An artificial insemination (AI) company seeks to allocate semen units globally by balancing perceived demand with uncertain product supply, in what is an arduous subjective process. This study aimed to objectivize this process by providing a user-friendly linear programming model to allocate bulls' semen units to regions for the next trimester sales period based on maximum revenue, and to describe the features and outcomes of this model when applied to a sample bull herd and global demand scenario reflective of a leading AI company. The objective function of maximizing revenue was calculated by summing the product of units allocated by bull and region with purchase prices assigned by bull and region. Constraints considered were regional demand for overall units, regional preferences for specific genetic traits, bulls' production capacity, and percentage of bulls' units allocated to a single region. A sensitivity analysis was performed to identify the effects of variables and constraints on total revenue. Production, sales, and bull demographic data from 2018 to 2021 from a leading AI company were used to establish base values and build a sample herd of 61 bulls and 5 global regions. The case study provided a maximum revenue of $8,287,197 in semen sales per trimester, with 634,700 units allocated. Of the 61 bulls in the case study, 9 were not allocated to any region. The most limiting constraint was regional demand, which resulted in a surplus of 274,564 units not allocated. A sensitivity analysis confirmed this finding, with the largest shadow prices assigned to regional demands, and indicated that a single unit increase in regional demand would add up to $14.84 in total revenue.
Keywords: allocation; linear program; sperm production.
The Authors. Published by Elsevier Inc. and Fass Inc. on behalf of the American Dairy Science Association®. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).