A stochastic chance-constraint framework for poultry planning and egg inventory management

This study addresses the capacitated lot-sizing problem in the poultry industry for egg production planning, aiming to minimize production, transportation, and inventory costs. This problem has already been investigated with data certainty and formulated as a mathematical model and a heuristic algorithm has been applied to solve it due to high complexity. In this study, we reformulate the same problem as a new mixed integer linear programming model to achieve optimal solution in a relatively short time without the need for heuristic algorithms. To evaluate the model performance, it is executed using the available data, and its efficiency is validated by comparing the obtained results. Subsequently, the uncertainty of weekly demand is considered, leading to potential shortage or surplus in storage. To address this uncertainty, the chance-constraints method is employed with various attitudes, and several production plans are proposed accordingly. The performance of these plans is compared using random data, and the most suitable programs are identified. The presented decision-making tool can provide production planning that meets customer demand with high reliability while also minimizing surplus inventory in the warehouse.