Strategic Inventory Models for International Dairy Commodity Markets

Abstract

Fonterra Co-operative Group Ltd is the largest exporter of dairy ingredient products in the world. Fonterra’s production planning is subject to uncertain milk supply in a production year. We describe a model for Fonterra’s supply chain, of which the important features are uncertain milk supply, price-demand curves and contracting. We derive the forecast milk supply for a production year assuming linear regional growth in milk supply over years, and then we develop an additive model and a multiplicative model for uncertain milk supply. We present six optimization models assuming uncertain milk supply, of which two are multistage stochastic programming models. We describe an algorithm DOASA to solve the multistage stochastic programming models, give a mathematical proof of the almost-sure convergence of DOASA for the linear case, and give a discussion on convergence for quadratic objectives. We assess the policies defined by the solutions of the optimization models in sampled milk supply scenarios in simulation. The policy generated from a multistage stochastic programming model has significant advantages over the other policies. Another situation affected by uncertainty occurs when Fonterra sells products to international spot markets, and other agents’ sales have an impact on the market prices. One of the main markets for Fonterra is the European dairy market where the regulations of the European Union Commission have an impact on Fonterra’s earnings. In the second part of this thesis, we describe the European dairy market and present a game-theoretic inventory model for this market. The important features include two leaders, Fonterra and Australia, a follower EU (representing the European Union), and price-demand curves. The model consists of an optimization problem for each leader and an optimization problem for each follower, and solves the leaders’ optimization problems simultaneously for an equilibrium of the game. We describe an approach using EPECs and our algorithm to solve the model. We perform computational experiments in a game with real data, which shows simple results. To illustrate the complicated game structure when the market situation is changed, we perform computational experiments in a game with fictitious data. First we present a simplified version of the game where Fonterra and Australia act together as a single leader, and describe five strategies for this leader. Then we present the game where Fonterra and Australia compete. We present five equilibria and illustrate them using the leaders’ best responses. We also use sequential best response to illustrate how the leaders’ strategies evolve given a leader’s starting strategy. Finally we investigate the impact of inventory holding cost on equilibrium.