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Online shopping is a complex multi-task, few-shot learning problem with a wide and evolving range of entities, relations, and tasks. However, existing models and benchmarks are commonly tailored to specific tasks, falling short of capturing the full complexity of online shopping. Large Language Models (LLMs), with their multi-task and few-shot learning abilities, have the potential to profoundly transform online shopping by alleviating task-specific engineering efforts and by providing users with interactive conversations. Despite the potential, LLMs face unique challenges in online shopping, such as domain-specific concepts, implicit knowledge, and heterogeneous user behaviors. Motivated by the potential and challenges, we propose Shopping MMLU, a diverse multi-task online shopping benchmark derived from real-world Amazon data. Shopping MMLU consists of 57 tasks covering 4 major shopping skills: concept understanding, knowledge reasoning, user behavior alignment, and multi-linguality, and can thus comprehensively evaluate the abilities of LLMs as general shop assistants. With Shopping MMLU, we benchmark over 20 existing LLMs and uncover valuable insights about practices and prospe

Flow shops are widely studied machine environments in which all jobs must visit all machines in the same order. While conventional flow shops assume that each job traverses the shop only once, many industrial environments require jobs to loop through the shop multiple times before completion. This means that after traversing the shop and completing its processing on the last machine, a job must return to the first machine and traverse the shop again until it has completed all its required loops. Such a setting, referred to as a flow shop with reentry, has numerous applications in industry, e.g., semiconductor manufacturing. The planning problem is to schedule all loops of all jobs while minimizing the total weighted completion time. In this paper, we consider reentrant flow shops with unit processing times. We show that this problem is strongly NP-hard if the number of machines is part of the input. We propose the Least Remaining Loops First (LRL) priority rule and show that it minimizes the total unweighted completion time. Then, we analyze the Weighted Least Remaining Loops First (WLRL) priority rule and show that it has a worst-case performance ratio of $(1+\sqrt{2})/2$ (about 1

We present a method based on graph neural network (GNN) for prediction of probabilities of usage of shopping-mall corridors. The heterogeneous graph network of shops and corridor paths are obtained from floorplans of the malls by creating vector layers for corridors, shops and entrances. These are subsequently assimilated into nodes and edges of graphs. The prediction of the usage probability is based on the shop features, namely, the area and usage categories they fall into, and on the graph connecting these shops, corridor junctions and entrances by corridor paths. Though the presented method is applicable for training on datasets obtained from a field survey or from pedestrian-detecting sensors, the target data of the supervised deep-learning work flow in this work are obtained from a probability method. We also include a context-specific representation learning of latent features. The usage-probability prediction is made on each edge, which is a connection by a section of corridor path between the adjacent nodes representing the shops or corridor points. To create a feature for each edge, the hidden-layer feature vectors acquired in the message-passing GNN layers at the nodes o

We study flow shop scheduling with stochastic reentry, where jobs must complete multiple passes through the entire shop, and the number of passes that a job requires for completion is drawn from a discrete probability distribution. The goal is to find policies that minimize performance measures in expectation. Our main contribution is a reduction to a classical parallel machine scheduling problem augmented with machine arrivals. This reduction preserves expected objective values and enables transferring structural results and performance guarantees from the auxiliary problems to the reentrant flow shop setting. We demonstrate the usefulness of this reduction by proving the optimality of simple priority policies for minimizing the makespan and the total completion time in expectation under geometric and, more generally, monotone hazard rate distributions. For minimizing the total weighted completion time, we derive an approximation guarantee that depends only on the squared coefficient of variation of the underlying distributions for a simple priority policy. Our results constitute the first optimality and approximation guarantees for flow shops with stochastic reentry and demonstra

