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

Abstract

Problem Definition: We study a dynamic finishing stage planning problem of a pork producer who, at the beginning of each week, gets to see how many market-ready hogs she has available for sale and the current market prices. Then, she must decide what hogs to sell to a meatpacker, on the open market, and what hogs to hold until the following week. The farmer is contracted to deliver a fixed quantity of hogs to the meatpacker each week, priced according to a contractually pre-determined market index. If the farmer under-delivers to the meatpacker, she pays a contractually pre-determined unit penalty also linked to a market index. Bio-security protocols prevent the farmer from buying hogs on the open market and selling them to the meatpacker. The farmer can, however, use the open market to sell hogs for prevailing market prices.

Methodology/Results: We treat the problem as a dynamic, multi-item, non-stationary inventory problem with multiple sources of uncertainty. The optimal policy is a threshold policy with multiple, price-dependent thresholds. The computational complexity required to evaluate the thresholds is the biggest impediment to using the optimal policy as a decision-support tool. So, we utilize an approximate dynamic programming approach that exploits 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 reveal that the optimal policy with the heuristically estimated thresholds substantially improves the existing practice (around 25\% on average). The success of the proposed model is attributed to recognizing the value of holding UWHs and effectively hedging supply uncertainty and future prices -- an insight missed in the planning actions of the current practice.