Simulating management policies on stock supplied by multiple production units: Application to a pig slurry treatment plant

Because of intensive animal farming, the problem of animal wastes disposal has become very acute in the Reunion Island, namely for liquid wastes such as pig slurry. In this paper we address the problem of determining efficient supply policies of a slurry treatment plant collectively managed by individual farmers. For this, we built a simulation model with a continuous part (i.e., slurry stocks modeled as ordinary differential equations) and a discrete part (i.e., transport allocation as a Linear Program). Simulations are carried out considering the specific constraints of farmers in a critical zone in the Reunion Island. The results emphasize the positive role of a closed-loop control, which means organizing slurry transportation according to the current states of individual stocks. INTRODUCTION With the development of intensive animal farming in the highlands of the Reunion Island in the past ten years, the problem of animal wastes disposal has become more acute, namely for liquid wastes such as pig slurry. In some places like Grand-Ilet, the available cultivated area is far too small to allow pig slurry spreading on crops in conditions complying with the regulation [Renault and Paillat, 1999]. This results in an excessive crop fertilization and related risks for the environment. Therefore, the treatment of pig slurry appears as a necessity in this area. Since all of the 56 pig farms of Grand-Ilet are very small (compared to European standards) and cannot afford individually the treatment costs, the choice is being oriented towards a collective solution. In this paper we address the problem of determining efficient supply policies of such a collective slurry treatment plant (STP) by the individual farms. Questions to be answered are typical of stock management problems: Who must deliver pig slurry to the STP? When? How much must be delivered? We present first, the system entities and describe the different types of supply policies to be envisaged. The criteria to compare alternative policies are the minimization of slurry stock overflow (losses to the environment) of both the farms and the STP. Then, we describe a conceptual view of the model as a block-diagram and its mathematical formalization made of: • a continuous part, as ordinary differential equations accounting for the dynamics of the stocks; 362 • a discrete part, as a Linear Program [Wolsey, 1998] representing the transport organization to deliver slurry to the STP. Finally, two simulation scenarios, based on the specific constraints of Grand-Ilet farms, are presented. APPLICATION BACKGROUND System description Waste flow Dynamic information Static information Sub-system System limits Supply policies Stock CU STP Transport Organization Delivery IJ elivery IJ Conveyor 1 onveyor 1 Conveyor J onveyor J ...