Neural approaches to the Flexible Job Shop Scheduling Problem (FJSP), particularly those based on deep reinforcement learning (DRL), have gained growing attention in recent years. However, existing methods rely on complex feature-engineered state representations (i.e., often requiring more than 20 handcrafted features) and graph-biased neural architectures. To reduce modeling complexity and advance a more generalizable framework for FJSP, we introduce \textsc{ReSched}, a minimalist DRL framework that rethinks both the scheduling formulation and model design. First, by revisiting the Markov Decision Process (MDP) formulation of FJSP, we condense the state space to just four essential features, eliminating historical dependencies through a subproblem-based perspective. Second, we employ Transformer blocks with dot-product attention, augmented by three lightweight but effective architectural modifications tailored to scheduling tasks. Extensive experiments show that \textsc{ReSched} outperforms classical dispatching rules and state-of-the-art DRL methods on FJSP. Moreover, \textsc{ReSched} also generalizes well to the Job Shop Scheduling Problem (JSSP) and the Flexible Flow Shop Sched

The paper discusses several extensions of the recursive representation of the flow shop scheduling problem. It is shown that recursive functions make it possible to describe multiple extensions in a single problem. The paper considers altogether six extensions. The examples consider three types of recursive functions: functions associated with the machine, functions that adjust the procession time based on constraints, and functions that control the feasibility of the schedule. The structure of the superpositions of these functions is presented, and also descriptions of several objective functions by recursive functions are presented. Then the general requirements for a recursive function are formulated and its properties are described. Finally, a demonstration of the formulation of new problems is provided using examples of simple flow shop extensions and branch and bound optimization.

The quick growth of shops using artificial intelligence (AI) techniques has changed digital marketing activities and changed how businesses interact and reach their consumers. (AI) techniques are reshaping digital interactions between shops and consumers interact digitally by providing a more efficient and customized experience, fostering deeper engagement and more informed decision-making. This study investigates how (AI) techniques affect consumer interaction and decision-making over purchases with shops that use digital marketing. The partial least squares method was used to evaluate data from a survey with 300 respondents. When consumer engagement mediates this relationship, artificial intelligence (AI) techniques have a more favorable impact on purchasing decision-making. Consequently, decision-making is positively impacted through consumer engagement. The findings emphasize that for a bigger impact of the (AI) techniques on decision-making, the consumer must initially interact with the (AI) techniques. This research unveils a contemporary pathway in the field of AI-supported shop engagements and illustrates the distinct impact of (AI) techniques on consumer satisfaction, trus

In dynamic manufacturing environments, disruptions such as machine breakdowns and new order arrivals continuously shift the optimal dispatching strategy, making adaptive rule selection essential. Existing LLM-powered Automatic Heuristic Design (AHD) frameworks evolve toward a single elite rule that cannot meet this adaptability demand. To address this, we present DSevolve, an industrial scheduling framework that evolves a quality-diverse portfolio of dispatching rules offline and adaptively deploys them online with second-level response time. Multi-persona seeding and topology-aware evolutionary operators produce a behaviorally diverse rule archive indexed by a MAP-Elites feature space. Upon each disruption event, a probe-based fingerprinting mechanism characterizes the current shop floor state, retrieves high-quality candidate rules from an offline knowledge base, and selects the best one via rapid look-ahead simulation. Evaluated on 500 dynamic flexible job shop instances derived from real industrial data, DSevolve outperforms state-of-the-art AHD frameworks, classical dispatching rules, genetic programming, and deep reinforcement learning, offering a practical and deployable sol

A mixed shop is a manufacturing infrastructure designed to process a mixture of a set of flow-shop jobs and a set of open-shop jobs. Mixed shops are in general much more complex to schedule than flow-shops and open-shops, and have been studied since the 1980's. We consider the three machine proportionate mixed shop problem denoted as $M3 \mid prpt \mid C_{\max}$, in which each job has equal processing times on all three machines. Koulamas and Kyparisis [{\it European Journal of Operational Research}, 243:70--74,2015] showed that the problem is solvable in polynomial time in some very special cases; for the non-solvable case, they proposed a $5/3$-approximation algorithm. In this paper, we present an improved $4/3$-approximation algorithm and show that this ratio of $4/3$ is asymptotically tight; when the largest job is a flow-shop job, we present a fully polynomial-time approximation scheme (FPTAS). On the negative side, while the $F3 \mid prpt \mid C_{\max}$ problem is polynomial-time solvable, we show an interesting hardness result that adding one open-shop job to the job set makes the problem NP-hard if this open-shop job is larger than any flow-shop job. We are able to design a

