A Review of Mixed Batch Scheduling with Fuzzy Processing Times on Parallel Machines

Abstract

Mixed batch scheduling has emerged as a pivotal scheduling paradigm for industrial processes such as vacuum heat treatment, where batch processing time depends on both the maximum and total physical attributes of workpieces. However, the inherent fuzzy uncertainty in processing time, driven by equipment fluctuations, operator variability, and raw material inconsistencies, poses significant challenges for scheduling optimization. Existing algorithms often fail to reconcile the unique weighted-sum characteristic of mixed batches with fuzzy uncertainty, resulting in compromised solution quality or inefficiency in practical applications. This paper focuses on the core pain points in algorithm design for mixed-batch scheduling with fuzzy processing times on parallel machines. It conducts an in-depth review of approximation and metaheuristic algorithms. Specifically, it elaborates on the derivation logic of key models (e.g., fuzzy processing time calculation and defuzzification methods). It emphasizes performance discrepancies between algorithms through quantitative analyses of solution quality, computational efficiency, and stability. By narrowing the research scope to algorithmic adaptability and optimization mechanisms in fuzzy-mixed batch coupling, this review identifies the limitations of current methods. It provides insights for future algorithmic improvements, aiming to bridge the gap between theoretical scheduling and industrial practice.