Dynamic Pricing Competition with Unobservable Inventory Levels: A Hidden Markov Model Approach

Dynamic Pricing Strategies in a Finite Horizon Duopoly with Partial Information

Hidden Markov Model(HMM) has a doubly embedded stochastic process with an underlying stochastic process that can be observed through another set of stochastic processes. This structure of HMM is useful for modeling vector sequence that doesn't look like a stochastic process but has a hidden stochastic process. So, HMM approach has become popular in various areas in last decade. The increasing popularity of HMM is based on two facts : rich mathematical structure and proven accuracy on critical application. In this paper, we applied continuous HMM (CHMM) approach with AR coefficient to detect and predict the chatter of lathe bite and to diagnose the wear of oil Journal bearing using rotor shaft displacement. Our examples show that CHMM approach is very efficient method for machine health monitoring and prediction.

In the past years, Hidden Markov Models have been used in several fields and applications with success. More recently, these models have been applied to improve the reliability of a machinery system. In many cases, failure is preceded by specific sequences of events (signature), which can be detected by an adequate Hidden Markov Model (HMM). Classical laws like lifetime models or survival functions are used to estimate the lifetime of a system. The default of these laws is that only the elapsed time is used to estimate the end of life of a system. The aim of this paper is to validate an HMM approach. We first use a synthetic HMM model of degradation to produce event sequences. This synthetic model has been inspired by a real process. In this case, we can adjust the failure rate by changing model parameters. All the parameters of this synthetic model are known and provide references which can be evaluated by different indicators. Classical survival functions used in reliability are computed on synthetic sequences. These laws validate the behavior of the synthetic model. The higher the failure rate, the shorter the lifetime duration. These results confirm that a four-state, left to right, HMM topology can represent the degradation level of a system. In a second time, this HMM approach is used in a real case, where degradation levels are unknown. Degradation estimates are compared with the results from classical survival functions used in the first case. Then we show that the degradation level provided by the HMM approach is more efficient than the survival functions approach. The HMM approach takes into account the events collected about a system, not only the elapsed time as is the case with survival functions.

We present a path planning framework that takes into account the human's safety perception in the presence of a flying robot. The framework addresses two objectives: (i) estimation of the uncertain parameters of the proposed safety perception model based on test data collected using Virtual Reality (VR) testbed, and (ii) offline optimal control computation using the estimated safety perception model. Due to the unknown factors in the human tests data, it is not suitable to use standard regression techniques that minimize the mean squared error (MSE). We propose to use a Hidden Markov model (HMM) approach where human's attention is considered as a hidden state to infer whether the data samples are relevant to learn the safety perception model. The HMM approach improved log-likelihood over the standard least squares solution. For path planning, we use Bernstein polynomials for discretization, as the resulting path remains within the convex hull of the control points, providing guarantees for deconfliction with obstacles at low computational cost. An example of optimal trajectory generation using the learned human model is presented. The optimal trajectory generated using the proposed model results in reasonable safety distance from the human. In contrast, the paths generated using the standard regression model have undesirable shapes due to overfitting. The example demonstrates that the HMM approach has robustness to the unknown factors compared to the standard MSE model.

This paper introduces two unsupervised learning methods for analyzing functional magnetic resonance imaging (fMRI) data based on hidden Markov model (HMM). HMM approach is focused on capturing the first-order statistical evolution among the samples of a voxel time series, and it can provide a complimentary perspective of the BOLD signals. Two-state HMM is created for each voxel, and the model parameters are estimated from the voxel time series and the stimulus paradigm. Two different activation detection methods are presented in this paper. The first method is based on the likelihood and likelihood-ratio test, in which an additional Gaussian model is used to enhance the contrast of the HMM likelihood map. The second method is based on certain distance measures between the two state distributions, in which the most likely HMM state sequence is estimated through the Viterbi algorithm. The distance between the on-state and off-state distributions is measured either through a t-test, or using the Kullback-Leibler distance (KLD). Experimental results on both normal subject and brain tumor subject are presented. HMM approach appears to be more robust in detecting the supplemental active voxels comparing with SPM, especially for brain tumor subject.

