Lost sales inventory models with batch ordering and handling costs

In this paper, we integrate inventory and handling into a single model for analysis and optimization of inventory replenishment decisions for a grocery retail store. We consider a retailer who periodically manages his inventory of a single item facing stochastic demand. The retailer may only order in multiples of a xed batch size, the lead time is less than the review period length and all unmet demand is lost, which is a realistic situation for a large part of the assortment of grocery retailers. The replenishment cost includes both xed and variable components, dependent on the number of batches and units in the order. This structure captures the shelf-stacking costs in retail stores. We investigate the optimal policy structure under the long-run average cost criterion. Our results show that it is worthwhile to explicitly take handling costs into account when making inventory decisions. We use parameter values typical for rocery retail environments. For an important subset of the retail assortment, we show that signicant cost reductions exist by explicitly considering handling in the inventory policy. Keywords: Retail inventory control, Handling, Lost sales, Periodic review, Fixed batch size

Learning Algorithms for Stochastic Dynamic Pricing and Inventory Control.

This dissertation considers joint pricing and inventory control problems in which the customer's response to selling price and the demand distribution are not known a priori, and the only available information for decision-making is the past sales data. Data-driven algorithms are developed and proved to converge to the true clairvoyant optimal policy had decision maker known the demand processes a priori, and, for the first time in literature, this dissertation provides theoretical results on the convergence rate of these data-driven algorithms. Under this general framework, several problems are studied in different settings. Chapter 2 studies the classical joint pricing and inventory control problem with backlogged demand, and proposes a nonparametric data-driven algorithm that learns about the demand on the fly while making pricing and ordering decisions. The performance of the algorithm is measured by regret, which is the average profit loss compared with that of the clairvoyant optimal policy. It is proved that the regret vanishes at the fastest possible rate as the planning horizon increases. Chapter 3 studies the classical joint pricing and inventory control problem with lost-sales and censored demand. Major challenges in this study include the following: First, due to demand censoring, the firm cannot observe either the realized demand or realized profit in case of a stockout, therefore only biased data is accessible; second, the data-driven objective function is always multimodal, which is hard to solve and establish convergence for. Chapter 3 presents a data-driven algorithm that actively explores in the inventory space to collect more demand data, and designs a sparse discretization scheme to jointly learn and optimize the multimodal data-driven objective. The algorithm is shown to be very computationally efficient. Chapter 4 considers a constraint that only allows the firm to change prices no more than a certain number of times, and explores the impact of number of price changes on the quality of demand learning. In the data-driven algorithm, we extend the traditional maximum likelihood estimation method to work with censored demand data, and prove that the algorithm converges at the best possible rate for any data-driven algorithms.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120721/1/boxchen_1.pd

Essays in Retail Operations and Humanitarian Logistics

This dissertation introduces and analyzes research problems related to Retail Operations and Humanitarian Logistics. In Retail Operations, the inventory that ends up as unsaleable at primary markets can be significant (up to 20% of the retail product). Thus retailers look for strategies like selling in secondary markets at a discounted price. In such a setting, the decisions of how much to order for a product of limited shelf life and when (if at all) to start selling the product in the secondary market become critical because these decisions not only affect the retailer's cost of procurement and sales revenues obtained from the product but also affect utilization of shelf space, product rollover and assortment decisions of the retailer. Apart from using secondary markets, retailers that sell seasonal products or products with sales horizons shorter than the typical production/procurement lead time also enter into contractual agreements with suppliers. These contracts are in place to share risks associated with unknown or uncertain demand for the product. Presence of such contracts does affect a retailer's order quantity as well as the time to start selling in the secondary market. In our two essays on retail operations, we analyze a retailer's optimal order quantity and when he/she starts selling in the secondary market. We refer to the former as the 'ordering decision' and the latter as the 'timing decision.' These two decisions are studied first without risk sharing contracts in Essay 1, and then in the presence of contracts in Essay 2. In Essay 1, we build a two-stage model with demand uncertainty. The ordering decision is made in the first stage considering cost of procurement and expected sales revenue. The timing decision is made in the second stage and is conditional on the order quantity determined in the first stage. We introduce a new class of aggregate demand model for this model. We study the structural properties of the retailer's timing and ordering problem and identify optimality conditions for the timing decision. Finally, we complement our analytical results with computational experiments and show how retailer's optimal decisions change when problem parameters are varied. In Essay 2, we extend the work in first essay to include the contracts between the retailer and a supplier. In this essay, we introduce a time-based Poisson demand model. We define three di®erent types of contracts and investigate the effect of each of these contracts on the retailer's ordering and timing decisions. We investigate how the analytical structure of the retailer's decision changes in the presence of these contracts. For a given order quantity, we show that the timing decision depends on the type of contract. Our analytical results on the timing decision are complemented with computational experiments where we investigate the impact of contract type on the optimal order quantity of the retailer. In Humanitarian Logistics, non-profit organizations receive several-billion-dollars-worth of donations every year but lack a sophisticated system to handle their complex logistics operations; the absence of expertly-designed systems is one of the significant reasons why there has been a weak link in the distribution of relief aid. The distribution of relief aid is a complex problem as the goal is humanitarian yet at the same time, due to limited resources, the operations have to be efficient. In the two essays on humanitarian logistics, we study the distribution of aid using homogeneous fleet, with and without capacity restrictions. In Essay 3, we discuss routing for relief operations using one vehicle without capacity restrictions. Contrary to the existing vehicle routing models, the key property of our routing models is that the nodes have priorities along with humanitarian needs. We formulate this model with d-Relaxed Priority rule that captures distance and response time. We formulate routing models with strict and relaxed forms of priority restrictions as Mixed Integer Programs (MIP). We derive bounds for this problem and show that this bound is attained in limiting condition for a worst-case example. Finally, we evaluate the optimal solutions on test problems for response time and distance and show that our vehicle routing model with priorities captures the trade-off between distance and response time unlike existing Vehicle Routing Problem (VRP) models without priorities. In Essay 4, we extend the problem dealt in third essay to consider fleet consisting of multiple vehicles (homogeneous) with capacity and route length restrictions. First, we show that the humanitarian aspect imposes additional challenges and develop routing models that capture performance metrics like fill rate, distance traversed, response time and number of victims satisfied. Proposed routing models are formulated as Mixed Integer Programs and are solved to optimality for small test problems. We conduct computational experiment and show that our models perform well on these performance metrics

