The Resource-Constrained Project Scheduling Problem (RCPSP) is a classical scheduling problem that has received significant attention due to of its numerous applications in industry. However, in practice, task durations are subject to uncertainty that must be considered in order to propose resilient scheduling. In this paper, we address the RCPSP variant with uncertain tasks duration (modeled using known probabilities) and aim to minimize the overall expected project duration. Our objective is to produce a baseline schedule that can be reused multiple times in an industrial setting regardless of the actual duration scenario. We leverage Graph Neural Networks in conjunction with Deep Reinforcement Learning (DRL) to develop an effective policy for task scheduling. This policy operates similarly to a priority dispatch rule and is paired with a Serial Schedule Generation Scheme to produce a schedule. Our empirical evaluation on standard benchmarks demonstrates the approach's superiority in terms of performance and its ability to generalize. The developed framework, Wheatley, is made publicly available online to facilitate further research and reproducibility.

The rapid growth of e-commerce in recent years has significantly transformed people's shopping habits [1]. Consumers increasingly favor online shopping over in-person purchases, leading to a substantial impact on product logistics, which plays a crucial role in customer satisfaction. In addition to product quality and other factors, the timely delivery of orders has become a key determinant of customer satisfaction. Picking and replenishment tasks are responsible for 65% of operating costs [2]. In a conventional manual order picking system, often referred to as a picker-to-parts system, pickers dedicate 70% of their working time to searching for items and traveling within the facility [3, 4].

The alignment problem in Large Language Models (LLMs) involves adapting them to the broad spectrum of human values. This requirement challenges existing alignment methods due to diversity of preferences and regulatory standards. This paper introduces a novel alignment paradigm, priority rule following, which defines rules as the primary control mechanism in each dialog, prioritizing them over user instructions. Our preliminary analysis reveals that even the advanced LLMs, such as GPT-4, exhibit shortcomings in understanding and prioritizing the rules. Therefore, we present PriorityDistill, a semi-automated approach for distilling priority following signals from LLM simulations to ensure robust rule integration and adherence. Our experiments show that this method not only effectively minimizes misalignments utilizing only one general rule but also adapts smoothly to various unseen rules, ensuring they are shielded from hijacking and that the model responds appropriately.

The Clustered Traveling Salesman Problem with a Prespecified Order on the Clusters, a variant of the well-known traveling salesman problem is studied in literature. In this problem, delivery locations are divided into clusters with different urgency levels and more urgent locations must be visited before less urgent ones. However, this could lead to an inefficient route in terms of traveling cost. This priority-oriented constraint can be relaxed by a rule called d-relaxed priority that provides a trade-off between transportation cost and emergency level. Our research proposes two approaches to solve the problem with d-relaxed priority rule. We improve the mathematical formulation proposed in the literature to construct an exact solution method. A meta-heuristic method based on the framework of Iterated Local Search with problem-tailored operators is also introduced to find approximate solutions. Experimental results show the effectiveness of our methods.

This paper considers multiprocessor task scheduling in a multistage hybrid flow-shop environment. The problem even in its simplest form is NP-hard in the strong sense. The great deal of interest for this problem, besides its theoretical complexity, is animated by needs of various manufacturing and computing systems. We propose a new approach based on limited discrepancy search to solve the problem. Our method is tested with reference to a proposed lower bound as well as the best-known solutions in literature. Computational results show that the developed approach is efficient in particular for large-size problems.

We characterize the search landscape of random instances of the job shop scheduling problem (JSP). Specifically, we investigate how the expected values of (1) backbone size, (2) distance between near-optimal schedules, and (3) makespan of random schedules vary as a function of the job to machine ratio (N/M). For the limiting cases N/M approaches 0 and N/M approaches infinity we provide analytical results, while for intermediate values of N/M we perform experiments. We prove that as N/M approaches 0, backbone size approaches 100%, while as N/M approaches infinity the backbone vanishes. In the process we show that as N/M approaches 0 (resp. N/M approaches infinity), simple priority rules almost surely generate an optimal schedule, providing theoretical evidence of an "easy-hard-easy" pattern of typical-case instance difficulty in job shop scheduling. We also draw connections between our theoretical results and the "big valley" picture of JSP landscapes.