Optimizing sustainable greenhouse flower-plant production: Managing trapezoidal demand dynamics and shortages

Rapid growth of the greenhouse, nursery, and flower industry, fueled by advancements in sustainability, technology, and innovative farming techniques, necessitates detailed exploration of sustainable production practices. This study delves into the complex dynamics of greenhouse flower-plant production (GFPP), focusing on strategies to minimize system costs while reducing environmental impacts. The production process is segmented into four critical stages: seed germination, development, maturation, and decline. Throughout the germination phase, no sales occur. In the development phase, trays are allocated for individual plants in preparation for marketing. As plants mature, demand rises, stabilizes, and gradually declines, following a trapezoidal demand pattern (TDP). Greenhouse farming operates in controlled environments, relying on heating, cooling, artificial lighting, and fertilizers, which contribute to emissions. These emissions are regulated under various frameworks, including carbon tax (CT), cap-and-trade (CAT), and cap-and-price (CAP) schemes, each imposing different cost and compliance requirements on the producer. Flower plant mortality is modeled as a continuous probability distribution function, adding further complexity to production planning. This research aims to identify the optimal stocking time that minimizes the producer’s costs while adhering to emission regulations. Analytical insights are developed and validated through multiple numerical scenarios. Findings demonstrate that sustainable GFPP can achieve balance between economic efficiency and environmental responsibility. By adopting proposed strategies, producers can enhance operational sustainability, contribute to ecological preservation, and strengthen flower industry resilience.