Mathematical programming models, as typically formulated for international trade applications, may contain certain implied restrictions limiting price responsiveness, intermediate product flows, and arbitrage possibilities. These restrictions are especially important in the case of dairy, and may lead to results which are technically infeasible, or if feasible, not consistent with market equilibrating behavior. The difficulties encountered when modeling dairy trade are described, and an alternative formulation of a spatial model is presented. This formulation allows joint-inputs, multi-products, intermediate markets, and pure transshipment and product substitution forms of arbitrage.