Technische Universitat¨ Munchen¨ Lehrstuhl f¨urLogistik und Supply Chain Management Optimal Procurement and Inventory Control in Volatile Commodity Markets Advances in Stochastic and Data-Driven Optimization Christian Mandl, M.Sc. Vollst¨andigerAbdruck der von der Fakult¨atf¨urWirtschaftswissenschaften der Technis- chen Universit¨atM¨unchen zur Erlangung des akademischen Grades eines Doktors der Wirtschaftswissenschaften (Dr. rer. pol.) genehmigten Dissertation. Vorsitzender: Univ.-Prof. Dr. Martin Grunow Pr¨uferder Dissertation: 1. Univ.-Prof. Dr. Stefan Minner 2. Univ.-Prof. Srinagesh Gavirneni, PhD Cornell University Ithaca, NY, USA Die Dissertation wurde am 04.04.2019 bei der Technischen Universit¨atM¨unchen eingere- icht und durch die Fakult¨atf¨urWirtschaftswissenschaften am 15.05.2019 angenommen. To my parents Acknowledgements First and foremost, I would like to express my sincere gratitude to my supervisor Profes- sor Stefan Minner for his continuous support and very constructive criticism throughout my PhD studies. I also want to thank him for encouraging and supporting me to spend five months of my PhD program abroad. I am very grateful that I was given the oppor- tunity to be part of his research group. I also want to express my gratitude to Professor Srinagesh Gavirneni from Samuel Curtis Johnson Graduate School of Management at Cornell University for being part of the examination committee and especially for inviting me to visit Cornell from May to September 2018, which was a great experience. I also want to thank Professor Martin Grunow for being the chairman of the examination committee. Further, I am very grateful for the support of my former and current colleagues at the chair of Logistics and Supply Chain Management at TUM: Yuka Akasaka, Szy- mon Albi´nski,Dr. Christian Bohner, Lachlan Bridges, Dr. Pirmin Fontaine, Michael Keilhacker, Dr. Miray K¨ozen,Sebastian Malicki, Layla Martin, Santiago Nieto-Isaza, Thitinan Pholsook, Dr. Partricia Rogetzer, Dr. Martin St¨oßlein,Josef Svoboda, Dr. Florian Taube, Dr. Dariush Tavaghof Gigloo and Francesco Zangaro. Thank you for all the research discussions and also for the after-work activities. I thank Evelyn Gemkow for her steady support and extensive proofreading of my work. Moreover, I would like to thank all the smart people I met during my time at Cornell for the inspiring discussions. I especially want to thank Assistant Professor Selva Nadarajah from the University of Illinois at Chicago for our joint work on Chapter 6 of this thesis. Finally, I would like to thank my parents and my brother Stefan for their constant support and encouragement over the last years. A special thanks goes to my wonderful girlfriend Anja for her love and patience - also and especially during the time of my research stay far-off in the U.S. - for which I am deeply grateful to her. i Abstract Volatile prices constitute a challenge for both commodity-processing and commodity- trading firms. This thesis investigates the implications of price uncertainty on the op- timal operating policies in multi-period procurement and inventory control. A central contribution to the existing literature that addresses the full information problem is the focus on the implications of price model uncertainty, i.e., incomplete information about the underlying price process. Based on advances in stochastic and data-driven optimiza- tion, we propose mathematical models for practical decision support and test them on real data. Hence, this thesis gives guidance to managers in the digital age on how to use real-time information and Big Data in combination with methods from statistical learning theory (Bayesian learning, machine learning) in an optimization framework in order to improve commodity procurement and inventory management decisions. The first problem considers operational hedging via inventory control. We show how a Bayesian belief structure can be used to express uncertainty about the price process, which is subject to switches in regimes. We prove the structure of the optimal storage policy and test its cost impact relative to several more practical but suboptimal control policies. We find that Bayesian learning yields significant cost savings. The second problem addresses commodity procurement via forward contracting. We propose a data-driven and machine learning-enabled mixed integer linear programming model that jointly optimizes forecasts and decisions by training optimal purchase signals as functions of features related to the price. Finally, we quantify the performance loss caused by ignoring feature information in procurement. The third problem considers optimal commodity storage from the perspective of a mer- chant with buying, storing and reselling opportunities. We propose several data-driven models for storage optimization. Based on empirical data of six major exchange-traded commodities, we find that optimally structured data-driven policies can outperform state-of-the-art reoptimization approaches. Keywords: price uncertainty; procurement; inventory control; stochastic and data- driven optimization iii Contents List of Tables ix List of Figures xi List of Abbreviations xv 1. Introduction1 1.1. Motivation . .1 1.2. Classification, Contribution and Research Questions . .4 2. Fundamentals of Commodity Markets9 2.1. Commodity Price Risk . .9 2.2. Financial and Operational Risk Management . 