Towards a Fuzzy Approach for Optimizing Single Machine Common Due Date Scheduling Problem under Uncertainty

This investigation explores the scheduling of n jobs on a single machine, where each job possesses a common due date, and processing time is characterized by pentagonal fuzzy numbers (PFNs). The primary objective is to minimize the aggregate of inventory holding and penalty costs, addressing the critical impact of earliness and tardiness on profitability. It is identified that earliness leads to increased inventory carrying costs and potential degradation in product quality, whereas tardiness undermines customer goodwill and inflicts reputational damage through delayed payments. Consequently, the scheduling dilemma that seeks to minimize the combined penalties of earliness and tardiness, whilst adhering to a common due date on a single machine, emerges as a pivotal and challenging endeavor in optimizing goods delivery within production settings. Recognized as a non-deterministic polynomial-time hardness (NP-hard) problem, this task underscores the complexity and competitive nature inherent in manufacturing operations. To navigate the uncertainties embedded in this problem, a fuzzy logic approach, augmented by a heuristic algorithm, is employed. Through this methodology, the problem is addressed in a manner that encapsulates the vagueness and imprecision inherent in processing time, thereby facilitating more resilient and adaptable scheduling decisions. The efficacy of this approach is demonstrated via a computational example, underscoring its potential to enhance decision-making in the realm of job scheduling.