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The Joint Replenishment Problem (JRP) is a classical inventory management problem, that aims to model the trade-off between coordinating orders for multiple commodities (and their cost) with holding costs incurred by meeting demand in advance. Moseley, Niaparast and Ravi introduced a natural online generalization of the JRP in which inventory corresponding to demands may be replenished late, for a delay cost, or early, for a holding cost. They established that when the holding and delay costs are monotone and uniform across demands, there is a 30-competitive algorithm that employs a greedy strategy and a dual-fitting based analysis. We develop a 5-competitive algorithm that handles arbitrary monotone demand-specific holding and delay cost functions, thus simultaneously improving upon the competitive ratio and relaxing the uniformity assumption. Our primal-dual algorithm is in the spirit of the work Buchbinder, Kimbrel, Levi, Makarychev, and Sviridenko, which maintains a wavefront dual solution to decide when to place an order and which items to order. The main twist is in deciding which requests to serve early. In contrast to the work of Moseley et al., which ranks early requests i

Flight delays due to holding maneuvers are a critical and costly phenomenon in aviation, driven by the need to manage air traffic congestion and ensure safety. Holding maneuvers occur when aircraft are instructed to circle in designated airspace, often due to factors such as airport congestion, adverse weather, or air traffic control restrictions. This study models the prediction of flight delays due to holding maneuvers as a graph problem, leveraging advanced Graph Machine Learning (Graph ML) techniques to capture complex interdependencies in air traffic networks. Holding maneuvers, while crucial for safety, cause increased fuel usage, emissions, and passenger dissatisfaction, making accurate prediction essential for operational efficiency. Traditional machine learning models, typically using tabular data, often overlook spatial-temporal relations within air traffic data. To address this, we model the problem of predicting holding as edge feature prediction in a directed (multi)graph where we apply both CatBoost, enriched with graph features capturing network centrality and connectivity, and Graph Attention Networks (GATs), which excel in relational data contexts. Our results indi

This study addresses a flexible holding tool for robotic disassembly. We propose a shell-type soft jig that securely and universally holds objects, mitigating the risk of component damage and adapting to diverse shapes while enabling soft fixation that is robust to recognition, planning, and control errors. The balloon-based holding mechanism ensures proper alignment and stable holding performance, thereby reducing the need for dedicated jig design, highly accurate perception, precise grasping, and finely tuned trajectory planning that are typically required with conventional fixtures. Our experimental results demonstrate the practical feasibility of the proposed jig through performance comparisons with a vise and a jamming-gripper-inspired soft jig. Tests on ten different objects further showed representative successes and failures, clarifying the jig's limitations and outlook.

In content moderation for social media platforms, the cost of delaying the review of a content is proportional to its view trajectory, which fluctuates and is apriori unknown. Motivated by such uncertain and evolving holding costs, we consider a queueing model where job states evolve based on a Markov chain with state-dependent instantaneous holding costs. We demonstrate that in the presence of such uncertain and evolving holding costs, the two canonical algorithmic principles, instantaneous-cost ($cμ$-rule) and expected-remaining-cost ($cμ/θ$-rule), are suboptimal. By viewing each job as a Markovian ski-rental problem, we develop a new index-based algorithm, Opportunity-adjusted Remaining Cost (OaRC), that adjusts to the opportunity of serving jobs in the future when uncertainty partly resolves. We show that the suboptimality gap of OaRC scales as $\tilde{O}(\sqrt{N})$, where $N$ is the system size. This bound shows that OaRC achieves asymptotic optimality for overloaded systems when the system size $N$ scales to infinity. Moreover, the bound is independent of the state-space size, which is a desirable property when job states contain contextual information. We corroborate our res

