Integrated Production Scheduling and Vehicle Routing Problem with Energy Consumption

Abstract

In contemporary manufacturing, the sequential planning of production scheduling and vehicle routing often leads to sub-optimal performance, characterized by excessive inventory and delivery delays. This study addresses the Integrated Production-Distribution Scheduling Problem (IPDS) within flow shop environments, a challenge traditionally categorized as NP-hard. While recent literature emphasizes the benefits of operational coordination-incorporating realistic constraints such as soft time windows, heterogeneous fleets, and multi-trip structures-a critical gap remains: the systematic integration of energy as a hard operational resource limitation. Although sustainability is an emerging trend, most existing “green” models treat energy or emissions solely as objective-function terms rather than as decision-space constraints. To bridge this gap, this paper proposes a Mixed-Integer Programming (MIP) model that jointly optimizes production sequencing and distribution routing under explicit energy constraints. By solving the generated instances, the results show that this model has the capabilities to generate quality output in optimization problems. The primary contribution of this work lies in providing a decision-making framework that ensures cost-effectiveness and high customer service levels while maintaining energy feasibility. By transforming environmental factors into fundamental operational constraints, the proposed approach enhances the realism of sustainable supply chain optimization, offering significant insights for both academic research and industrial applications.