Automated clinical analyzers must handle large worklists under strict throughput requirements, where physical operations associated with consumable access can become a bottleneck. This paper addresses a novel plate-aware scheduling problem arising in the VirClia Lotus 360 analyzer, where reagent strips are stored in a refrigerated area and can only be accessed by extracting entire plates into a working area. The goal is to jointly decide (i) the execution order of diagnostic requests and (ii) the assignment of each request to a specific reagent strip, so as to minimize plate handling operations while incorporating soft expiration-aware preferences. To tackle the resulting combinatorial problem, we propose a domain-tailored genetic algorithm with plate-aligned crossover and two complementary mutation operators.