Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments

The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue $\pi$ and then choosing all products with revenue at least $\pi$. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. (2014). An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition. We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.Comment: Minor changes following referees' comment

Measurement of Trustworthiness of the Online Reviews

In electronic commerce (e-commerce)markets, a decision-maker faces a sequential choice problem. Third-party intervention plays an important role in making purchase decisions in this choice process. For instance, while purchasing products/services online, a buyer's choice or behavior is often affected by the overall reviewers' ratings, feedback, etc. Moreover, the reviewer is also a decision-maker. After purchase, the decision-maker would put forth their reviews for the product, online. Such reviews would affect the purchase decision of another potential buyer, who would read the reviews before conforming to his/her final purchase. The question that arises is \textit{how trustworthy are these review reports and ratings?} The trustworthiness of these review reports and ratings is based on whether the reviewer is a rational or an irrational person. Indexing the reviewer's rationality could be a way to quantify a reviewer's rationality but it does not communicate the history of his/her behavior. In this article, the researcher aims at formally deriving a rationality pattern function and thereby, the degree of rationality of the decision-maker or the reviewer in the sequential choice problem in the e-commerce markets. Applying such a rationality pattern function could make it easier to quantify the rational behavior of an agent who participates in the digital markets. This, in turn, is expected to minimize the information asymmetry within the decision-making process and identify the paid reviewers or manipulative reviews

Market Demand Elasticity and Income Inequality

This paper deals with the analysis of the relation between aggregate demand for a consumption good and the distribution of income across consumers. We obtain sufficient conditions under which changes in income inequality lead to an increase or decrease in the market demand elasticities. The conditions are satisfied for individual demand functions commonly used in economic models, in particular, for the typical demand functions on luxury goods and necessities.Economic

Fuzzy Sets in Business Management, Finance, and Economics

This book collects fifteen papers published in s Special Issue of Mathematics titled “Fuzzy Sets in Business Management, Finance, and Economics”, which was published in 2021. These paper cover a wide range of different tools from Fuzzy Set Theory and applications in many areas of Business Management and other connected fields. Specifically, this book contains applications of such instruments as, among others, Fuzzy Set Qualitative Comparative Analysis, Neuro-Fuzzy Methods, the Forgotten Effects Algorithm, Expertons Theory, Fuzzy Markov Chains, Fuzzy Arithmetic, Decision Making with OWA Operators and Pythagorean Aggregation Operators, Fuzzy Pattern Recognition, and Intuitionistic Fuzzy Sets. The papers in this book tackle a wide variety of problems in areas such as strategic management, sustainable decisions by firms and public organisms, tourism management, accounting and auditing, macroeconomic modelling, the evaluation of public organizations and universities, and actuarial modelling. We hope that this book will be useful not only for business managers, public decision-makers, and researchers in the specific fields of business management, finance, and economics but also in the broader areas of soft mathematics in social sciences. Practitioners will find methods and ideas that could be fruitful in current management issues. Scholars will find novel developments that may inspire further applications in the social sciences

Application of Optimization in Production, Logistics, Inventory, Supply Chain Management and Block Chain

The evolution of industrial development since the 18th century is now experiencing the fourth industrial revolution. The effect of the development has propagated into almost every sector of the industry. From inventory to the circular economy, the effectiveness of technology has been fruitful for industry. The recent trends in research, with new ideas and methodologies, are included in this book. Several new ideas and business strategies are developed in the area of the supply chain management, logistics, optimization, and forecasting for the improvement of the economy of the society and the environment. The proposed technologies and ideas are either novel or help modify several other new ideas. Different real life problems with different dimensions are discussed in the book so that readers may connect with the recent issues in society and industry. The collection of the articles provides a glimpse into the new research trends in technology, business, and the environment

Uncertain Multi-Criteria Optimization Problems

Most real-world search and optimization problems naturally involve multiple criteria as objectives. Generally, symmetry, asymmetry, and anti-symmetry are basic characteristics of binary relationships used when modeling optimization problems. Moreover, the notion of symmetry has appeared in many articles about uncertainty theories that are employed in multi-criteria problems. Different solutions may produce trade-offs (conflicting scenarios) among different objectives. A better solution with respect to one objective may compromise other objectives. There are various factors that need to be considered to address the problems in multidisciplinary research, which is critical for the overall sustainability of human development and activity. In this regard, in recent decades, decision-making theory has been the subject of intense research activities due to its wide applications in different areas. The decision-making theory approach has become an important means to provide real-time solutions to uncertainty problems. Theories such as probability theory, fuzzy set theory, type-2 fuzzy set theory, rough set, and uncertainty theory, available in the existing literature, deal with such uncertainties. Nevertheless, the uncertain multi-criteria characteristics in such problems have not yet been explored in depth, and there is much left to be achieved in this direction. Hence, different mathematical models of real-life multi-criteria optimization problems can be developed in various uncertain frameworks with special emphasis on optimization problems

Enhancing Produce Safety: State Estimation-based Robust Adaptive Control of a Produce Wash System

The rapid introduction of fresh-cut produce into a produce wash system can dramatically decrease the free chlorine (FC) concentration level in the wash water, resulting in potential widespread cross-contamination throughout the entire wash system. To minimize such contamination, a sufficient level of FC must be maintained in the wash water. This paper presents a state estimation-based robust adaptive sliding mode (RASM) control strategy for the wash system to stabilize the FC concentration level during fresh-cut iceberg lettuce washing. This feedback control law for FC dosing is suggested to provide a sufficient FC injection rate (FCIR) to the wash system in order to compensate for the fall in the FC level and in turn to minimize the Escherichia coli (E. coli) O157:H7 levels on washed lettuce and in the wash water. The proposed controller uses the estimated chemical oxygen demand (COD) and FC concentration as feedback signals while system states are estimated by a hybrid extended Kalman filter (HEKF) and the unknown noise statistics are identified by a noise identification (NI) algorithm. Uniformly ultimately boundedness (UUB) of the FC concentration tracking error in the presence of unmodelled dynamics is proven using the Lyapunov framework and Barbalat\u27s lemma. The E. coli O157:H7 contamination levels are predicted from the joint estimator and controller properties. Simulation results show that the proposed NI-based HEKF/RASM control methodology achieves FC tracking while the pathogens converge to their predicted levels. The E. coli O157:H7 levels decrease as FC concentration increases and in particular, no E. coli O157:H7 is detected when FC concentration is regulated at 15 mg/L. Two robustness tests are performed to show the performance of the proposed controller in the presence of chlorine actuator failure and system parameter uncertainties. Finally, cross-contamination management is examined in terms of the prevalence and mean pathogen levels of incoming pre-wash lettuce in the context of FC regulation at 15 mg/L

Sustainable Industrial Engineering along Product-Service Life Cycle/Supply Chain

Sustainable industrial engineering addresses the sustainability issue from economic, environmental, and social points of view. Its application fields are the whole value chain and lifecycle of products/services, from the development to the end-of-life stages. This book aims to address many of the challenges faced by industrial organizations and supply chains to become more sustainable through reinventing their processes and practices, by continuously incorporating sustainability guidelines and practices in their decisions, such as circular economy, collaboration with suppliers and customers, using information technologies and systems, tracking their products’ life-cycle, using optimization methods to reduce resource use, and to apply new management paradigms to help mitigate many of the wastes that exist across organizations and supply chains. This book will be of interest to the fast-growing body of academics studying and researching sustainability, as well as to industry managers involved in sustainability management