Masquerade detection is the ability to detect attackers known as masqueraders that intrude on another user’s system and pose as legitimate users. Once a masquerader obtains access to a user’s system, the masquerader has free reign over whatever data is on that system. In this research, we focus on masquerade detection and user classi cation using the following two di erent approaches: the heavy hitter approach and 2 di erent approaches based on hidden Markov models (HMMs), the dueling-HMM and threshold-HMM strategies. The heavy hitter approach computes the frequent elements seen in the training data sequence and test data sequence and computes the distance to see whether the test data sequence is masqueraded or not. The results show very misleading classi cations, suggesting that the approach is not viable for masquerade detection. A hidden Markov model is a tool for representing probability distributions over sequences of observations [9]. Previous research has shown that using a threshold-based hidden Markov model (HMM) approach is successful in a variety of categories: malware detection, intrusion detection, pattern recognition, etc. We have veri ed that using a threshold-based HMM approach produces high accuracy with low amounts of a false positives. Using the dueling- HMM approach, which utilizes multiple training HMMs, we obtain an overall accuracy of 81.96%. With the introduction of the bias in the dueling-HMM approach, we produce similar results to the results obtained in the threshold-based HMM approach, where we see many non-masqueraded data detected, while many masqueraded data avoid detection, yet still result in an high overall accuracy.

We study the effects of different pricing strategies available to a continuous review inventory system with capacitated supply, which operates in a fluctuating environment. The system has a single server with exponential processing time. The inventory holding cost is nondecreasing and convex in the inventory level, the production cost is linear with no set-up cost. The potential customer demand is generated by a Markov-Modulated (environment-dependent) Poisson process, while the actual demand rate depends on the offerred price. For such systems, there are three possible pricing strategies: Static pricing, where only one price is used at all times, environment-dependent pricing, where the price changes with the environment, and dynamic pricing, where price depends on both the current environment and the stock level. The objective is to find an optimal replenishment policy under each of these strategies. This paper presents some structural properties of optimal replenishment policies, and a numerical study which compares the performances of these three pricing strategies.

Sleep quantity affects an individual's personal health. The gold standard of measuring sleep and diagnosing sleep disorders is Polysomnography (PSG). Although PSG is accurate, it is expensive and it lacks portability. A number of wearable devices with embedded sensors have emerged in the recent past as an alternative to PSG for regular sleep monitoring directly by the user. These devices are intrusive and cause discomfort besides being expensive. In this work, we present an algorithm to detect sleep using a smartphone with the help of its inbuilt accelerometer sensor. We present three different approaches to classify raw acceleration data into two states - Sleep and Wake. In the first approach, we take an equation from Kushida's algorithm to process accelerometer data. Henceforth, we call it Kushida's equation. While the second is based on statistical functions, the third is based on Hidden Markov Model (HMM) training. Although all the three approaches are suitable for a phone's resources, each approach demands different amount of resources. While Kushida's equation-based approach demands the least, the HMM training-based approach demands the maximum. We collected data from mobile phone's accelerometer for four subjects for twelve days each. We compare accuracy of sleep detection using each of the three approaches with that of Zeo sensor, which is based on Electroencephalogram (EEG) sensor to detect sleep. EEG is an important modality in PSG. We find that HMM training-based approach is as much as 84% accurate. It is 15% more accurate as compared to Kushida's equation-based approach and 10% more accurate as compared to statistical method-based approach. In order to concisely represent the sleep quality of people, we model their sleep data using HMM. We present an analysis to find out a tradeoff between the amount of training data and the accuracy provided in the modeling of sleep. We find that six days of sleep data is sufficient for accurate modeling. We compare accuracy of our HMM training-based algorithm with a representative third party app SleepTime available from Google Play Store for Android. We find that the detection done using HMM approach is closer to that done by Zeo by 13% as compared to the third party Android application SleepTime. We show that our HMM training-based approach is efficient as it takes less than ten seconds to get executed on Moto G Android phone.

PurposeThe purpose of this study is to test the impact of time and price sensitivity on consumer satisfaction and purchase intention on online-to-offline (O2O) takeout platforms and explore the moderating effect of purchase preference on time sensitivity and satisfaction, as well as price sensitivity and satisfaction, in order to guide market pricing.Design/methodology/approachA structural equation model (SEM) of customer purchase intention was constructed, and the relationships between the variables (time sensitivity, price sensitivity, satisfaction and purchase intention) were examined. The completed questionnaires of 349 respondents were collected from the Questionnaire Star platform in China. The research model and hypotheses were then tested. Analytic hierarchy procedure was used to determine the moderating effect of purchase preference. Finally, the study proposes a pricing strategy for customer-active selective services.FindingsSatisfaction positively influences purchase intention, and price sensitivity significantly increases satisfaction and further increases purchase intention; however, time sensitivity negatively affects satisfaction. Specifically, purchase preference has strongly moderated the relationship between time, price sensitivity and satisfaction. In addition, the findings show that when purchase preference is high, the effect of price sensitivity on satisfaction is stronger, suggesting the importance of purchase preference in strengthening purchase intentions. The research work recommends a pricing strategy involving value-added pricing primarily for time-sensitive customers, which can help build a high-end brand image and reduce price competition. Reduced pricing is mainly for price-sensitive customers, which is conducive to stimulating consumption within a specific time. This pricing strategy is important for adjusting market sensitivity and flexibility.Originality/valueThis research provides new ideas for related disciplines and guidance for the differentiated pricing and promotion of takeout platforms, as well as a theoretical basis for the diversified development of takeout platforms, improvement of personalized service quality and enhancement of customer stickiness. This study fills gaps in the existing literature on the moderating effect of purchase preference on time sensitivity and satisfaction and price sensitivity and satisfaction.

