scheduling

This paper investigates fair scheduling of multi-weighted strategic jobs on identical machines, jointly ensuring game-theoretic stability (Nash equilibrium) and fairness—namely, load equality among equally weighted jobs, weighted envy-freeness, and its natural relaxations. We first establish a hierarchical framework for weighted fairness and introduce *weight-aware relaxed envy-freeness*. Systematically analyzing the joint satisfiability of fairness properties—individually and in combination—with Nash equilibrium, we derive a complete computational complexity landscape. Crucially, under makespan minimization, we prove that several key fairness constraints admit polynomial-time algorithms. Our primary contribution is a unified model integrating fairness and strategic robustness, bridging fair allocation theory and strategic scheduling through combinatorial game-theoretic analysis and constrained optimization.

This study addresses the trade-off between fairness and efficiency in single-machine multi-agent scheduling, where each self-interested agent’s utility decreases with job completion time. Focusing on settings with release times, deadlines, and processing time constraints, the work introduces—for the first time—the fairness objective of maximizing the minimum utility into time-dependent utility scheduling models. By integrating binary search with a greedy strategy, the authors develop polynomial-time exact algorithms and establish computational complexity boundaries—distinguishing between strongly and weakly NP-hard variants—for several problem formulations. The framework is further extended to novel scenarios involving tunable utility functions, rescheduling with inserted jobs, and bilevel optimization. The research elucidates how utility adjustments mediate the fairness–efficiency trade-off and provides an efficient solution methodology applicable across these generalized settings.

This work addresses the challenge of balancing performance and fairness in dynamic task graph scheduling, where traditional approaches often neglect adjustments to existing task assignments. To overcome this limitation, the authors propose the Last-K Preemption model, which introduces a controlled, localized preemption mechanism that reschedules only the most recent K task graphs while preserving earlier allocations. This strategy effectively balances scheduling efficiency against system overhead. Extensive experiments are conducted using synthetic, RIoTBench, WFCommons, and adversarial workloads, comparing fully preemptive, non-preemptive, and partially preemptive strategies. The results demonstrate that the proposed moderate preemption approach achieves makespan and resource utilization comparable to full preemption, while significantly reducing scheduling overhead and ensuring fairness.

This paper addresses the fair and efficient allocation of periodic tasks under recurring schedules. While conventional approaches optimize efficiency by minimizing the number of workers, we formally define long-term workload fairness—measuring equitable task distribution across workers over time—and characterize its fundamental trade-off with efficiency. Contribution/Results: We prove that achieving fairness incurs at most one additional worker beyond the optimal efficient solution, and this bound is tight; we further derive necessary and sufficient conditions for joint fairness-efficiency feasibility. Method: We propose an exact *O*(*n* log *n*) algorithm and an efficient nearest-neighbor heuristic, both constructing one-to-one fair allocations without resorting to aperiodic scheduling. Experiments confirm that the theoretical fairness-cost upper bound is attainable and demonstrate that our approach guarantees optimal efficiency while ensuring strict long-term fairness.

This study systematically evaluates the faithfulness and consistency of large language models (LLMs) in adhering to constraints when solving natural language scheduling problems that are semantically equivalent but differ in surface form. To this end, we introduce SCHEDBench, the first natural language benchmark for combinatorial scheduling tasks, encompassing diverse problem types such as job shop scheduling (JSP), resource-constrained project scheduling (RCPSP), workforce rostering, and timetabling. We generate varied surface formulations through lexical-syntactic rewrites and constraint reordering. Using scheduling solvers for validation and domain-specific templates for generation, our evaluation across 13 state-of-the-art LLMs reveals a critical lack of invariance: surface-level variations significantly degrade solution feasibility, with constraint reordering most frequently causing violations of hard constraints. This work is the first to expose the pronounced sensitivity of LLMs to linguistic surface form in scheduling reasoning.

This study addresses the Resource-Constrained Project Scheduling Problem (RCPSP) by proposing a modeling approach based on timed Petri nets, wherein scheduling decisions are represented as transitions in the state space triggered by relative delay tokens. Building upon this formulation, the authors design an admissible A* heuristic that integrates critical path information with resource-constrained lower bounds to enable efficient optimal search. Experimental results on the PSPLIB benchmark suite demonstrate that the proposed method outperforms state-of-the-art mixed-integer programming solvers such as SCIP and CBC in both solution success rate and computational time. Furthermore, the findings reveal a complementary performance relationship between heuristic search and mixed-integer programming approaches across varying problem scales.

This work addresses the NP-hard problem of shift scheduling that simultaneously satisfies complex hard constraints—such as labor regulations, mandatory rest periods, and cross-midnight shifts—and optimizes multiple soft objectives, including employee preferences and workload fairness. The authors propose a declarative, configurable framework based on CP-SAT, enabling flexible specification of 14 hard constraints and 15 soft objectives via JSON without code modification, thereby guaranteeing zero-constraint violations and enabling trade-offs among objectives. Key innovations include shift-window variable decomposition for centralized rest enforcement, a sensitivity-weighted workload fairness mechanism, multi-granularity temporal modeling, inter-week stability preservation, and a grid-offset preprocessing technique for cross-midnight shifts. Experiments on INRC-II and 36 synthetic configurations demonstrate the framework’s efficiency in handling scheduling granularities from 30 minutes to 2 hours while strictly adhering to all hard constraints.