several small to medium-sized instances and a case study. The effectiveness of the proposed methods is evaluated and shown by examining various multi-objective performance measures. The case study is researched in more depth to obtain managerial insights, and the results show that depending on the risk or cost efficiency of the solutions on a Pareto frontier, the risk of traversing longer routes or transporting larger amounts of cash can be determining in locating new bank vaults.

In the aftermath of the COVID-19 pandemic, supply chains experienced an unprecedented challenge to fulfill consumers' demand. As a vital operational component, manual order picking operations are highly prone to infection spread among the workers, and thus, susceptible to interruption. This study revisits the well-known order batching problem by considering a new overlap objective that measures the time pickers work in close vicinity of each other and acts as a proxy of infection spread risk. For this purpose, a multi-objective optimization model and three multi-objective metaheuristics with an effective seeding procedure are proposed and are tested on the data obtained from a major US-based logistics company. Through extensive numerical experiments and comparison with the company's current practices, the results are discussed, and some managerial insights are offered. It is found that the picking capacity can have a determining impact on reducing the risk of infection spread through minimizing the picking overlap.

Detecting the communities that exist within complex social networks has a wide range of application in business, engineering, and sociopolitical settings. As a result, many community detection methods are being developed by researchers in the academic community. If the communities within social networks can be more accurately detected, the behavior or characteristics of each community within the networks can be better understood, which implies that better decisions can be made. In this paper, a discrete version of an unconscious search algorithm was applied to three widely explored complex networks. After these networks were formulated as optimization problems, the unconscious search algorithm was applied, and the results were compared against the results found from a comprehensive review of state-of-the-art community detection methods. The comparative study shows that the unconscious search algorithm consistently produced the highest modularity that was discovered through the comprehensive review of the literature.

In viral marketing campaigns, incentivized consumers can act as sales agents by sharing information. In this study, we investigate the problem of incentive rate determination over a network of consumers to maximize the profit of a single good by a monopolist. For this purpose, we develop an epidemic spreading model to explore the dynamics of a viral marketing campaign under network externalities and incentivized individuals. We will examine two cases of homogeneous and heterogeneous incentive rates. In each case, we derive an N-intertwined dynamics model and obtain the existence and stability conditions of a trade-free or an endemic equilibrium. By treating the incentive as a control parameter, we investigate the problem of maximizing the monopolist's profit by formulating two nonlinear programming models. In the case of homogeneous incentive rates, results show that the optimal incentive is determined by devising a balance between the consumers' states in the Markov process. In the heterogeneous case, it is observed that despite the existence of a strong correlation with different centrality measures, the optimal incentive allocation cannot be solely determined by centrality measures. (C) 2020 Elsevier B.V. All rights reserved.

At an operational level, order picking is the main activity in fulfillment centers. Motivated by and through collaboration with a third party logistic company, this study presents a novel hybrid column generation (CG), genetic algorithm (GA), and artificial neural network (ANN) heuristic for minimizing makespan in manual order picking operations. The results of column generation heuristic is compared against a mixed integer programming model solved by Gurobi, and a parallel simulated annealing and ant colony optimization (PSA-ACO) previously proposed in the literature. Through numerical experiments, the superiority of CG heuristic compared to other methods is shown, and some managerial insights regarding the relationship between makespan optimization, workload balance, picking capacity, and number of pickers in order picking operations is presented. (C) 2020 Elsevier Ltd. All rights reserved.

The second smallest eigenvalue of the Laplacian matrix is determinative in characterizing many network properties and is known as algebraic connectivity. In this paper, we investigate the problem of maximizing algebraic connectivity in multilayer networks by allocating interlink weights subject to a budget while allowing arbitrary interconnections. For budgets below a threshold, we identify an upper-bound for maximum algebraic connectivity which is independent of interconnections pattern and is reachable with satisfying a certain regularity condition. For efficient numerical approaches in regions of no analytical solution, we cast the problem into a convex framework that explores the problem from several perspectives and, particularly, transforms into a graph embedding problem that is easier to interpret and related to the optimum diffusion phase. Allowing arbitrary interconnections entails regions of multiple transitions, giving more diverse diffusion phases with respect to one-to-one interconnection case. When there is no limitation on the interconnections pattern, we derive several analytical results characterizing the optimal weights by individual Fiedler vectors. We use the ratio of algebraic connectivity and the layer sizes to explain the results. Finally, we study the placement of a limited number of interlinks by greedy heuristics, using the Fiedler vector components of each layer.

In this study, a three-stage methodology for carton set optimization in e-commerce warehouses is proposed and evaluated on three DHL Supply Chain warehouses. The methodology includes order cubing, carton grouping, and optimal carton set selection. A modified largest area fits first algorithm for order cubing is proposed. For optimal carton set selection, a genetic algorithm with a novel crossover strategy is introduced. The results show that the proposed carton set optimization approach can improve the shipping cost and carton utilization by 7% and 7.8%, and considerably improve the carbon footprint of the operations, even when the number of carton types is not changed.

