Optimizing facility location, sizing, and growth time for a cultivated resource: A case study in coral aquaculture.

Production of cultivated resources require additional planning that takes growth time into account. We formulate a mathematical programming model to determine the optimal location and sizing of growth facilities, impacted by resource survival rate as a function of its growth time. Our method informs strategic decisions regarding the number, location, and sizing of facilities, as well as operational decisions of optimal growth time for a cultivated resource in a facility to minimize total costs. We solve this facility location and sizing problem in the context of coral aquaculture for large-scale reef restoration using a two-stage algorithm and a linear mixed-integer solver. We assess growth time in a facility in terms of its impact on survival (post-deployment) considering growth quantity requirements and growth facility production constraints. We explore the sensitivity of optimal facility number, location, and sizing to changes in the geographic distribution of demand and cost parameters computationally. Results show that the relationship between growth time and survival is critical to optimizing operational decisions for grown resources. These results inform the value of data certainty to optimize the logistics of coral aquaculture production.