Confidence-based Optimization for the Newsvendor Problem

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach can produce an upper and a lower bound for the associated cost. We apply our novel approach to three demand distribution in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist - e.g. based on maximum likelihood estimators - or Bayesian strategies.Comment: Working draf

Models for Retail Inventory Management with Demand Learning

Matching supply with demand is key to success in the volatile and competitive retail business. To this end, retailers seek to improve their inventory decisions by learning demand from various sources. More interestingly, retailers' inventory decisions may in turn obscure the demand information they observe. This dissertation examines three problems in retail contexts that involve interactions between inventory management and demand learning. First, motivated by the unprecedented adverse impact of the 2008 financial crisis on retailers, we consider the inventory control problem of a firm experiencing potential demand shifts whose timings are known but whose impacts are not known. We establish structural results about the optimal policies, construct novel cost lower bounds based on particular information relaxations, and propose near-optimal heuristic policies derived from those bounds. We then consider the optimal allocation of a limited inventory for fashion retailers to conduct "merchandise tests" prior to the main selling season as a demand learning approach. We identity a key tradeoff between the quantity and quality of demand observations. We also find that the visibility into the timing of each sales transaction has a pivotal impact on the optimal allocation decisions and the value of merchandise tests. Finally, we consider a retailer selling an experiential product to consumers who learn product quality from reviews generated by previous buyers. The retailer maximizes profit by choosing whether to offer the product for sale to each arriving customer. We characterize the optimal product offering policies to be of threshold type. Interestingly, we find that it can be optimal for the firm to withhold inventory and not to offer the product even if an arriving customer is willing to buy for sure. We numerically demonstrate that personalized offering is most valuable when the price is high and customers are optimistic but uncertain about product quality.Doctor of Philosoph

Data-driven reconfigurable supply chain design and inventory control

In this dissertation, we examine resource mobility in a supply chain that attempts to satisfy geographically distributed demand through resource sharing, where the resources can be inventory and manufacturing capacity. Our objective is to examine how resource mobility, coupled with data-driven analytics, can result in supply chains that without customer service level reduction blend the advantages of distributed production-inventory systems (e.g., fast fulfillment) and centralized systems (e.g., economies of scale, less total buffer inventory, and reduced capital expenditures). We present efficient and effective solution methods for logistics management of multi-location production-inventory systems with transportable production capacity. We present a novel, generalized representation of demand uncertainty and propose data-driven responses to the manage a single location inventory system under such demands.Ph.D

Demand Estimation at Manufacturer-Retailer Duo: A Macro-Micro Approach

This dissertation is divided into two phases. The main objective of this phase is to use Bayesian MCMC technique, to attain (1) estimates, (2) predictions and (3) posterior probability of sales greater than certain amount for sampled regions and any random region selected from the population or sample. These regions are served by a single product manufacturer who is considered to be similar to newsvendor. The optimal estimates, predictions and posterior probabilities are obtained in presence of advertising expenditure set by the manufacturer, past historical sales data that contains both censored and exact observations and finally stochastic regional effects that cannot be quantified but are believed to strongly influence future demand. Knowledge of these optimal values is useful in eliminating stock-out and excess inventory holding situations while increasing the profitability across the entire supply chain. Subsequently, the second phase, examines the impact of Cournot and Stackelberg games in a supply-chain on shelf space allocation and pricing decisions. In particular, we consider two scenarios: (1) two manufacturers competing for shelf space allocation at a single retailer, and (2) two manufacturers competing for shelf space allocation at two competing retailers, whose pricing decisions influence their demand which in turn influences their shelf-space allocation. We obtain the optimal pricing and shelf-space allocation in these two scenarios by optimizing the profit functions for each of the players in the game. Our numerical results indicate that (1) Cournot games to be the most profitable along the whole supply chain whereas Stackelberg games and mixed games turn out to be least profitable, and (2) higher the shelf space elasticity, lower the wholesale price of the product; conversely, lower the retail price of the product, greater the shelf space allocated for that product

Optimal Learning Algorithms for Stochastic Inventory Systems with Random Capacities

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156225/2/poms13178_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156225/1/poms13178.pd

Hindsight Learning for MDPs with Exogenous Inputs

Many resource management problems require sequential decision-making under uncertainty, where the only uncertainty affecting the decision outcomes are exogenous variables outside the control of the decision-maker. We model these problems as Exo-MDPs (Markov Decision Processes with Exogenous Inputs) and design a class of data-efficient algorithms for them termed Hindsight Learning (HL). Our HL algorithms achieve data efficiency by leveraging a key insight: having samples of the exogenous variables, past decisions can be revisited in hindsight to infer counterfactual consequences that can accelerate policy improvements. We compare HL against classic baselines in the multi-secretary and airline revenue management problems. We also scale our algorithms to a business-critical cloud resource management problem -- allocating Virtual Machines (VMs) to physical machines, and simulate their performance with real datasets from a large public cloud provider. We find that HL algorithms outperform domain-specific heuristics, as well as state-of-the-art reinforcement learning methods.Comment: 53 pages, 6 figure