Management Insights

Peak reduction in decentralised electricity systems : Markets and prices for flexible planning

We study dynamic pricing and inventory control of substitute products for a retailer who faces a long supply lead time and a short selling season. Within a multinomial logit model of consumer choice over substitutes, we develop a stochastic dynamic programming formulation and derive the optimal dynamic pricing policy. We prove that dynamic pricing converges to static pricing as inventory levels of all variates approach the number of remaining selling periods (assuming at most one customer arrival within each period). Our extensive numerical study of the effects of time and inventory depletion on the optimal pricing reveals two fundamental underlying driving forces of the complex price behavior: the level of inventory scarcity and the quality difference among products. We also compare the performance of three restricted pricing strategies: static, unified dynamic, and mixed dynamic pricing. We find that full-scale dynamic pricing is of great value in the presence of inventory scarcity, and initial inventory decisions are quite robust in the pricing scheme employed in the selling season. Based on the above insights, we propose a computationally efficient approach to the initial inventory decision, which delivers close-to-optimal inventory levels for all testing cases.

The cost of obtaining good information regarding the various probability distributions needed for the solution of most stochastic decision problems is considerable. It is important to consider questions such as: (1) what minimal amounts of information are sufficient to determine optimal decision rules; (2) what is the value of obtaining knowledge of the actual realization of the random vectors; and (3) what is the value of obtaining some partial information regarding the actual realization of the random vectors. This paper is primarily concerned with questions two and three when the decision maker has an a priori knowledge of the joint distribution function of the random variables. Some remarks are made regarding results along the lines of question one. Mention is made of assumptions sufficient so that knowledge of means, or of means, variances, co-variances and n-moments are sufficient for the calculation of optimal decision rules. The analysis of the second question leads to the development of bounds on the value of perfect information. For multiperiod problems it is important to consider when the perfect information is available. Jensen's inequality is the key tool of the analysis. The calculation of the bounds requires the solution of nonlinear programs and the numerical evaluation of certain functions. Generally speaking, tighter bounds may be obtained only at the expense of additional information and computational complexity. Hence, one may wish to compute some simple bounds to decide upon the advisability of obtaining more information. For the analysis of the value of partial information it is convenient to introduce the notion of a signal. Each signal represents the receipt of certain information, and these signals are drawn from a given probability distribution. When a signal is received, it alters the decision maker's perception of the probability distributions inherent in his decision problem. The choice between different information structures must then take into account these probability distributions as well as the decision maker's preference function. A hierarchy of bounds may be determined for partial information evaluation utilizing the tools of the multiperiod perfect information case. However, the calculation of these bounds is generally considerably more dicult than the calculation of similar boulids in the perfect information case. Most of the analysis is directed towards problems in which the decision maker has a linear utility function over profits, costs or some other numerical variable. However, some of the bounds generalize to the case when the utility function is strictly increasing and concave.

Systems and methods for automatically segmenting speech inventories. A set of Hidden Markov Models (HMMs) are initialized using bootstrap data. The HMMs are next re-estimated and aligned to produce phone labels. The phone boundaries of the phone labels are then corrected using spectral boundary correction. Optionally, this process of using the spectral-boundary-corrected phone labels as input instead of the bootstrap data is performed iteratively in order to further reduce mismatches between manual labels and phone labels assigned by the HMM approach.

In this chapter we introduce an original approach to predict a day-ahead energy demand, based on machine learning and pattern recognition. Our Hidden Markov Model (HMM) is a simple and explainable model that uses integer sequences to define emission probability distributions attached to states. We develop a Mathematica code which relies on the maximum likelihood principle in HMM environment. Based on these exploratory results, we conclude that the HMM approach is an efficient way in modeling short-term/day-ahead energy demand prediction, especially during peak period(s) and in accounting for the inherent stochastic nature of demand conditions. The model can be easily extended to predict energy demand values for more than one day in the future. However, the accuracy of such predictions would decrease as we expect.