Some relevant literature I did manage to find...thanks Scopus
Boes, K.E. (2010). Honeybee colony drone production and maintenance in accordance with environmental factors: An interplay of queen and worker decisions. Insectes Sociaux, 57: 1-9.
Seeley, T.D. and Mikheyev, A.S. (2003). Reproductive decisions by honey bee colonies: Tuning investment in male production in relation to success in energy acquisition. Insectes Sociaux, 50:134-138.