Style goods pricing with demand learning

For many industries (e.g., apparel retailing) managing demand through price adjustments is often the only tool left to companies once the replenishment decisions are made. A significant amount of uncertainty about the magnitude and price sensitivity of demand can be resolved using the early sales information. In this study, a Bayesian model is developed to summarize sales information and pricing history in an efficient way. This model is incorporated into a periodic pricing model to optimize revenues for a given stock of items over a finite horizon. A computational study is carried out in order to find out the circumstances under which learning is most beneficial. The model is extended to allow for replenishments within the season, in order to understand global sourcing decisions made by apparel retailers. Some of the findings are empirically validated using data from U.S. apparel industry.     

Robust optimal dynamic production/pricing policies in a closed-loop system

Hybrid manufacturing/remanufacturing systems play a key role in implementing closed-loop production systems which have been considered due to increasingly environmental concerns and latent profit of used products. Manufacturing and remanufacturing rates, selling price of new products, and acquisition price of used products are the most critical variables to optimize in such hybrid systems. In this paper, we develop a dynamic production/pricing problem, in which decisions should be made in each period confronting with uncertain demand and return. The manufacturer is able to control the demand and return by adjusting selling price and acquisition price respectively, also she can stock inventories of used and new products to deal with uncertainties. Modeling a nominal profit maximization problem, we go through robust optimization approach to reformulate it for the uncertain case. Final robust optimization model is obtained as a quadratic programming model over discrete periods which can be solved by optimization packages of QP. A numerical example is defined and sensitivity analysis is performed on both basic parameters and parameters associated with uncertainty to create managerial views.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

Pricing to accelerate demand learning in dynamic assortment planning for perishable products

Retailers, from fashion stores to grocery stores, have to decide what range of products to offer, i.e., their product assortment. Frequent introduction of new products, a recent business trend, makes predicting demand more difficult, which in turn complicates assortment planning. We propose and study a stochastic dynamic programming model for simultaneously making assortment and pricing decisions which incorporates demand learning using Bayesian updates. We show analytically that it is profitable for the retailer to use price reductions early in the sales season to accelerate demand learning. A computational study demonstrates the benefits of such a policy and provides managerial insights that may help improve a retailer’s profitability.     

Optimal dynamic pricing and inventory control with stock deterioration and partial backordering

This paper studies the optimal dynamic pricing and inventory control policies in a periodic-review inventory system with fixed ordering cost and additive demand. The inventory may deteriorate over time and the unmet demand may be partially backlogged. We identify two sufficient conditions under which (s,S,p) policies are optimal.     

Censored lifetime learning: Optimal Bayesian age-replacement policies

We consider a sequence of age-replacement problems with a general lifetime distribution parametrized by an a-priori unknown parameter. There is a trade-off: Preventive replacements are censored but cheap, whereas corrective replacements are uncensored but costly observations of the lifetime distribution. We first analyze the optimal policy for a finite sequence and establish some properties. We then propose a myopic Bayesian policy that almost surely learns the unknown parameter and converges to the optimal policy with full knowledge of the parameter.     

Two-period dynamic versus fixed-ratio pricing in a capacity constrained duopoly

This paper analyzes the impact of dynamic and fixed-ratio pricing policies on firm profits and equilibrium prices under competition. Firms that have equal inventories of perfectly substitutable and perishable products compete for customer segments that demand the product at different times. In each period, customers first purchase from the low price firm and then from the high price firm up to their inventories, provided the prices are lower than the maximum they are willing to pay. The main conclusions of this paper are as follows: although dynamic pricing is a more sophisticated policy than fixed-ratio pricing, it may lead to decreased equilibrium profits; under both pricing policies, one firm assumes the role of a low-cost high-output firm while the other assumes the role of a high-cost low-output firm; and, the supply demand ratio has more impact on the outcome of the competition than the heterogeneity in consumer reservation prices.     

