Dynamic Pricing Strategy for Imitative and Habit‐Forming CustomersChen, Wen
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2917
This study employs finite‐horizon dynamic programming to examine markets with imitative and habit‐forming (IH) customers. Our findings indicate that optimal pricing and base demand increase as the number of customers who exhibit imitative and habit‐forming behaviors grows. Additionally, we analyze the impact of various stochastic parameters on optimal pricing, revealing that retailers should reduce prices when the variability among IH customers increases and raise prices when the average number of such customers rises. Notably, we challenge the conventional belief that greater uncertainty reduces profits, demonstrating that higher additive variability among IH customers can unexpectedly enhance profitability. These findings offer valuable insights for retailers into optimal pricing strategies for markets with imitative and habit‐forming customers, potentially aiding businesses in achieving growth and profitability.
On the Equivalence of Likelihood‐Based Confidence Bands for Fatigue‐Life and Fatigue‐Strength DistributionsLiu, Peng; Hong, Yili; Escobar, Luis A.; Meeker, William Q.
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2911
Fatigue data arise in many research and applied areas, and there have been statistical methods developed to model and analyze such data. The distributions of fatigue life and fatigue strength are often of interest to engineers designing products that might fail due to fatigue from cyclic‐stress loading. Based on a specified statistical model and the maximum likelihood method, the cumulative distribution function (cdf) and quantile function (qf) can be estimated for the fatigue‐life and fatigue‐strength distributions. Likelihood‐based confidence bands can then be obtained for the cdf and qf. This paper provides equivalence results for confidence bands for fatigue‐life and fatigue‐strength models. These results are useful for data analysis and computing implementation. We show (a) the equivalence of the confidence bands for the fatigue‐life cdf and the fatigue‐life qf, (b) the equivalence of confidence bands for the fatigue‐strength cdf and the fatigue‐strength qf, and (c) the equivalence of confidence bands for the fatigue‐life qf and the fatigue‐strength qf. Then we illustrate the usefulness of those equivalence results with two examples using experimental fatigue data.
Estimating the Size and Composition of Customer Base Using Retail Transaction DataSokol, Ondřej; Holý, Vladimír
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2914
The knowledge of the number of customers is the pillar of retail business analytics. In our setting, we assume that a portion of customers is monitored and easily counted due to the loyalty program while the rest is not monitored. The behavior of customers in both groups may significantly differ making the estimation of the number of unmonitored customers a nontrivial task. We identify shopping patterns of several customer segments which allows us to estimate the distribution of customers without the loyalty card using the maximum likelihood method. In a simulation study, we find that the proposed approach is quite precise even when the data sample is very small and its assumptions are violated to a certain degree. When a major violation is suspected, we suggest an interval approach. In an empirical study of a drugstore chain, we validate and illustrate the proposed approach in practice. The actual number of customers estimated by the proposed method is much higher than the number suggested by the naive estimate assuming the constant customer distribution. The proposed method can also be utilized to determine penetration of the loyalty program in the individual customer segments.
Comparing Risks for Binomial Reliability Assurance Test PlanningKim, Hyoshin; Wilson, Alyson G.
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2912
Balancing consumer's and producer's risk is an important consideration when planning tests. Instead of focusing on finding a single best test plan, we introduce a general framework to systematically identify a set of binomial test plans by leveraging the inverse relationship between the two risks. The framework is applied to compare a variety of assurance testing frameworks, including classical tests, and Bayesian reliability assurance tests such as the Bayesian assurance test, the assurance reliability demonstration test, and the coverage criterion test. Efficient algorithms are presented to compute the set of test plans, providing practitioners with a comprehensive range of options to choose from. In addition, we include a comparison to the sequential probability ratio test. We also provide formal proofs for the inverse relationship between consumer's and producer's risk in Bayesian reliability assurance tests that underlie our algorithms. A case study is presented to illustrate the framework's application and compare the risks associated with different test plans.
Credibility Theory Under the Least Squared Relative Loss FunctionYong, Yaodi; Zhang, Yiying; Zhu, Xiaobai
2024 Applied Stochastic Models in Business and Industry
doi: 10.1002/asmb.2913
The classical Bühlmann model employs a least squared loss criterion that penalizes pricing errors equally across all risk classes. In contrast, this paper develops a new credibility theory based on the least squared relative loss (LSRL) function to address scenarios where the classical approach may fall short. We derive explicit expressions of LSRL‐based credibility estimators, including non‐parametric versions and Bühlmann–Straub extensions. Through a comparative study, we illustrate the real‐world applicability of the LSRL estimator across different scenarios, highlighting its advantages and limitations in comparison to the classical model. Additionally, we explore different LSRL formulations to provide deeper insights into their practical viability.