A Linear Programming Model of Seasonality in Milk Production

Abstract

Intra-year milk supply patterns depend largely on the distribution of cow calving dates which in turn are influenced by climatic factors. The most important and least costly input to milk production is grass and the fresh growth and high digestibility of grass in spring and early summer often gives rise to a highly seasonal distribution of calvings resulting in a seasonal milk supply pattern. However, milk for liquid consumption and production of certain perishable milk products must be produced to meet a constant consumer demand throughout the year, necessitating a considerable amount of production outside the least cost period. The solution to this linear programming model gives the distribution of calving dates which will ensure the demand constraints are satisfied while minimizing production costs, and the solution to the dual gives a set of seasonal prices which should be paid to producers, equitably compensating them for the costs they incur.