Large Language Models (LLMs) have recently demonstrated strong potential in generating 'believable human-like' behavior in web environments. Prior work has explored augmenting training data with LLM-synthesized rationales and applying supervised fine-tuning (SFT) to enhance reasoning ability, which in turn can improve downstream action prediction. However, the performance of such approaches remains inherently bounded by the reasoning capabilities of the model used to generate the rationales. In this paper, we introduce Shop-R1, a novel reinforcement learning (RL) framework aimed at enhancing the reasoning ability of LLMs for simulation of real human behavior in online shopping environments. Specifically, Shop-R1 decomposes the human behavior simulation task into two stages: rationale generation and action prediction, each guided by distinct reward signals. For rationale generation, we leverage internal model signals (e.g., logit distributions) to guide the reasoning process in a self-supervised manner. For action prediction, we propose a hierarchical reward structure with difficulty-aware scaling to prevent reward hacking and enable fine-grained reward assignment. This design evalu

Recommendation systems can provide accurate recommendations by analyzing user shopping history. A richer user history results in more accurate recommendations. However, in real applications, users prefer e-commerce platforms where the item they seek is at the lowest price. In other words, most users shop from multiple e-commerce platforms simultaneously; different parts of the user's shopping history are shared between different e-commerce platforms. Consequently, we assume in this study that any e-commerce platform has a complete record of the user's history but can only access some parts of it. If a recommendation system is able to predict the missing parts first and enrich the user's shopping history properly, it will be possible to recommend the next item more accurately. Our recommendation system leverages user shopping history to improve prediction accuracy. The proposed approach shows significant improvements in both NDCG@10 and HR@10.

Coordinating production and material transfers is increasingly important in modern manufacturing systems equipped with mobile transfer robots, known as transbots. This study considers a flexible job shop environment in which heterogeneous transbots transport parts between machines. The shop floor is partitioned into zones, with each transbot assigned to a specific zone, and inter-zone movements are facilitated through designated handoff points. These zoning constraints, transbot heterogeneity, and inter-zone handoffs give rise to a challenging variant of the flexible job shop problem with embedded transbot-routing features, resulting in substantial computational complexity. Motivated by a real manufacturing setting, two constraint programming formulations that integrate production scheduling with transbot routing are proposed: an arc-based formulation that explicitly models machine-to-machine transfers, and an operation-embedded formulation that embeds transfer decisions directly within the operation scheduling structure, leading to tighter synchronization between production and transportation decisions. Both formulations capture machine flexibility, zoning restrictions, handoff co

Job shop scheduling problems address the routing and sequencing of tasks in a job shop setting. Despite significant interest from operations research and machine learning communities over the years, a comprehensive platform for testing and comparing solution methods has been notably lacking. To fill this gap, we introduce a unified implementation of job shop scheduling problems and their solution methods, addressing the long-standing need for a standardized benchmarking platform in this domain. Our platform supports classic Job Shop (JSP), Flow Shop (FSP), Flexible Job Shop (FJSP), and Assembly Job Shop (AJSP), as well as variants featuring Sequence-Dependent Setup Times (SDST), variants with online arrivals of jobs, and combinations of these problems (e.g., FJSP-SDST and FAJSP). The platfrom provides a wide range of scheduling solution methods, from heuristics, metaheuristics, and exact optimization to deep reinforcement learning. The implementation is available as an open-source GitHub repository, serving as a collaborative hub for researchers, practitioners, and those new to the field. Beyond enabling direct comparisons with existing methods on widely studied benchmark problems,

