Dynamic Pricing and Inventory Management with Dual Suppliers of Different Lead Times and Disruption Risks

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109985/1/poms12221-sup-0001-OnlineSupplement.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/109985/2/poms12221.pd

Dynamic Pricing and Inventory Management with Regular and Expedited Supplies

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102647/1/poms12047.pd

Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case

We analyze a finite horizon, single product, periodic review model in which pricing and production/inventory decisions are made simultaneously. Demands in different periods are random variables that are independent of each other and their distributions depend on the product price. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. Ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered. The objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon. We show that when the demand model is additive, the profit-to-go functions are k-concave and hence an (s,S,p) policy is optimal. In such a policy, the period inventory is managed based on the classical (s,S) policy and price is determined based on the inventory position at the beginning of each period. For more general demand functions, i.e., multiplicative plus additive functions, we demonstrate that the profit-to-go function is not necessarily k-concave and an (s,S,p) policy is not necessarily optimal. We introduce a new concept, the symmetric k-concave functions and apply it to provide a characterization of the optimal policy.Singapore-MIT Alliance (SMA

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

Evaluating the impact of adopting 3d printing services on the retailers

As additive manufacturing technology becomes more responsive to consumers’ demand, one important question for the retailers is whether they should provide 3D printing services in their brick-and-mortar store in addition to the traditional off-the-shelf product? If so, what should be the retailers pricing scheme to achieve a higher profit? What should be the optimal inventory level of off-the-shelf products? What is the optimal capacity of 3D printers? In this study, stochastic models are examined to capture the joint optimal 3D product price and capacity of 3D printers to maximize retailer’s expected profit while considering consumer product choices. Moreover, a stochastic model is developed to capture joint optimal pre-made inventory level and 3D product price to maximize retailer’s expected profit considering 3D services are offered in the off-the-shelf stock-out situations as a one-way substitution. Utilizing the Markov Decision Process, a framework for queuing systems is developed to examine the performance of various production/inventory strategies that optimize the system’s performance. Here, four strategies are developed: (i) providing only off-the-shelf products, (ii) providing only 3D printed products, (iii) substituting the shortage of the off-the-shelf products by 3D printed products, and (iv) providing consumers the options of selecting either the off-the-shelf product or the customized product produced by additive manufacturing. In essence, this approach assists decision makers in both capacity planning and inventory management. For all models, analytical results and numerical examples are given in order to demonstrate managerial insights

The newsvendor problem with advertising: an overview with extensions

The effect of advertising on sales has been the subject of recent studies as an important aspect in many demand-based problems. Herein, we deal with the newsvendor problem, due to its simple structure, as a suitable tool for illustrating how facets of marketing may affect decision-making concerning operational problems. In the setting presented, the newsvendor is faced with advertising-sensitive stochastic demand, where a demand-related random element comprises an advertising decision of the multiplicative or additive form. We assume that a suitable advertising strategy results in increased sales. Two advertising response functions are considered, these being concave downward and S-shaped. We review and extend the existing results relating to the newsvendor problem with marketing effects, which mostly pertain to the concave function. These are generalized by defining the S-shaped function, and some original insights into the effect of advertising are given. We establish that the optimal advertising expenditure for the multiplicative case is always less than or equal to the optimal amount in the equivalent deterministic model while it is always equal in the additive case. We finally illustrate the results that are obtained by providing numerical examples involving various advertising response functions, as well as management-related interpretations. © 2016, Springer-Verlag Berlin Heidelberg.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; specific research project entitled "Modern Methods of Applied Mathematics for the Use in Technical Sciences'' [FSI-S-14-2290, 25053]; Ministry of Education, Youth and Sports under National Sustainability Programme I [LO1202]; Norway Grants via the EEA Scholarship Programme: Bilateral Scholarship Programme; Institutional cooperation projects [NF-CZ07-ICP-4-345-2016