Dual-resource-constrained distributed flexible job shop scheduling problems (DCDFJSSPs), which involve coupled decisions on cross-factory job allocation and within-factory machine–worker scheduling, have attracted increasing research attention. However, most existing studies remain time- and workload-driven and rarely incorporate explicit energy-control policies, leaving the joint effects of cross-factory allocation, machine–worker matching, and energy control underexplored. To bridge this gap, we introduce an energy-efficient DCDFJSSP (EDCDFJSSP) and formulate a bi-objective model that integrates machine speed scaling to jointly optimize makespan and energy consumption. We further propose a hierarchical graph reinforcement learning (HGRL) method, where a high-level agent balances workloads across factories, and low-level agents jointly decide machine selection, worker assignment, and speed level using multi-level graph representations and a factored action space. Experiments on instances of varying sizes demonstrate that HGRL consistently outperforms competitive baselines and achieves superior makespan–energy trade-offs.
Increasingly stringent decarbonization targets and growing penetration of variable renewables are driving the need for multi-energy systems that can coordinate electricity and heat supply while remaining reliable under uncertainty. This paper addresses the optimal design of a hybrid multi-energy system supplying electricity and heat to a residential complex under multiple sources of uncertainty. The proposed system integrates combined heat and power generators, boilers, photovoltaic panels, solar thermal collectors, and electrical and thermal storage units. To hedge against variability in energy demands, renewable generation, and electricity/fuel prices without assuming known probability distributions, we formulate a two-stage adjustable robust optimization model that couples first-stage investment, i.e., sizing, decisions with fully adaptive second-stage operational decisions. Uncertainty is modeled via a budgeted uncertainty set that controls conservatism through uncertainty budgets. The resulting mixed-integer min–max–min problem is solved using a nested column-and-constraint generation algorithm, since the second-stage (recourse) problem includes binary variables and cannot be handled by standard column-and-constraint generation. Computational experiments on a realistic case study for Turin, Italy, show that uncertainty affects both total cost and the preferred technology mix. In the in-set stress tests, robust designs require no reimbursement in any of the scenarios, whereas the nominal and finite-scenario stochastic designs exhibit violations in several cases. Comparison of the proposed method with static robust design demonstrates the economic value of operational adjustability. Outside the prescribed uncertainty set, which neither the proposed model nor the static robust model is designed to protect against, performance is case-dependent and our model performs better in general.
Two-echelon delivery systems and Mobile Parcel Lockers (MPLs) are emerging urban last-mile solutions that reduce failed home deliveries, ease curbside pressure, and support cleaner electric operations. This study introduces the Two-Echelon Electric Vehicle Routing Problem with Mobile Parcel Lockers (2E-EVRP-MPL), which jointly optimizes first-echelon e-truck replenishment, second-echelon MPL routing, satellite activation, stopping-point selection, customer assignment, and charging decisions in a self-collection system. We formulate a mixed-integer linear program that captures battery and payload limits in both echelons, customer-to-stopping-point coverage, parking capacity, locker-compartment capacity, the stationary energy drawn by a parked locker, satellite activation, and stopping-point costs. We then develop a three-stage matheuristic combining an Adaptive Large Neighborhood Search with Variable Neighborhood Descent (ALNS-VND) for the second echelon, an exact dynamic-programming replenishment solver for the first echelon whose optimality we establish analytically and verify against an independent exact formulation, and an integrated post-local search for cross-echelon improvement. On newly generated benchmark instances, the method attains the proven optimum on every small instance closed by Gurobi, matches or improves its incumbent on all medium instances, and returns feasible solutions on all large instances, including those where Gurobi finds none within one hour, at a fraction of the exact solver’s runtime. When adapted to related benchmark instances, it matches or improves the published best-known values for 87 of 96 tested instances. A scenario analysis quantifies how total cost changes with the walking radius, stopping-point price, and MPL and satellite design under the tested operating conditions.
Dynamic flexible job shop scheduling (DFJSS) couples routing and sequencing decisions under stochastic arrivals, heterogeneous machine capabilities, and due date constraints. This study develops a decomposed deep reinforcement learning framework with independently trained routing and sequencing policies optimized by generalized fractional derivative stochastic classical momentum (GFD–SCM). The update modulates momentum attenuation and gradient scale as functions of the iteration without storing historical gradients or changing the computational order at each iteration. Under uniformly bounded stochastic gradients, the analysis establishes boundedness and asymptotic forgetting of the internal momentum state. The policies use compact state descriptors, slack sensitive rewards, and asynchronous transitions. In the primary routing experiments, the routing policy improves normalized performance by approximately 1.2 to 4.5 percentage points relative to CT and records win rates of 65 to 70%. In a separate benchmark, the GFD–SCM policy pair yields lower cumulative tardiness than Transformer–RL, Hierarchical–RL, and MLP after Holm correction.
The Flexible Job Shop Scheduling Problem with Transportation involves complex spatio-temporal coupling that challenges traditional scheduling methods. While deep reinforcement learning offers promise, existing approaches often suffer from the curse of dimensionality and fail to generalize across varying problem scales. To address these limitations, this study proposes a transfer-learning-enabled deep reinforcement learning system designed for rapid adaptation to large-scale instances. We first construct a dimension-independent composite action space that coordinates machine and automated guided vehicle dispatching rules, ensuring the action dimension remains invariant to resource quantity. Subsequently, a dual-agent framework is established to bridge the generalization gap. A generalist agent captures invariant scheduling priors using NoisyLinear-enhanced exploration, while a specialist agent rapidly adapts to specific instances via a transferred backbone and an LSTM-based temporal projection interface. Furthermore, an annealed probability sampling mechanism is integrated into the policy network to dynamically balance exploration and exploitation, thereby preventing premature convergence. This generalization-to-adaptation mechanism alleviates the cold-start training burden of deep reinforcement learning by providing a transferable initialization for rapid fine-tuning on target instances. Experimental results on benchmarks and large-scale synthetic datasets demonstrate that the proposed method significantly outperforms classical heuristics and state-of-the-art meta-heuristics, exhibiting superior stability and solution quality in complex manufacturing scenarios.
