Bayesian Inference of Arrival Rate and Substitution Behavior from Sales Transaction Data with Stockouts

When an item goes out of stock, sales transaction data no longer reflect the original customer demand, since some customers leave with no purchase while others substitute alternative products for the one that was out of stock. Here we develop a Bayesian hierarchical model for inferring the underlying customer arrival rate and choice model from sales transaction data and the corresponding stock levels. The model uses a nonhomogeneous Poisson process to allow the arrival rate to vary throughout the day, and allows for a variety of choice models. Model parameters are inferred using a stochastic gradient MCMC algorithm that can scale to large transaction databases. We fit the model to data from a local bakery and show that it is able to make accurate out-of-sample predictions, and to provide actionable insight into lost cookie sales

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.Revenue management, estimation, multi-nomial logit, risk-ratio

Managing demand uncertainty: probabilistic selling versus inventory substitution

Demand variability is prevailing in the current rapidly changing business environment, which makes it difficult for a retailer that sells multiple substitutable products to determine the optimal inventory. To combat demand uncertainty, both strategies of inventory substitution and probabilistic selling can be used. Although the two strategies differ in operation, we believe that they share a common feature in combating demand uncertainty by encouraging some customers to give up some specific demand for the product to enable demand substitution. It is interesting to explore which strategy is more advantageous to the retailer. We endogenize the inventory decision and demonstrate the efficiency of probabilistic selling through demand substitution. Then we analyze some special cases without cannibalization, and computationally evaluate the profitability and inventory decisions of the two strategies in a more general case to generate managerial insights. The results show that the retailer should adjust inventory decisions depending on products' substitution possibility. The interesting computational result is that probabilistic selling is more profitable with relatively lower product similarity and higher price-sensitive customers, while inventory substitution outperforms probabilistic selling with higher product similarity. Higher demand uncertainty will increase the profitability advantage of probabilistic selling over inventory substitution.Peer ReviewedPostprint (author's final draft

Introduction to disaggregate demand models

Demand information is an input for a great deal of operations research models. Assumed as given in many problem instances addressed in the literature, demand data are difficult to generate. In this tutorial, we provide an introduction to disaggregate demand models that are designed to capture in detail the underlying behavioral mechanisms at the foundation of the demand

Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items

Problem definition: Mining for heterogeneous responses to an intervention is a crucial step for data-driven operations, for instance to personalize treatment or pricing. We investigate how to estimate price sensitivity from transaction-level data. In causal inference terms, we estimate heterogeneous treatment effects when (a) the response to treatment (here, whether a customer buys a product) is binary, and (b) treatment assignments are partially observed (here, full information is only available for purchased items). Methodology/Results: We propose a recursive partitioning procedure to estimate heterogeneous odds ratio, a widely used measure of treatment effect in medicine and social sciences. We integrate an adversarial imputation step to allow for robust inference even in presence of partially observed treatment assignments. We validate our methodology on synthetic data and apply it to three case studies from political science, medicine, and revenue management. Managerial Implications: Our robust heterogeneous odds ratio estimation method is a simple and intuitive tool to quantify heterogeneity in patients or customers and personalize interventions, while lifting a central limitation in many revenue management data

A Petri net based simulation to study the impact of customer response to stock-out on supply chain performance

Abstract: Based on a Petri-net based simulation model, we investigate the effect of different customer response to stock-out on both the stock-out supply chain and the competing supply chain. Five types of customer stock-out responses are incorporated in the model to quantitatively assess the correlation between customer response and supply chain performance including bullwhip effect (BWE), on-hand inventory, and backlog level. After presenting the results of a series of Petri-net based simulation experiments, we discuss opportunities for both manufacturers and retailers to work better together to mitigate supply chain disruption. We also discuss the value of information sharing on mitigating BWE