Two-level lot-sizing with raw-material perishability and deterioration

In many production systems, it is common to face significant rates of product deterioration, referring to physical exhaustion, loss of functionality and volume, or even obsolescence. This deterioration property, known as perishability, prevents such products from being used after their expiration time. We present lot-sizing problems that incorporate raw-material perishability and analyse how these considerations enforce specific constraints on a set of fundamental decisions, particularly for multi-level structures. We study three variants of the two-level lot-sizing problem incorporating different types of raw-material perishability: (a) fixed shelf-life, (b) functionality deterioration, and (c) functionality-volume deterioration. We propose mixed-integer programming formulations for each of these variants and perform computational experiments with sensitivity analyses. We analyse the added value of explicitly incorporating perishability considerations into production planning problems. For this, we compare the results of the proposed formulations with those obtained by implementing a sequential approach that adapts a standard two-level lot-sizing solution with a Silver-Meal-based rolling-horizon algorithm.