Integrated Production Scheduling and Vehicle Routing Problem with Energy Consumption

Mixed fleet sizing and scheduling for green distribution with time-based shipment consolidation

Multi-Ob jective Stochastic Electric Vehicle Routing Problem with Time Windows

Solving a Real-World Integrated Production–Distribution Scheduling Problem with a GRASP

In make-to-order manufacturing environments, production scheduling and outbound transportation are strongly interdependent, particularly when delivery commitments and vehicle departures are fixed. This paper addresses an integrated production-distribution scheduling problem arising in a real-world food packaging company. The production system consists of unrelated parallel machines with sequence-dependent, machine-specific setup times, while outbound transportation involves a heterogeneous fleet of vehicles with limited capacity, fixed delivery departure times, and customer-specific delivery constraints. The objective function combines total weighted delivery tardiness and total setup times. To address the problem, we propose a GRASP metaheuristic that incorporates several local search procedures. Computational experiments on real-world instances demonstrate the effectiveness of the proposed approach in producing high-quality solutions within limited computational times. The proposed approach has been implemented within a decision support system and validated in collaboration with the industrial partner, confirming its effectiveness in real-world decision-making.

Integrated Production and Transportation Scheduling in a Distributed Hybrid Flow Shop Considering Dynamic Orders Under an E-Commerce Environment

Real-time order arrivals and stringent timeliness demands in e-commerce pose significant challenges to production-distribution coordinated scheduling in distributed manufacturing systems. This paper tackles the integrated production and distribution scheduling problem within a dynamic distributed hybrid flow shop. We formulate a mixed-integer linear programming model aimed at minimizing average order tardiness and total operational cost. To address dynamic uncertainties, we propose an improved decomposition-based multi-objective evolutionary algorithm (I-MOEA/D) operating within a rolling horizon framework. The algorithm integrates three critical components: an urgency-based emergency window management strategy that caps computational complexity, a 2-opt local search operator that boosts vehicle routing efficiency, and acceleration techniques—including order dictionary indexing, lightweight object replication, and distance caching—that guarantee real-time responsiveness. The window size is determined as Wmax = 50 through sensitivity analysis. Extensive experiments conducted on 100, 200, and 300-order scenarios with 30 independent random seeds demonstrate that I-MOEA/D markedly outperforms NSGA-II, MOALNS, and a reinforcement learning-driven hyper-heuristic (RL-HH). For 200 orders, I-MOEA/D reduces average tardiness by 18.5%, 41.0%, and 58.7% compared to NSGA-II, MOALNS, and RL-HH, respectively, while maintaining competitive cost performance (a cost gap of 16.99% relative to the static lower bound). The IGD metric achieves 0.0031, confirming good convergence and diversity. Acceleration techniques cut computation time by 56% without sacrificing solution quality. The algorithm scales efficiently with problem size. These results validate that I-MOEA/D delivers effective real-time decision support for dynamic distributed production-distribution systems.

Fairness-Aware Energy-Effective Electricity Technician Dispatch Problem

Combinatorial optimization problems involve identifying the best solution from a wide set of alternatives; these often arise in logistics, scheduling, and resource allocation. These problems, such as the Traveling Salesman Problem (TSP) and the Multi-Depot Vehicle Routing Problem (MDVRP), are generally NP-hard, with solution spaces that increase exponentially, making brute-force methods impractical. We address a specific application of the MDVRP: the Electricity Technician Dispatch Problem (ETDP), which involves planning and optimizing technician routes for maintenance services to customers at various geographical locations while satisfying specific constraints and objectives. We focus on a variant of the ETDP that optimizes multiple objectives, including economic, environmental, and social. Economic objectives aim to reduce operational costs, such as fuel costs and technician wages. Environmental objectives focus on sustainability, for example, by minimizing gas emissions. Social objectives include fairness of workload and customer satisfaction. We will explore the ETDP problem in single- and multi-objective contexts and solve it using nature-inspired techniques.

Integrating Petri net heuristics within MILP for optimizing energy-efficient scheduling of flexible manufacturing systems

Flexible Manufacturing Systems (FMSs) increasingly need to reconcile flexibility, high productivity and energy efficiency. This paper addresses the energy-efficient scheduling of routing-flexible FMSs with multiple job instances, shared machines and route-level Work-in-Process (WIP) constraints, where makespan and production energy consumption are jointly optimized. A Petri Net–Mixed-Integer Linear Programming (PN–MILP) hybrid framework is proposed, in which a Timed and Energy-aware Transition Petri Net (TETPN) models the discrete-event scheduling logic of the FMS, including routing alternatives, operation precedence, machine sharing and route-level WIP limits. Based on the TETPN representation and simulation, feasible timed schedules are generated by a Hybrid Filtered Beam Search Algorithm (HFBSA) and its Randomized Beam-Retention extension (RBR-HFBSA). These schedules are then translated into feasible warm starts for a time-indexed MILP formulation, which enforces the same scheduling constraints in optimization form and refines the final solution through exact search. The resulting PN–MILP hybrid schemes, HFBSA+MILP and RBR-HFBSA+MILP, therefore, connect PN-based feasible-schedule generation with MILP-based exact optimization. Computational experiments on a 60-scenario benchmark show that PN-based warm starts substantially improve the robustness of the exact solution process relative to solving the MILP model without any PN-derived warm start, particularly in large-scale and unbalanced production settings, by increasing the probability of attaining a feasible incumbent within the imposed time limit. The proposed framework thus enables more reliable and effective exact optimization for complex routing-flexible FMS scheduling problems.