We consider a periodic-review perishable inventory system with multiple demand classes, each characterized by a different lost-sales cost and the least freshness requirement. Demands of different classes in the same period could be correlated, while demands across periods are independent but not necessarily identical. In each period, the firm jointly makes the decisions regarding demand fulfillment, production/ordering, and disposal. The objective is to minimize the total discounted expected cost over the entire planning horizon including linear ordering cost, inventory holding/lost-sales cost, expiration cost, and disposal cost. By establishing new properties of multimodularity, we explore some monotonicity and bounded sensitivity properties of the optimal policies. The optimality analysis enables us to propose a novel approximation approach, called adaptive approximation approach, which can be recursively calculated through a single-dimension dynamic program. Numerical studies demonstrate that our proposed approximation approach is nearly optimal with the average optimality gap 0.30% and significantly outperforms the existing heuristics in the literature.

中文翻译：

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管理具有年龄差异化需求的易腐烂库存系统

我们考虑具有多个需求类别的定期审查易腐烂库存系统，每个类别的特点是不同的销售损失成本和最少的新鲜度要求。同一时期不同类别的需求可能是相关的，而跨时期的需求是独立的，但不一定相同。在每个时期，企业共同做出有关需求满足、生产/订购和处置的决策。目标是最小化整个计划范围内的总折扣预期成本，包括线性订购成本、库存持有/销售损失成本、到期成本和处置成本。通过建立多模性的新特性，我们探索了最优策略的一些单调性和有界敏感性特性。最优性分析使我们能够提出一种新的近似方法，自适应逼近法，可以通过单维动态程序进行递归计算。数值研究表明，我们提出的近似方法几乎是最优的，平均最优差距为 0.30%，并且明显优于文献中现有的启发式方法。