Managing Operations of a Hog Farm Facing Volatile Markets: Inventory and Selling Strategies

Problem Definition: We study a dynamic finishing stage planning problem of a pork producer who gets to see how many market-ready hogs she has available for sale at the beginning of each week and the current market prices. Then, she must decide how many hogs to sell to a meatpacker and on the open market. The producer has a contract to deliver a fixed quantity to the meatpacker each week priced according to a predetermined formula that depends on market commodity indices. She pays a penalty if she fails to deliver. The numbers of hogs that become market-ready every week, all costs, and all prices fluctuate over time. Academic/Practical Relevance: We solve the finishing stage planning problem as a dynamic, multi-item (hogs of different weight fetch different prices) inventory model with uncertain supply and stochastic prices. Methodology: We use a dynamic programming approach to derive an optimal policy and a one-period look-ahead heuristic informing the farmer on what hogs to sell at the beginning of each week. Results: We show there are sell/hold thresholds that depend on the available hogs' weights, quantities, and prices. Unfortunately, identifying the thresholds requires messy computations. So, we propose an approximate dynamic programming approach that preserves the optimal policy structure and produces a sharp heuristic that is easy to implement. Managerial Implications: Numerical experiments calibrated to a pork producer's data (The Maschhoffs) reveal the optimal policy is a substantial improvement over the existing practice (around 25% on average), and the one-period look-ahead policy is as close as 1.76% from the optimal. The majority of the improvement value over the current practice is recognizing and exploiting the ``real option'' value of under-weight hogs in hedging supply uncertainty and stochastic prices.