A dynamic pricing approach for returned products in integrated forward/reverse logistics network design

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics network. In this paper, we address the problem of designing and planning a multi-echelon, multi-period, multi-commodity and capacitated integrated forward/reverse logistics network. Returned products are categorized with respect to their quality levels, and a different acquisition price is offered for each return type. Furthermore, the reservation incentive of customers, the expected price of customers for one unit of used product described by uniform distribution, is applied to model the customers’ return willingness. Due to the fact that the remaining worthwhile value in the used products is the corporation’s key motivation for buying them from customers, a dynamic pricing approach is developed to determine the acquisition price for these products and based on it determine the percentage of returned products collected from customer zones. The used products’ acquisition prices at each time period are determined based on the customers’ return willingness by each collection center.     

Leaders and followers in mutual funds: A dynamic Bayesian approach

This article proposes a dynamic Bayesian framework to analyze the leadership relationships between mutual funds. To this end, a two‐step procedure is proposed. First, a Bayesian rolling window based on the Capital Asset Pricing Model is used to estimate the evolution of mutual funds' market exposure over time. Then, a vector autoregressive (VAR) model is used to analyze the leader‐follower relationship between pair of mutual funds. Several leadership measures are studied. An application to Spanish mutual funds is carried out. In addition, the study examines the determining factors of mutual fund leadership.     

Price coordination in distribution channels: A dynamic perspective

In this study, we investigate two important questions related to dynamic pricing in distribution channels: (i) Are coordinated pricing decisions efficient in a context where prices have carry-over effects on demand? (ii) Should firms practice a skimming or a penetration strategy if they choose to coordinate or to decentralize their activities? To answer these questions, we consider a differential game that takes place in a bilateral monopoly where the past retail prices paid by consumers contribute to the building of a reference price. The latter is used by consumers as a benchmark to evaluate the value of the product, and by firms to decide whether to adopt a skimming or a penetration strategy.     

Transient policies in discrete dynamic programming: Linear programming including suboptimality tests and additional constraints

This paper investigates the computation of transient-optimal policies in discrete dynamic programming. The model, is quite general: it may contain transient as well as nontransient policies. and the transition matrices are not necessarily substochastic. A functional equation for the so-called transient-value-vector is derived and the concept of superharmonicity is introduced. This concept provides the linear program to compute the transientvalue-vector and a transient-optimal policy. We also discuss the elimination of suboptimal actions, the solution of problems with additional constraints, and the computation of an efficient policy for a multiple objective dynamic programming problem.     

A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information

In this paper, we study quantity discount pricing policies in a channel of one manufacturer and one retailer. The paper assumes that the channel faces a stochastic price-sensitive demand but the retailer can privately observe the realization of an uncertain demand parameter. The problem is analyzed as a Stackelberg game in which the manufacturer declares quantity discount pricing schemes to the retailer and then the retailer follows by selecting the retail price and associated quantity. Proposed in the paper are four quantity-discount pricing policies: “regular quantity discount”; “fixed percentage discount”; “incremental volume discount” and “fixed marginal-profit-rate discount”. Optimal solutions are derived, and numerical examples are presented to illustrate the efficiency of each discount policy.     

Production planning and pricing policy in a make-to-stock system with uncertain demand subject to machine breakdowns

We consider a make-to-stock system served by an unreliable machine that produces one type of product, which is sold to customers at one of two possible prices depending on the inventory level at the time when a customer arrives (i.e., the decision point). The system manager must determine the production level and selling price at each decision point. We first show that the optimal production and pricing policy is a threshold control, which is characterized by three threshold parameters under both the long-run discounted profit and long-run average profit criteria. We then establish the structural relationships among the three threshold parameters that production is off when inventory is above the threshold, and that the optimal selling price should be low when inventory is above the threshold under the scenario where the machine is down or up. Finally we provide some numerical examples to illustrate the analytical results and gain additional insights.     