AN EMPIRICAL EXAMINATION OF NEW INNOVATIVE PROCESSES IN RETAIL

Retailers constantly innovate to improve their operations to maintain a competitive advantage, which has become even more apparent following the challenges from the COVID-19 pandemic. One challenge with innovating, however, is that limited information is available to evaluate the effectiveness of the operations. Fortunately empirical methodologies of structural estimation and field experimentation can be used to help determine if innovative processes at retail chains are fruitful when implemented. Field experiments provide direct causal evidence on whether the innovations will work while structural estimation allows for examining counterfactual scenarios to evaluate outcomes from such process innovations. In this dissertation, we leverage structural estimation and field experimentation to study three topics on the frontier of innovations in retail operations: a) dynamic pricing of product drops in the presence of resellers, b) localization of inventory for e-commerce retailers, and c) increasing customer recycling through operational incentives. The key results are as follows. In Chapter 2, through structural estimation we show that incorporating resellers into pricing improves retailer profit by 7% on average, and the impacts of the resale market to firm profit are heterogeneous across products based on the initial inventory relative to the initial demand. In Chapter 3, through structural estimation we find that distribution centers closer to the customer (front DCs) allow the e-commerce retailer to capture an average 10.7% benefit to profit by improving average promised delivery time by 28.3%. Front DCs allow to capture sales from high-margin SKUs with high demand where backup fulfillment results in much longer promised delivery time. In Chapter 4, through field experiments we find that the chosen value-based incentives and convenience-based incentives are ineffective at inducing customers to engage in recycling behavior, despite importance of these incentives toward recycling intentions reported in the literature. Our results suggest that offering programs to encourage e-waste recycling behavior can be a costly endeavor.Doctor of Philosoph

Stochastic Optimal Control of Grid-Level Storage

The primary focus of this dissertation is the design, analysis and implementation of stochastic optimal control of grid-level storage. It provides stochastic, quantitative models to aid decision-makers with rigorous, analytical tools that capture high uncertainty of storage control problems. The first part of the dissertation presents a $p$-periodic Markov Decision Process (MDP) model, which is suitable for mitigating end-of-horizon effects. This is an extension of basic MDP, where the process follows the same pattern every $p$ time periods. We establish improved near-optimality bounds for a class of greedy policies, and derive a corresponding value-iteration algorithm suitable for periodic problems. A parallel implementation of the algorithm is provided on a grid-level storage control problem that involves stochastic electricity prices following a daily cycle. Additional analysis shows that the optimal policy is threshold policy. The second part of the dissertation is concerned with grid-level battery storage operations, taking battery aging phenomenon (battery degradation) into consideration. We still model the storage control problem as a MDP with an extra state variable indicating the aging status of the battery. An algorithm that takes advantage of the problem structure and works directly on the continuous state space is developed to maximize the expected cumulated discounted rewards over the life of the battery. The algorithm determines an optimal policy by solving a sequence of quasiconvex problems indexed by a battery-life state. Computational results are presented to compare the proposed approach to a standard dynamic programming method, and to evaluate the impact of refinements in the battery model. Error bounds for the proposed algorithm are established to demonstrate its accuracy. A generalization of price model to a class of Markovian regime-switching processes is also provided. The last part of this dissertation is concerned with how the ownership of energy storage make an impact on the price. Instead of one player in most storage control problems, we consider two players (consumer and supplier) in this market. Energy storage operations are modeled as an infinite-horizon Markov Game with random demand to maximize the expected discounted cumulated welfare of different players. A value iteration framework with bimatrix game embedded is provided to find equilibrium policies for players. Computational results show that the gap between optimal policies and obtained policies can be ignored. The assumption that storage levels are common knowledge is made without much loss of generality, because a learning algorithm is proposed that allows a player to ultimately identify the storage level of the other player. The expected value improvement from keeping the storage information private at the beginning of the game is then shown to be insignificant

