Optimization models for coordinating flock procurement in a poultry company

Abstract

A poultry company must coordinate the collection of flocks of chickens from farms subject to supply management to meet demand while fulfilling the facility's operational constraints. A modified version of the multi-period lot sizing with supplier selection problem framework is used to formulate three models: an integer program, a weighted goal program, and a minmax goal program. A two-stage stochastic variation of the problem is then considered, in which forecasts of each average flock weight are uncertain, and the three models are adapted to solve it. Soft robust optimization is used with the integer program. The deterministic and stochastic minmax goal programming approaches significantly reduce the maximum expected deviation from optimality without significantly impacting quota fulfillment, reducing risk of a large deviation from optimality for all parties. The stochastic approach reduces the maximum expected deviation from optimality by between 40.3% and 86.6% of its original value for five test weeks.