Joint Monitoring of Several Types of Shocks in Normal Dynamic Linear Models: A Bayesian Decision Theoretic Approach

In this article we consider the sequential monitoring process in normal dynamic linear models as a Bayesian sequential decision problem. We use this approach to build a general procedure that jointly analyzes the existence of outliers, level changes, variance changes, and the development of local correlations. In addition, we study the frequentist performance of this procedure and compare it with the monitoring algorithm proposed in an earlier article.     

Double optimal stopping times and dynamic pricing problem: description of the mathematical model

In many industries, managers face the problem of selling a given stock of items by a deadline. We investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm’s objective is to maximize expected revenues. Examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry, which markets space such as seats on airline flights, cabins on vacation cruises, hotels renting rooms before midnight and theaters selling seats before curtain time that become worthless if not sold by a specific time. Given a fixed number of seats, rooms, or coats, the objective for these industries is to maximize revenues in excess of salvage value. When demand is price sensitive and stochastic, pricing is an effective tool to maximize revenues. In this paper, we address the problem of deciding the optimal timing of a double price changes from a given initial price to given lower or higher prices. Under mild conditions, it is shown that it is optimal to decrease the initial price as soon as the time-to-go falls below a time threshold and increase the price if time-to-go is longer than adequate time threshold. These thresholds depend on the number of yet unsold items.      

Labor market underrepresentation results in minority discrimination: A dynamic hiring model with employer learning

This paper develops a dynamic model of minority labor market discrimination. Employers repeatedly decide to hire either minority or majority job candidates whose productivities are unobservable beforehand. Hiring decisions are based on productivity expectations derived from the observable productivity of employers’ previously hired workers. If employers have fewer minority workers initially—a plausible assumption for (numerical) minorities—they discriminate against minority workers over time. Discrimination results from more dispersed minority expectations across the employer population and stronger effects of additional productivity observations on minority expectations. Both effects are a direct consequence of the minority’s initial underrepresentation in firms. I demonstrate the emergence of minority discrimination formally in a two-period hiring model and show simulation results for longer time frames.     

Learning dynamic prices in electronic retail markets with customer segmentation

In this paper, we use reinforcement learning (RL) techniques to determine dynamic prices in an electronic monopolistic retail market. The market that we consider consists of two natural segments of customers, captives and shoppers. Captives are mature, loyal buyers whereas the shoppers are more price sensitive and are attracted by sales promotions and volume discounts. The seller is the learning agent in the system and uses RL to learn from the environment. Under (reasonable) assumptions about the arrival process of customers, inventory replenishment policy, and replenishment lead time distribution, the system becomes a Markov decision process thus enabling the use of a wide spectrum of learning algorithms. In this paper, we use the Q-learning algorithm for RL to arrive at optimal dynamic prices that optimize the seller’s performance metric (either long term discounted profit or long run average profit per unit time). Our model and methodology can also be used to compute optimal reorder quantity and optimal reorder point for the inventory policy followed by the seller and to compute the optimal volume discounts to be offered to the shoppers.     

Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control

This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio.     

The effect of information in separable Bayesian semi-Markov control models and its application to investment planning

We consider a separable Bayesian semi-Markov control model to describe economic decisions under uncertainty. Our main interest is to examine the influence of the possibility of learning on the economic decisions and on the total expected return in a multi-period framework. We make use of the concept of Blackwell-sufficiency and apply the results to multi-period investment planing under uncertainty.     

Control and scheduling in a two-station queueing network: Optimal policies and heuristics

Consider a two-station queueing network with two types of jobs: type 1 jobs visit station 1 only, while type 2 jobs visit both stations in sequence. Each station has a single server. Arrival and service processes are modeled as counting processes with controllable stochastic intensities. The problem is to control the arrival and service processes, and in particular to schedule the server in station 1 among the two job types, in order to minimize a discounted cost function over an infinite time horizon. Using a stochastic intensity control approach, we establish the optimality of a specific stationary policy, and show that its value function satisfies certain properties, which lead to a switching-curve structure. We further classify the problem into six parametric cases. Based on the structural properties of the stationary policy, we establish the optimality of some simple priority rules for three of the six cases, and develop heuristic policies for the other three cases.