This paper considers a stochastic inventory management problem where a capital-constrained firm can obtain additional working capital through an inventory-based financing facility by pledging its inventory to obtain loans from a lender. We show that it is optimal to deploy a state-dependent base-stock policy through which the firm may order new inventory up to or salvage existing inventory down to certain levels in each period depending on whether it has an initial net capital or debt defined as the on-hand capital minus all outstanding loans and interests. Through analytical and numerical studies, we offer a number of new insights regarding the optimal inventory management for a capital-constrained firm with access to inventory-based financing. In particular, we find that when the firm anticipates a shortage of capital with which to meet high demands in a future period, it may strategically over-stock its inventory in earlier periods in order to secure the necessary capital. Through extensive numerical experiments, our paper also demonstrates how some of the key parameters may affect the optimal inventory and financing decisions and the associated profits. Finally, we discuss three model extensions that allow finite storage capacity, per-unit inventory holding cost, and demand backlogging.
Globalization and increased product variety have impacted the uncertainty in demand and supply. The recent financial instability adds another layer of uncertainty regarding financing and investment. The changes, while gradual, have accumulated over time and posed enormous difficulties in planning procurement. This thesis focuses on inventory procurement strategies that help firms tackle challenges due to uncertainties in the demand/supply and financial concerns. The first part is on employing dynamic inventory procurement strategies to achieve cost efficiency and tackle the uncertainties in demand and supply. The second and third parts focus on the interaction between Finance and Operations in both its analytic aspects and empirical aspects. A synopsis of the three parts of the thesis follows. Part 1: "Inventory Management and Stochastic Lead Time" This chapter analyzes a continuous time back-ordered inventory system with stochastic demand and stochastic delivery lags for placed orders. This problem in general has an infinite dimensional state space and is hence intractable. We first obtain the set of minimal conditions for reducing such a system's state space to one-dimension and show how this reduction is done. Next, by modeling demand as a diffusion process, we reformulate the inventory control problem as an impulse control problem. We simplify the impulse control problem to a Quasi-Variation Inequality (QVI). Based on the QVI formulation, we obtain the optimality of the (s, S) policy and the limiting distribution of the inventory level. We also obtain the long run average cost of such an inventory system. Finally, we provide a method to solve the QVI formulation. Using a set of computational experiments, we show that significant losses are incurred in approximating a stochastic lead time system with a fixed lead time system, thereby highlighting the need for such stochastic lead time models. We also provide insights into the dependence of this value loss on various problem parameters. Part 2: "Inventory Financing and Trade Credit" In this chapter, we study the inventory performance of publicly listed retailers between 1980 and 2010 based on a panel dataset from COMPUSTAT, CRSP, I/B/E/S and a hand-collected dataset on bankruptcy. We quantify the effect of a carefully-defined financial holding cost on inventory decisions, after controlling for operational factors and considering access to trade credit. This finding provides empirical evidence of the failure of the Modigliani-Miller Theorem in the inventory management context. We are also able to infer several unobservable costs based on historical inventory decisions. For example, the average cost of trade credit is estimated to be about 20% per year, which matches the typical trade credit terms in the United States. We find that the cost of trade credit computed has a strong connection to inventory per- formance. Our findings are robust to alternative econometric specifications, alternative measures of variables and model estimates for subsets of data. Part 3: "Joint Inventory and Cash Management Decisions" In this chapter, we address this question by considering a general continuous time model of a dynamic inventory system that incurs costs in both managing the inventory and managing the cash flow. To support its inventory and operational cost, this system has access to both the financial market and trade credit from suppliers. We show how the inventory procurement decision and financing decision are made jointly. Specifically, we show that, with friction of financing, not only does the Modigliani-Miller Theorem not hold but also the two decisions interact in a dynamic and complex manner. We are also able to show how the value of the inventory system can be improved by using trade credit.
Small-to-medium size enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this paper, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. Our study shows that the optimal ordering policy is characterized by a pair of threshold variables for each period as function of the initial state of the period. Further, upper and lower bounds for the threshold values are developed using two simple-to-compute ordering policies. Based on these bounds, we provide an efficient algorithm to compute the two threshold values. Since the underlying state space is two-dimensional which leads to high computational complexity of the optimization algorithm, we also derive upper bounds for the optimal value function by reducing the optimization problem to one dimension. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with numerical studies.
This book provides several inventory models for making the right decision in inventory management under different environments. Basically, the optimal ordering policies are determined for situations with and without shortages in production-inventory systems. The chapters in the book include various features of inventory modeling i.e., inflation, deterioration, supply chain, learning, credit financing, carbon emission policy, stock-dependent demand, among others. The book is a useful resource for academicians, researchers, students, practitioners, and managers who can be benefited with the policies provided in the chapters of the book.
This comprehensive Handbook provides an overview of state-of-the-art research on quantitative models for inventory management. Despite over half a century’s progress, inventory management remains a challenge, as evidenced by the recent Covid-19 pandemic. With an expanse of world-renowned inventory scholars from major international research universities, this Handbook explores key areas including mathematical modelling, the interplay of inventory decisions and other business decisions and the unique challenges posed to multiple industries.