10 2.3. Stochastic Modeling of Commodity Prices . 16 3. Related Literature 19 3.1. Commodity Finance . 19 3.2. Commodity Operations . 20 3.2.1. Inventory Control under Stochastic Purchase Price . 21 3.2.2. Inventory Control under Stochastic Purchase and Sales Price . 22 3.2.3. Financial Contracting under Stochastic Purchase Price . 24 3.3. Stochastic Optimization with Partial Information and Learning . 25 3.3.1. Bayesian Inventory Control under Partial Information . 25 3.3.2. Data-Driven and Machine Learning-Enabled Optimization . 26 4. Operational Hedging from a Bayesian Inventory Control Perspective 29 4.1. Introduction . 30 4.2. Model Formulation . 33 4.2.1. MRS Spot Price Model and Bayesian Updating Scheme . 33 4.2.2. Inventory Control Model . 35 v 4.3. Optimal Policy Structure and Monotonicity Properties . 37 4.3.1. Optimality of Price(s)- and Belief-Dependent Base-Stock Policies 37 4.3.2. Monotonicity of the Optimal Base-Stock Functions . 38 4.3.3. Illustration of Policy Structure and Monotonicity Properties . 40 4.4. Controlled Numerical Study . 43 4.4.1. Setup . 43 4.4.2. Cost of Price Regime Misspecification . 44 4.4.3. Performance of Suboptimal Control Policies . 46 4.5. Results on Empirical Data . 49 4.6. Conclusion . 54 5. Financial Hedging from a Data-Driven Procurement Perspective 59 5.1. Introduction . 60 5.2. Model Formulation . 64 5.2.1. Problem Setting . 64 5.2.2. Linear Decision Rule Approximation . 66 5.2.3. Data-Driven Models for Policy Parameter Optimization . 68 5.2.4. Data-Driven Models under ML-Based Regularization . 70 5.3. Performance Bounds and Performance Metrics . 72 5.4. Controlled Numerical Study . 76 5.4.1. Setup . 76 5.4.2. Results . 79 5.5. Results on Empirical Data . 84 5.5.1. Setup . 84 5.5.2. Results . 87 5.6. Conclusion . 90 6. Commodity Storage from a Data-Driven Merchant Perspective 91 6.1. Introduction . 92 6.2. Model Formulation . 97 6.2.1. Problem Setting . 97 6.2.2. Optimal and Myopic Policy for Fully Flexible Storage . 100 6.2.3. Optimal and Myopic Policy for Limited Flexible Storage . 103 6.2.4. Sequential Reoptimization: The Rolling Intrinsic Approach . 106 6.3. Data-Driven Optimization for the SCWP . 108 6.3.1. Unstructured Linear Decision Rule Approach (DDA-LDR) . 108 vi Contents 6.3.2. Optimally Structured Policy Approach (DDA-OSP) . 111 6.3.3. Value Function Approximation Approach (DDA-VFA) . 115 6.4. Results on Empirical Data . 117 6.4.1. Setup and Descriptive Analysis . 117 6.4.2. Deterministic Analysis . 120 6.4.3. Stochastic Analysis: Performance of RIA . 124 6.4.4. Stochastic Analysis: Performance of DDA . 131 6.5. Conclusion . 135 7. Conclusion 137 7.1. Summary of Insights . 137 7.2. Directions for Future Research . 138 A. Appendix of Chapter 4 141 A.1. Proof of Theorem 1 . 141 A.2. Proof of Proposition 1 . 143 A.3. Cost of Price Regime Misspecification . 145 A.4. Performance of Suboptimal Control Policies . 146 B. Appendix of Chapter 5 147 B.1. Proof of Theorem 2 . 147 B.2. Model Formulation for the Best Subset Selection Problem . 150 B.3. Model Formulation with Indicator Constraints . 150 B.4. Computation Times . 151 B.5. Results of the Controlled Numerical Study . 151 B.6. Results on Empirical Data: Procurement of Natural Gas . 154 C. Appendix of Chapter 6 157 C.1. SCWP with Fixed Costs, Storage Efficiency, Demand and Market Power 157 C.2. Empirical Forecast Error of Futures Prices . 158 C.3. Deterministic Analysis under Perfect Foresight . 159 C.3.1. Profit over Time . 159 C.3.2. Optimal versus Myopic Performance . 160 C.3.3. Impact of the Planning Horizon . 162 C.4. Stochastic Analysis: Performance of RIA and DDA . 164 Bibliography 167 vii List of Tables 4.1. Summary of optimality and monotonicity results . 40 4.2. Corn: Performance of different control policies . 51 4.3. Average inventory in tons and average price paid in USD/ton . 54 4.4. Potential of MRS price models in inventory control . 55 5.1. General notation (Additional notation defined as required) . 68 5.2. Summary of the numerical design . 78 5.3. In-sample and out-of-sample VIEO in % for DDA-BD vs. SEO and DDA- ML vs. SEO-AIC under constant demand . 83 5.4. Prescription error (PE): % above perfect foresight cost CPF ....... 89 5.5. Average annual savings (07-2008 to 06-2017) by DDA-ML1 compared to various benchmark policies for the real-world setting at our industry partner with annual gas demand of 10 × 106 MWh . 89 6.1. Summary of policy parameter characterization .