We study an online generalization of the classic Joint Replenishment Problem (JRP) that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning systems. A retailer places orders to a supplier for multiple items over time: each request is for some item that the retailer needs in the future, and has an arrival time and a soft deadline. If a request is served before its deadline, the retailer pays a holding cost per unit of the item until the deadline. However, if a request is served after its deadline, the retailer pays a backlog cost per unit. Each service incurs a fixed joint service cost and a fixed item-dependent cost for every item included in a service. These fixed costs are the same irrespective of the units of each item ordered. The goal is to schedule services to satisfy all the online requests while minimizing the sum of the service costs, the holding costs, and the backlog costs. Constant competitive online algorithms have been developed for two special cases: the make-to-order version when the deadlines are equal to arrival times (Buchbinder et al., 2013), and the make-to-stock version with hard deadlines with zero holding co

The measurement of the velocity of money is still a significant topic. In this paper, we proposed a method to calculate the velocity of money by combining the holding-time distribution and lifespan distribution. By derivation, the velocity of money equals the holding-time distribution's value at zero. When we have much holding-time data, this problem can be converted to a regression problem. After a numeric simulation, we find that the calculating accuracy is high even if we used only a small part of the holding time data, which implies a potential application in measuring the velocity of money in reality, such as digital money. We also tested the methods on Cardano and found that the method can also provide a reasonable estimation of velocity in some cases.

In their seminal paper Moseley, Niaparast, and Ravi introduced the Joint Replenishment Problem (JRP) with holding and backlog costs that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning systems. Their model generalized the classical the make-to-order version as well make-to-stock version. For the case where holding costs function of all items are the same and all backlog costs are the same, they provide a constant competitive algorithm, leaving designing a constant competitive algorithm for arbitrary functions open. Moreover, they noticed that their algorithm does not work for arbitrary (request dependent) holding costs and backlog costs functions. We resolve their open problem and design a constant competitive algorithm that works for arbitrary request dependent functions. Specifically, we establish a 4-competitive algorithm for the single-item case and a 16-competitive for the general (multi-item) version. The algorithm of Moseley, Niaparast, and Ravi is based on fixed priority on the requests to items, and request to an item are always served by order of deadlines. In contrast, we design an algorithm with dynamic priority ove

Judicial reasoning in criminal judgments typically consists of three elements: Holding , evidentiary considerations, and subsumption. These elements form the logical foundation of judicial decision-making but remain unstructured in court documents, limiting large-scale empirical analysis. In this study, we design annotation guidelines to define and distinguish these reasoning components and construct the first dedicated datasets from Taiwanese High Court and Supreme Court criminal judgments. Using the bilingual large language model ChatGLM2, we fine-tune classifiers for each category. Preliminary experiments demonstrate that the model achieves approximately 80% accuracy, showing that judicial reasoning patterns can be systematically identified by large language models even with relatively small annotated corpora. Our contributions are twofold: (1) the creation of structured annotation rules and datasets for Holding, evidentiary considerations, and subsumption; and (2) the demonstration that such reasoning can be computationally learned. This work lays the foundation for large-scale empirical legal studies and legal sociology, providing new tools to analyze judicial fairness, consis

We study the temporal evolution of the holding-time distribution of bitcoins and find that the average distribution of holding-time is a heavy-tailed power law extending from one day to over at least $200$ weeks with an exponent approximately equal to $0.9$, indicating very long memory effects. We also report significant sample-to-sample variations of the distribution of holding times, which can be best characterized as multiscaling, with power-law exponents varying between $0.3$ and $2.5$ depending on bitcoin price regimes. We document significant differences between the distributions of book-to-market and of realized returns, showing that traders obtain far from optimal performance. We also report strong direct qualitative and quantitative evidence of the disposition effect in the Bitcoin Blockchain data. Defining age-dependent transaction flows as the fraction of bitcoins that are traded at a given time and that were born (last traded) at some specific earlier time, we document that the time-averaged transaction flow fraction has a power law dependence as a function of age, with an exponent close to $-1.5$, a value compatible with priority queuing theory. We document the existen