'Joe Thomas is a true renaissance academic who has integrated research, teaching, practice and leadership. He's advised numerous companies through board positions and consulting engagements. His research has identified and focused on real issues in operations management, like overcoming the dark side of worker flexibility and other aspects of the human component of operations. And he has then incorporated research findings into his teaching, including cases on issues like global operations that we can all benefit from. Joe is so admired by his colleagues that they chose him to lead the Johnson School as Dean. Joe is a model and an inspiration for all of us. This book, with its emphasis on cross-functional approaches to inventory management, is an excellent way to honor Joe on his retirement.'Marshall L FisherUniversity of Pennsylvania'Joe Thomas is one of the Grand Masters in our field of operations management. I will always remember him fondly as someone who has accomplished so much, with such a high status in our profession, and yet at the same time, a humble, warm and gentle scholar. In my early student days, I read of Joe's work in multi-echelon inventory systems. He has made deep contributions in manufacturing and distribution network designs and operations management, before the term 'supply chain management' became popular. He is also one of the early scholars in operations management who recognized and promoted the importance of looking at manufacturing and operations as a strategy for a firm. I have learned a great deal from both his writings and from interactions with him face to face. Of course, Joe has also been serving our community as an editor and through professional society leadership. I had first-hand experience from his editorship directly, since he processed some of the papers that I published. That experience also taught me how to have high standards, be encouraging, and be generous in giving advice and inputs in the editorial process. As a junior researcher at the time, such editorial support was both helpful and served as a great model. As a senior colleague, Joe has always treated me as a friend, making me feel comfortable and easy to exchange with him. Over the years, many of our colleagues have benefited tremendously from his mentorship and support. While he is a very serious researcher and holds very high standards in his work, Joe's personality radiates warmth and energy to those around him. And then he adds humor at the right time. I will never forget when Joe led all of us at a conference honoring the retirement of El Buffa to sing a song with lyrics that he composed himself, titled 'Just-in-Time.' The lyrics contained lessons in a very funny way. Joe is a pioneer in research (as well as in teaching and practice) that connected inventory management to other business functions such as human resources, marketing, finance and accounting. Thus, with its emphasis on cross-functional inventory research, this book is an excellent way to honor him on his retirement. It is a privilege for us to recognize and celebrate with him all he has done for our profession!'Hau L LeeStanford UniversityCross-Functional Inventory Research details path-breaking analytical, empirical and behavioral operations management research that interfaces inventory with the business functions of human resources, finance, accounting, information technology, and globalization.For about fifty years, inventory research was conducted with a silo mentality with assumptions of exogenous pricing, price-independent demand distribution, rational human decision making, and lack of information sharing. Over the past few years, there is increased realization that this kind of analysis and thinking will not be useful for the modern business world. This has motivated inventory researchers to reach across different business functional areas such as finance, marketing, human capital and information technology and identify research questions that are more appropriate for the modern, complex, data-driven business environments. Cross-Functional Inventory Research contains path-breaking research developments in cross-functional inventory research. The methodologies applied to answer these research questions cover the complete gamut of empirical, analytical, and behavioral approaches.
This book discusses inventory models for determining optimal ordering policies using various optimization techniques, genetic algorithms, and data mining concepts. It also provides sensitivity analyses for the models’ robustness. It presents a collection of mathematical models that deal with real industry scenarios. All mathematical model solutions are provided with the help of various optimization techniques to determine optimal ordering policy. The book offers a range of perspectives on the implementation of optimization techniques, inflation, trade credit financing, fuzzy systems, human error, learning in production, inspection, green supply chains, closed supply chains, reworks, game theory approaches, genetic algorithms, and data mining, as well as research on big data applications for inventory management and control. Starting from deterministic inventory models, the book moves towards advanced inventory models. The content is divided into eight major sections: inventory control and management – inventory models with trade credit financing for imperfect quality items; environmental impact on ordering policies; impact of learning on the supply chain models; EOQ models considering warehousing; optimal ordering policies with data mining and PSO techniques; supply chain models in fuzzy environments; optimal production models for multi-items and multi-retailers; and a marketing model to understand buying behaviour. Given its scope, the book offers a valuable resource for practitioners, instructors, students and researchers alike. It also offers essential insights to help retailers/managers improve business functions and make more accurate and realistic decisions.
Risk management has become an essential issue in supply chain management, from the modeling of the decision maker's risk preference, and the studies on uncertain elements such as demand, supply, price, lead time, etc., to the consideration of more practical background including cash flow constraints, inventory financing and delayed cash payment. In this new volume, the authors provide a framework to study the interaction of various factors related to risk and their influence on supply chain management. The scope of areas covered includes operations management, decision analysis, and business administration. This book focuses on several key issues of risk management in supply chains. Specifically, an analysis framework is presented for studying the supplier selection problem and identifying the optimal sourcing strategy in a one-retailer two-suppliers supply chain with random yields. The optimal sourcing strategy of a retailer and the pricing strategies of two suppliers under an environment of supply disruption are investigated. Besides, the authors study the dynamic inventory control problems with cash flow constraints, financing decisions as well as delayed cash payment. In addition, originating from the annual international iron ore price negotiation, the authors model the bargaining process to deal with the risk of wholesale price in the game analysis context. Within the three perspectives of risk management in supply chains, the modeling of decision maker's risk preference has been extensively studied and many results have been obtained to guide the practice. However, the analysis on the other two kinds of topics is still in its infancy, and needs more efforts from academia. It is thus the ambition and innovation for this book to contribute on risk management in supply chains in the following ways: (1) characterizing the explicit sourcing strategy (i.e., single sourcing or dual sourcing) to deal with supply disruption risk; (2) introducing the concepts of financial risk measurement by incorporating cash flow constraints, inventory financing and delayed cash payment into inventory management models; and (3) providing insights for the iron ore price negotiation to help steel manufacturers handle the risk of price increase.
(Cont.) Lastly, as an extension to the model, we study the optimal policies of expediting and regular ordering when there is an expiry date on outstanding orders. The optimal expediting policy identifies a number of base stock levels depending on the age of the orders, but the structure of the optimal policy remains simple for sequential systems.
As markets become more dynamic and competitive, companies must reconsider how they view inventory and make changes to their production and inventory systems. They must begin to think outside the classical box and develop a new paradigm of inventory management. Exploring the trend away from classical models based on economic order quantities to depe
