Dynamic and multi-resource flexible job shop scheduling in pharmaceutical manufacturing: A MILP-based decision support tool
针对制药车间多资源约束和动态订单到达问题，提出混合整数线性规划模型，用于离线与实时调度，帮助计划员根据当前状态决定是否接单，降低延误和资源占用。
This paper addresses a scheduling problem arising in a pharmaceutical manufacturing plant that provides particle size reduction services for active pharmaceutical ingredients. The production environment is characterized by strict quality requirements—such as contamination avoidance—and limited resource availability, making the scheduling task both complex and critical. We model the problem as a Multi-Resource Flexible Job Shop Scheduling Problem, extending the classical job shop formulation to incorporate additional resource and process constraints. The primary objective is to ensure the timely fulfillment of customer orders, with a secondary goal of reducing the time jobs occupy resources in order to improve overall responsiveness. We propose a Mixed-Integer Linear Programming (MILP) model to solve the problem. The MILP is used in both an offline deterministic setting, where all orders are known in advance, and in a real-time dynamic setting, where orders arrive incrementally. In the latter case, the model can be easily integrated into a real-time decision support tool that can assist planners in accepting or not incoming orders based on current system status. An extensive computational study on realistic pharmaceutical scenarios shows that the proposed approach produces reliable schedules with low weighted earliness and tardiness and reduced resource occupation, even under dynamic conditions, highlighting its practical value in constrained pharmaceutical manufacturing.