Recent deep reinforcement learning (DRL) methods in finance show promising outcomes. However, there is limited research examining the behavior of these DRL algorithms. This paper aims to investigate their tendencies towards holding or trading financial assets as well as purchase diversity. By analyzing their trading behaviors, we provide insights into the decision-making processes of DRL models in finance applications. Our findings reveal that each DRL algorithm exhibits unique trading patterns and strategies, with A2C emerging as the top performer in terms of cumulative rewards. While PPO and SAC engage in significant trades with a limited number of stocks, DDPG and TD3 adopt a more balanced approach. Furthermore, SAC and PPO tend to hold positions for shorter durations, whereas DDPG, A2C, and TD3 display a propensity to remain stationary for extended periods.

We consider the mean field game of cross--holding introduced in \citeauthor*{DjeteTouzi} \cite{DjeteTouzi} in the context where the equity value dynamics are affected by a common noise. In contrast with \cite{DjeteTouzi}, the problem exhibits the standard paradigm of mean--variance trade off. Our crucial observation is to search for equilibrium solutions of our mean field game among those models which satisfy an appropriate notion of no--arbitrage. Under this condition, it follows that the representative agent optimization step is reduced to a standard portfolio optimization problem with random endowment.

This study aimed to examine the correlation between the stock prices of two major Indonesian holding companies, MNC Group and Elang Mahkota Teknologi (Emtek) Group, and their respective subsidiaries as case studies. The data for the analysis were collected from 2013 to 2022, and Spearman correlation was used to determine the strength and direction of the relationship between the stock prices of the holding companies and their subsidiaries. The results of the analysis revealed that there were varying degrees of correlation between the stock prices of the holding companies and their subsidiaries. The strongest positive correlation was observed between BHIT and BMTR, while the weakest correlations were found between BHIT and IPTV, and BHIT and MSIN. The correlations were also found to have changed over time, possibly due to market conditions, company-specific events, or changes in industry sectors.In the case of Emtek Group, the analysis suggested that EMTK's stock price movements had a significant impact on the stock prices of its subsidiaries, with varying strengths of relationships. The negative correlation between EMTK and SCMA over the entire period suggested an inverse relations

Ground Delay Programs (GDPs) mitigate demand-capacity imbalances by holding flights on the ground when an airport's arrival capacity is reduced, thereby reducing costly airborne holding. A central challenge is that day-to-day demand-capacity balancing relies on accurate predictions of airport capacities. However, these predictions are deeply uncertain: forecast errors, operational disruptions, and climate change-driven shifts in weather severity can induce distribution shifts in capacity outcomes. Thus, policies optimized for a single predicted distribution may be brittle out of sample. We address this challenge by developing a \emph{distributionally robust} framework for the single airport ground holding problem (dr-SAGHP). We also propose a method integrates Kelly's cutting plane method with the integer L-shaped method, and that is applicable more broadly to two-stage distributionally robust integer programs with relatively complete recourse and continuous second-stage decision variables. Our method includes a novel dual bisection and primal recovery algorithm that makes use of the structure of the distributionally robust integer program in order to quickly generate subgradients

Bus holding control is a widely-adopted strategy for maintaining stability and improving the operational efficiency of bus systems. Traditional model-based methods often face challenges with the low accuracy of bus state prediction and passenger demand estimation. In contrast, Reinforcement Learning (RL), as a data-driven approach, has demonstrated great potential in formulating bus holding strategies. RL determines the optimal control strategies in order to maximize the cumulative reward, which reflects the overall control goals. However, translating sparse and delayed control goals in real-world tasks into dense and real-time rewards for RL is challenging, normally requiring extensive manual trial-and-error. In view of this, this study introduces an automatic reward generation paradigm by leveraging the in-context learning and reasoning capabilities of Large Language Models (LLMs). This new paradigm, termed the LLM-enhanced RL, comprises several LLM-based modules: reward initializer, reward modifier, performance analyzer, and reward refiner. These modules cooperate to initialize and iteratively improve the reward function according to the feedback from training and test results f