Combinatorial optimization problems are considered to be an application, where quantum computing can have transformative impact. In the industrial context, job shop scheduling problems that aim at finding the optimal schedule for a set of jobs to be run on a set of machines are of immense interest. Here we introduce an efficient encoding of job shop scheduling problems, which requires much fewer bit-strings for counting all possible schedules than previously employed encodings. For problems consisting of $N$ jobs with $N$ operations, the number of required bit-strings is at least reduced by a factor $N / \log_2(N)$ as compared to time indexed encodings. This is particularly beneficial for solving job shop scheduling problems on quantum computers, since much fewer qubits are needed to represent the problem. Our approach applies to the large class of flexible and usual job-shop scheduling problems, where operations can possibly be executed on multiple machines. Using variational quantum algorithms, we show that the encoding we introduce leads to significantly better performance of quantum algorithms than previously considered strategies. Importantly, the encoding we develop also enab

This paper represents the metaheuristics proposed for solving a class of Shop Scheduling problem. The Bacterial Foraging Optimization algorithm is featured with Ant Colony Optimization algorithm and proposed as a natural inspired computing approach to solve the Mixed Shop Scheduling problem. The Mixed Shop is the combination of Job Shop, Flow Shop and Open Shop scheduling problems. The sample instances for all mentioned Shop problems are used as test data and Mixed Shop survive its computational complexity to minimize the makespan. The computational results show that the proposed algorithm is gentler to solve and performs better than the existing algorithms.

Job shop scheduling problems represent a significant and complex facet of combinatorial optimization problems, which have traditionally been addressed through either exact or approximate solution methodologies. However, the practical application of these solutions is often challenged due to the complexity of real-world problems. Even when utilizing an approximate solution approach, the time required to identify a near-optimal solution can be prohibitively extensive, and the solutions derived are generally not applicable to new problems. This study proposes an innovative attention-based reinforcement learning method specifically designed for the category of job shop scheduling problems. This method integrates a policy gradient reinforcement learning approach with a modified transformer architecture. A key finding of this research is the ability of our trained learners within the proposed method to be repurposed for larger-scale problems that were not part of the initial training set. Furthermore, empirical evidence demonstrates that our approach surpasses the results of recent studies and outperforms commonly implemented heuristic rules. This suggests that our method offers a promis

We study heuristic algorithms for job shop scheduling problems. We compare classical approaches, such as the shifting bottleneck heuristic with novel strategies using decision diagrams. Balas' local refinement is used to improve feasible solutions. Heuristic approaches are combined with Mixed Integer Programming and Constraint Programming approaches. We discuss our results via computational experiments.

Increased flexibility in job shops leads to more complexity in decision-making for shop floor engineers. Partial Flexible Job Shop Scheduling (PFJSS) is a subset of Job shop problems and has substantial application in the real world. Priority Dispatching Rules (PDRs) are simple and easy to implement for making quick decisions in real-time. The present study proposes a novel method of integrating Multi-Criteria Decision Making (MCDM) methods and the Discrete Event Simulation (DES) Model to define job priorities in large-scale problems involving multiple criteria. DES approach is employed to model the PFJSS to evaluate Makespan, Flow Time, and Tardiness-based measures considering static and dynamic job arrivals. The proposed approach is implemented in a benchmark problem and large-scale PFJSS. The integration of MCDM methods and simulation models offers the flexibility to choose the parameters that need to govern the ranking of jobs. The solution given by the proposed methods is tested with the best-performing Composite Dispatching Rules (CDR), combining several PDR, which are available in the literature. Proposed MCDM approaches perform well for Makespan, Flow Time, and Tardiness-ba

We study a repairable inventory system dedicated to a single component that is critical in operating a capital good. The system consists of a stock point containing spare components, and a dedicated repair shop responsible for repairing damaged components. Components are replaced using an age-replacement strategy, which sends components to the repair shop either preventively if it reaches the age-threshold, and correctively otherwise. Damaged components are replaced by new ones if there are spare components available, otherwise the capital good is inoperable. If there is free capacity in the repair shop, then the repair of the damaged component immediately starts, otherwise it is queued. The manager decides on the number of repairables in the system, the age-threshold, and the capacity of the repair shop. There is an inherent trade-off: A low (high) age-threshold reduces (increases) the probability of a corrective replacement but increases (decreases) the demand for repair capacity, and a high (low) number of repairables in the system leads to higher (lower) holding costs, but decreases (increases) the probability of downtime. We first show that the single capital good setting can