Dairy Product Manufacturing Costs at Cooperative Plants

Cost data are summarized for 14 plants manufacturing cheese, butter, and powder and average costs are presented for each product. Average cost curves are estimated for each plant. The scale of plant for least-cost operations is identified for plants of each product type. Plant capacity utilization and seasonal volume variation and their impacts on manufacturing cost are delineated.Cooperatives, dairy, average cost curve, productivity, capacity utilization, seasonal variation, economies of scale, Agribusiness,

A Reserve-Balancing Pool for Services by Dairy Cooperatives

The rationale for compensating dairy cooperatives for the costs incurred in balancing milk supply for the fluid market is examined. A reserve-balancing pool is proposed to facilitate deducting supply-balancing service credit from a marketwide producer pool and making payment to cooperatives for providing the services. The volume of necessary reserves maintained for the fluid market determines the size of the reserve-balancing pool. A dairy cooperative qualifies for pool payment based on the volume of milk delivered for fluid uses and on the volume of necessary reserves actually balanced. An alternative qualification is to allocate the volume of necessary reserves each cooperative has to balance according to a cooperative's market share of milk for fluid and other uses.Cooperative, milk, reserve-balancing pool, seasonality, manufacturing costs, marketwide services, Agribusiness,

Convergence of the Abelian sandpile

The Abelian sandpile growth model is a diffusion process for configurations of chips placed on vertices of the integer lattice $\mathbb{Z}^d$, in which sites with at least 2d chips {\em topple}, distributing 1 chip to each of their neighbors in the lattice, until no more topplings are possible. From an initial configuration consisting of $n$ chips placed at a single vertex, the rescaled stable configuration seems to converge to a particular fractal pattern as $n\to \infty$. However, little has been proved about the appearance of the stable configurations. We use PDE techniques to prove that the rescaled stable configurations do indeed converge to a unique limit as $n \to \infty$. We characterize the limit as the Laplacian of the solution to an elliptic obstacle problem.Comment: 12 pages, 2 figures, acroread recommended for figure displa