We study a single-server scheduling problem for the objective of minimizing the expected cumulative holding cost incurred by jobs, where parameters defining stochastic job holding costs are unknown to the scheduler. We consider a general setting allowing for different job classes, where jobs of the same class have statistically identical holding costs and service times, with an arbitrary number of jobs across classes. In each time step, the server can process a job and observes random holding costs of the jobs that are yet to be completed. We consider a learning-based $cμ$ rule scheduling which starts with a preemption period of fixed duration, serving as a learning phase, and having gathered data about jobs, it switches to nonpreemptive scheduling. Our algorithms are designed to handle instances with large and small gaps in mean job holding costs and achieve near-optimal performance guarantees. The performance of algorithms is evaluated by regret, where the benchmark is the minimum possible total holding cost attained by the $cμ$ rule scheduling policy when the parameters of jobs are known. We show regret lower bounds and algorithms that achieve nearly matching regret upper bounds

In ``Infinite families of near MDS codes holding $t$-designs, IEEE Trans. Inform. Theory, 2020, 66(9), pp. 5419-5428'', Ding and Tang made a breakthrough in constructing the first two infinite families of NMDS codes holding $2$-designs or $3$-designs. Up to now, there are only a few known infinite families of NMDS codes holding $t$-designs in the literature. The objective of this paper is to construct new infinite families of NMDS codes holding $t$-designs. We determine the weight enumerators of the NMDS codes and prove that the NMDS codes hold $2$-designs or $3$-designs. Compared with known $t$-designs from NMDS codes, ours have different parameters. Besides, several infinite families of optimal locally recoverable codes are also derived via the NMDS codes.

In this paper, the impact of holding umbrella on the uni- and bi-directional flow has been investigated via experiment and modeling. In the experiments, pedestrians are required to walk clockwise/anti-clockwise in a ring-shaped corridor under normal situation and holding umbrella situation. No matter in uni- or bi-directional flow, the flow rate under holding umbrella situation decreases comparing with that in normal situation. In bidirectional flow, pedestrians segregate into two opposite moving streams very quickly under normal situation, and clockwise/anti-clockwise walking pedestrians are always in the inner/outer lane due to right-walking preference. Under holding umbrella situation, spontaneous lane formation has also occurred. However, when holding umbrella, pedestrians may separate into more than two lanes. Moreover, the merge of lanes have been observed, and clockwise/anti-clockwise pedestrians are not always in the inner/outer lane. To model the flow dynamics, an improved force-based model has been proposed. The contact force between umbrellas has been taken into account. Simulation results are in agreement with the experimental ones.

We introduce the possibility of default in the mean field game of mutual holding of Djete and Touzi [11]. This is modeled by introducing absorption at the origin of the equity process. We provide an explicit solution of this mean field game. Moreover, we provide a particle system approximation, and we derive an autonomous equation for the time evolution of the default probability, or equivalently the law of the hitting time of the origin by the equity process. The systemic risk is thus described by the evolution of the default probability.

This paper defines the average holding period of money and proposes a methodology for fully disaggregated measurement. Our measure is shown to be the inverse of the transfer velocity of money under stationary conditions, which is implicitly assumed in conventional aggregate measurement. Our methodology does not require stationarity. We leverage a recent computational technique to extract empirical holding periods from micro-level transaction data as recorded by real-world payment systems. This enables novel empirical analyses of money velocity under non-stationarity conditions. We illustrate several such analyses on Sarafu, a small digital community currency in Kenya, where transaction data is available from 25 January 2020 to 15 June 2021. Our measure implies faster circulation than does the aggregate transfer velocity; we can say that 58% of Sarafu was effectively static. We also disaggregate by geography to study the heterogeneous impact of economic disruptions related to the COVID-19 pandemic on Sarafu. Finally, we consider an ad-hoc currency management operation that took place in October 2020. Measuring the average holding period of money makes it possible to track money velo