U.S. Commission on Immigration Reform

The U.S. Commission on Immigration Reform was created by Congress to assess U.S. immigration policy and make recommendations regarding its implementation and effects. Mandated in the Immigration Act of 1990 to submit an interim report in 1994 and a final report in 1997, the Commission has undertaken public hearings, fact-finding missions, and expert consultations to identify the major immigration-related issues facing the United States today.LBJ School of Public Affair

Linear programming based models for resilient supply systems design

Ph.DDOCTOR OF PHILOSOPH

Processes of International Negotiations

Negotiations are essential mechanisms for the peaceful resolution of disputes and for maintaining stability in international relations. Negotiations can and should contribute to predictability, equity, and security among states. In achieving these goals, negotiations become important confidence-building measures. The increasing role of negotiations and of international organizations for managing the system of international order and for pursuing/achieving states' interests/policies through peaceful means has produced a fundamental evolution in the agenda, functions, and intensity of international negotiations. In the view of both researchers and negotiators over the recent past, the negotiations process that is organized along traditional lines is becoming more complex, difficult, and less effective. The processes of negotiations are in general taking more and more time and lagging behind the evolution of the international environment. Not only are the issues themselves more complex, but also, in the implementation of any agreements reached, the resolution of the issues involved will need to take place over a longer time and therefore to be managed jointly or multilaterally. Because of the increasing complexity of issues and the fast pace of changes affecting both national and international interests, it has become essential for international agreements to contain sufficient flexibility in certain of their provisions to permit dealing with uncertainty and the needs of the parties to adapt to new and changing circumstances. In this sense, international negotiations and agreements must be not only reactive but also anticipatory. These considerations indicate that a much-needed approach is one which is concerned specifically with bringing about a multinational, multicultural, and multidisciplinary understanding of and perspective on international negotiations and which also bridges the gap between practitioners and researchers. A specific objective and unique aspect of the IIASA Project on the Processes of International Negotiations (PIN Project), which started in April 1986 and was funded by the Carnegie Corporation, is the international, multidisciplinary approach brought to bear on all of the Project's activities. This was especially evident at the IIASA Conference on the Processes of International Negotiations, held in May 1987. The PIN networks in IIASA's member countries played an essential role in this Conference. To keep the focus of the work on substantive issues and on relevant applications-oriented results, while taking into account the importance and impact of different cultural and political systems in the various national approaches to negotiations, both practitioners and researchers involved in the processes of negotiations made presentations at the PIN Conference and took part in the panel discussions. These presentations form the basis for the chapters of this book. The goals of the Conference were to foster increased communication and understanding between practitioners and researchers and among various research disciplines, to present and discuss research results, and to identify possible future research activities. The participation and interaction of both high-level negotiations practitioners and researchers were considered especially valuable and unique aspects of the Conference. All of the subjects dealt with at the Conference have direct and obvious relevance to improving negotiations outcomes on, and the ability to deal effectively with, such issues as the transboundary effects (environmental, economic, etc.) of technological risk, security and confidence-building measures, and international economic cooperation -- all of which are high on the negotiations agenda of many countries

Stochastic Optimization; Proceedings of the International Conference, Kiev, USSR, September 1984

The purpose of this conference, which was attended by 240 scientists from 20 countries, was to survey the latest developments in the field of controlled stochastic processes, stochastic programming, control under incomplete information and applications of stochastic optimization techniques to problems in economics, engineering, modeling of energy systems, etc. The conference reflected a number of recent important developments in the field, notably new results in control theory with incomplete information, stochastic maximum principle, new numerical techniques for stochastic programming and related software, application of probabilistic methods to the modeling of the economy. The contributions to this book are divided into three categories: (1) Controlled stochastic processes; (2) Stochastic extremal problems; and (3) Stochastic optimization problems with incomplete information