Optimizing vertically integrated pork production supply chain: A Lagrangian heuristic approach

Pork stands out as the most extensively produced and consumed meat globally. With advancements in technology, genetics, and management, the structure of the pig supply chain has transformed from the traditional birth-to-slaughter raising method to incorporate four primary specialized operations: breeding, farrowing, nursery, and fattening. Fattening, constituting approximately 70% of a market pig's entire life cycle, heavily relies on resources, notably in feed consumption. Despite the integration of feed production with pig farming in modern industrial setups through farming contracts, separate decision-making processes for production planning in both stages often result in overall inefficiency. This research proposes an optimization-based methodology to plan production for a vertically integrated setting of three supply chain echelons: a feed mill, fattening farms, and a slaughterhouse. Key coordinated decisions include creating production plans for specific feed formulations at the feed mill and organizing farming cycles at fattening farms to meet the demand of the slaughterhouse The aim is to optimize pig growth while minimizing the overall costs. The methodology includes a mixed-integer linear programming model for the pig supply chain, and a Lagrangian heuristic as method to make coordinated production plans. Computational experiments were conducted using diverse case-study data based on pig supply chains in Thatland. Compared with the results using a commercial software, Lingo's Simplex method, our proposed heuristic could find optimal solutions quicker for smaller problem instances and produce more effective feasible solutions within limited time frames for larger scenarios.