Parallel machine scheduling with tardiness and waiting penalties under fixed shipment dates and destinations

Synchronization of production with outbound logistics is essential for most manufacturing companies because directly impacts resource usage, supply chain management, customer satisfaction, and operating expenses. Such a synchronization can help reducing costs and inefficiencies resulting from producing goods earlier than needed as well as reduction of tardiness in deliveries. This study aims to minimize tardiness and waiting penalties by integrating production scheduling and fixed shipment schedule. This problem has real-world limitations like vehicle capacity limits and set shipment dates, making its solutions highly applicable to business operations. Jobs are assigned to parallel machines and vehicles based on their processing times, due dates, ready times, shipment dates, and destinations. Each job can only be processed on one machine, and vehicles have limited capacity. The goal is to optimize assignments using a cost function that minimizes tardiness and waiting penalties. We developed two Mixed-Integer Linear Programming (MILP) models to address the problem. Given the complexity of solving these models, we employed a Simulated Annealing based matheuristic approach . To achieve this, we decomposed the problem into two subproblems: parallel machine scheduling and vehicle allocation. The simulated annealing algorithm optimizes machine scheduling, while the MILP formulation determines the objective for vehicle allocation. This method effectively balances the trade-offs between minimizing tardiness, waiting penalties, and adhering to constraints, ultimately providing a practical solution.