We discuss the design of interlayer edges in a multiplex network, under a limited budget, with the goal of improving its overall performance. We analyze the following three problems separately; first, we maximize the smallest nonzero eigenvalue, also known as the algebraic connectivity; second, we minimize the largest eigenvalue, also known as the spectral radius; and finally, we minimize the spectral width. Maximizing the algebraic connectivity requires identical weights on the interlayer edges for budgets less than a threshold value. However, for larger budgets, the optimal weights are generally nonuniform. The dual formulation transforms the problem into a graph realization (embedding) problem that allows us to give a fuller picture. Namely, before the threshold budget, the optimal realization is one-dimensional with nodes in the same layer embedded to a single point, while beyond the threshold, the optimal embeddings generally unfold into spaces with dimension bounded by the multiplicity of the algebraic connectivity. Finally, for extremely large budgets the embeddings again revert to lower dimensions. Minimizing the largest eigenvalue is driven by the spectral radius of the individual networks and its corresponding eigenvector. Before a threshold, the total budget is distributed among interlayer edges corresponding to the nodal lines of this eigenvector, and the optimal largest eigenvalue of the Laplacian remains constant. For larger budgets, the weight distribution tends to be almost uniform. In the dual picture, the optimal graph embedding is one-dimensional and nonhomogeneous at first, with the nodes corresponding to the layer with the largest spectral radius distributed on a line according to its eigenvector, while the other layer is embedded at the origin. Beyond this threshold, the optimal embedding expands to be multidimensional, and for larger values of the budget, the two layers fill the embedding space. Finally, we show how these two problems are connected to minimizing the spectral width.

In this study, a multi-objective order batching and picker routing model for minimising the total travel time and makespan in a put wall-based picking system is proposed. A put wall is a hardware composed of containers that is usually used as a sorting station. Put walls usually have limited capacity and can accommodate only a part of received orders at a time. Thus, in put wall-based picking systems, order batching and picker routing should be considered along with the scheduling of the orders on the put wall. To solve the problem, a genetic algorithm (GA), a coevolutionary genetic algorithm (COGA) and an archived multi-objective simulated annealing (AMOSA) are proposed. It is found that GA and COGA offer a more diverse set of solutions to the problem compared to AMOSA.

The impact of appropriate E-waste management practices on the environment, human health, and natural resources has made E-waste management an interesting research topic in recent decades. Research also shows that government intervention is an important factor in controlling the emission volume produced by waste management systems. This study considers a base E-waste supply chain in which a collection center is responsible for collecting E-waste and delivering it to a recycling center. The recycling center recovers valuable material and sells it to electronic device manufacturing companies using a price/sustainability-sensitive demand. E-waste material recovery generates emissions that are undesirable for manufacturing companies. Two extended cases regarding the base supply chain are studied, as well: (1) the recycling center is also active in E-waste collection. (2) There are two active recycling centers. Although the sustainability-sensitive demand is a controlling factor for material recovery emissions, government interferences through tariff and emission penalties make sure that sustainable issues are considered in the material recovery process. Each plant in this study makes a marginal profit by processing E-waste; therefore, it is important to know which plant is the primary decision-maker when it comes to price. Because of its capability in terms of solving interactive decision-making problems, game theory is used to model different scenarios in our problem. Equilibrium values are derived, and a numerical example with parameter sensitivity analysis is provided to show the applicability of the proposed models. The results show that the E-waste supply chain makes more profit and selects a higher level of material recovery sustainability if the plants work under a centralized decision-making framework. Moreover, it is more profitable for the entire E-waste supply chain if the recycling center undertakes a portion of the E-waste collection activity.

A put wall is a hardware composed of containers that is usually used as a sorting station. In this study, the order picking operations, including order batching and picker routing, in a put wall based picking system is studied. Put walls usually have limited capacity and can accommodate only a part of received orders at a time. Hence, scheduling of the orders on the put wall should be considered along with the order batching and picker routing. For this, a mathematical formulation for order batching and picker routing in a put wall based picking system is proposed. To solve the problem, two genetic algorithms (GAs) with random shuffling and inverse–insert–swap mutation operators, a list-based simulated annealing (LBSA) and a hybrid GA–LBSA are proposed. To show the effectiveness of the proposed methods, their results are compared against the best solutions found by Gurobi 7.0. It is found that while for smaller size problems LBSA is a better choice in terms of solution quality, when CPU time is considered, depending on the problem size, GA and GA–LBSA might be the better options.

Purpose The purpose of this paper is to review the current literature in the field of tourism demand forecasting. Design/methodology/approach Published papers in the high quality journals are studied and categorized based their used forecasting method. Findings There is no forecasting method which can develop the best forecasts for all of the problems. Combined forecasting methods are providing better forecasts in comparison to the traditional forecasting methods. Originality/value This paper reviews the available literature from 2007 to 2017. There is not such a review available in the literature.