Applying Stochastic Optimisation to the New Zealand Dairy Industry

Abstract

Pastoral dairy farmers continually make sequential decisions in the face of long-term environmental uncertainty and price volatility. Decisions made early in the season, such as the number of cows to farm per hectare, can have significant effects later in the season if, for example, the farmer is forced to import additional feed to meet the cows' energy demands during a drought. This thesis analyses the problems faced by pastoral dairy farmers through the lens of multistage stochastic optimisation. The thesis is structured in two distinct parts that are approximately equal in content.The first part of this thesis, Multistage Stochastic Optimisation , addresses the theory and computation of multistage stochastic optimisation. We focus on the stochastic dual dynamic programming algorithm as a solution technique for multistage stochastic optimisation models.There are three main chapters in Part I. First, we conduct a literature review of the current state-of-the-art stochastic dual dynamic programming implementation. We also discuss our experience of a range of numerical issues related to stochastic dual dynamic programming. Second, we describe SDDP.jl, a soft-ware package we have developed for solving multistage stochastic optimisation problems using stochastic dual dynamic programming. Finally, we describe an extension to the stochastic dual dynamic programming algorithm to enable the solution of problems with stagewise-dependent objective uncertainty. The second part of the thesis, Applications in the Dairy Industry, applies the theory and techniques developed in the first part of the thesis to the problems faced by pastoral dairy farmers in New Zealand.We develop two models: MOO - the Milk Output Optimiser, and POWDER - the milk Production Optimiser incorporating Weather Dynamics and Economic Risk. We use these models to analyse the decision-making of a farmer in the Bay of Plenty region of New Zealand in a variety of circumstances. Finally, we introduce forward contracting for milk and show how a risk-averse farmer can use forward contracts to effectively manage their downside risk.