Date of Award
5-9-2024
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Chair and Committee
Panos Kouvelis
Committee Members
na
Abstract
This dissertation is inspired by a real-world problem of dynamic planning decisions in a hog farming setting, involving transactions in both the contractual and open markets with stochastic inventories and prices of inputs and outputs. I utilize real datasets and various dynamic optimization techniques to address the following topics: (i) Optimal inventory strategies, (ii) optimal optimization methods, and (iii) the role of risk preferences in optimal dynamic decision-making. In the first chapter, we use approximate dynamic programming techniques to solve a problem in agriculture. Specifically, we study a terminal phase in the growth trajectory of farm hogs, which ensues before the dispatch of hogs into the pork supply chain for trading and processing. Every week, the farmer must evaluate the number of hogs primed for sale at this juncture and assess the prevailing market prices. This requires making informed decisions on which hogs to sell in the open market, which to retain for an additional week, and which to deliver to a meatpacker. The farmer is contractually obligated to supply a specified quantity of hogs weekly to the meatpacker, priced under a predetermined market index. If the delivery falls short, a penalty proportionate to the deficit based on a market index is imposed. 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 at current market prices. This problem constitutes a dynamic, multi-item inventory challenge with stochastic prices and quantities of input and outputs. The inputs comprise piglets aged one month, that require approximately 22 weeks to reach market maturity. Their numbers vary due to birth and mortality rate fluctuations. The outputs consist of market-ready hogs classified into two weight categories: regular-weight and underweight. Their numbers vary due to inconsistent weight gain influenced by exogenous factors, such as weather. These two types of hogs exhibit pricing and feeding differences. Regular-weight hogs command a higher market price than underweight hogs, yet underweight hogs can rapidly appreciate due to the accumulation of valuable lean weight with continued feeding. On the contrary, regular-weight hogs predominately gain fat when fed, which is not highly valued in the market. 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. We utilize the real dataset provided by the hog producer to calibrate the model. We 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 under-weight hogs and effectively hedging supply uncertainty and future prices -- an insight missed in the planning actions of the current practice. The second chapter examines the same dynamic planning decisions but proposes an industrial solution deployable as decision support within a farming environment. The objectives for using the dataset differ between these two papers. The first paper uses classical dynamic programming techniques according to Puterman (2014) to derive an optimal policy structure, utilizing the dataset to generate illustrative numerical examples with realistic parameters. In contrast, the second paper directly utilizes the rich dataset to develop an AI livestock management support agent. Currently, the hog producer implements a heuristic "always fulfill'' (AF) policy to manage marketable hogs. This policy ensures the meatpacking contract is met under all circumstances, with any excess hogs sold on the open market. If a shortage in the supply of regular-weight hogs arises, underweight hogs are used as a substitute at a reduced price. Our study implements a Deep Reinforcement Learning (DRL) approach to find an alternative to the AF policy. Our research is generalizable beyond the specific application context, and we contribute to the existing literature by extending the use of neural networks into a complex application with continuous and unbounded spaces, and modifying an existing DRL algorithm to accommodate operational constraints. We also show how one can use other machine learning techniques, including optimal classification trees, to interpret the DRL agent's actions to optimize the farm's performance. Our numerical experiments show that their DRL agent outperforms the current heuristic policy by 24.94 percent on average. Compared to an exact dynamic solution derived for a smaller, analytically tractable operating horizon, the DRL agent is less than 1 percent worse on average. In the third chapter, we investigate risk management strategies for a risk-averse hog production farm, focusing on both inventory allocations and hedging in the futures market. Applying both a dynamic programming approach and an empirically grounded DRL approach, we aim to maximize the firm's mean-variance utility dynamically and delineate the optimal integrated policy of inventory allocation and hedging. We find that a farmer who dynamically maximizes the mean-variance utility will keep a smaller inventory than a farmer who doesn't consider risk. However, they will keep a larger inventory than a farmer who doesn't have the option to hedge. This happens for two reasons. First, previous research (Kouvelis et al. 2023a) has shown that it can be a good strategy for farms that don't consider risk to hold onto some hogs for longer periods of time to manage uncertain prices, costs, and yields. A risk-averse farmer will want to hold fewer hogs because doing so introduces more risk from potential future price changes and uncertain yields. Second, hedging reduces the overall risk for the farm, which lets the risk-averse farmer hold more hogs than they would have without hedging. However, this benefit of hedging gets smaller as the farm holds more and more hogs. We show that the decision to hedge revenue or costs depends on both operational and financial characteristics. Revenue hedging is more advantageous when there is high volatility in selling prices, a high correlation with factor markets, and large sales volumes. Conversely, cost hedging is more valuable in the presence of high volatility in operational costs, a high correlation with the fodder market, and large inventory sizes. We also find that a more risk-averse farm is likely to hedge costs, whereas a less risk-averse farm finds greater value in hedging revenue. Lastly, hedging is more valuable when the volatility of factor markets is lower. As the volatility of these markets increases, hedging loses its value since the risks from financial markets begin to propagate to the farm, contributing more variance to cash flow. The hedging strategies are difficult to evaluate analytically because the farmer's problem is inherently dynamic. For this reason, we obtain the exact hedging policy through deep reinforcement learning (DRL).
Recommended Citation
Liu, Ye, "Empirically Grounding Analytics (EGA) for Commodity Markets: Study of the Hog Production Industry" (2024). Olin Business School Electronic Theses and Dissertations. 47.
https://openscholarship.wustl.edu/olin_etds/47