Heterogeneous Customers Research Articles

Inventory Rationing on a One-for-One Inventory Model with Backorders and Lost Sales

In this study, we are primarily motivated by the research problem of recognizing heterogeneous customer behavior towards waiting for order fulfillment under the 'threshold rationing policy' (also known as the 'critical level policy'), and aim to find its effect on system stock levels and performance measures. We assume a continuous review one-for-one ordering policy with generally distributed lead times. In the first model, we consider the case in which low-priority customer class exhibits zero patience for waiting if the demand is not satisfied immediately (a lost sale), while the demand of high-priority customer class can be backordered. This is the first study in the literature to consider this model. We provide an exact analysis for the derivation of the steady-state probability distribution and the average infinite horizon cost per unit time. We then develop an efficient procedure to minimize the average expected cost rate by deriving bounds on the optimal cost, which reduces the enumeration space considerably. In the numerical study, we show the relative savings achieved by implementing the proposed threshold rationing policy over some of the traditional industry practices. In the second model, we study the opposite case in which the high-priority customer class exhibits zero patience for waiting. The existing study in the literature uses simulation to demonstrate that the performance of the critical level policy is robust with respect to the form and variability of the lead time distribution provided the mean lead times are identical. Then it proposes using the Continuous-Time Markov Chain (CTMC) equivalent of the model as an approximation. In this study, we establish a theoretical basis for the rationale of using the CTMC approach as an approximation. We show that under certain assumptions the steady-state probabilities of the system with generally distributed lead times are identical to the steady-state probabilities of the CTMC system with the same mean. This result enables us to link the dynamics of the studied model to the CTMC model, which then allows us to provide a theoretical explanation to the empirically observed phenomenon that why the steady-state probabilities and performance measures are near-insensitive to the form and variability of the lead time distribution as long as mean lead times are identical.

Numerical Validation of the Continuous Time Markov Chain Approximation as a Service Level Estimation Method for Heterogeneous Customer Demand Classes

In this article, we study a threshold level based inventory allocation and replenishment problem for two priority-demand classes under the lot-for-lot replenishment policy. Demands of low-priority class are backordered when on-hand stock is at or below a certain threshold level, while high-priority class demands are lost in case of stock-out situations. We assume a continuous review lot-for-lot ordering policy with both deterministic and stochastic replenishment lead times. Both priority classes exhibit mutually independent, stationary, Poisson demand processes. There is no exact solution yet in the literature except for the special case of exponentially distributed lead times. In this complementary study, we aim to numerically validate the Continuous-Time Markov Chain (CTMC) approximation as a service level approximation method by thoroughly analyzing the effect of the type of lead time distribution, lead time variability, and value of system parameters on the quality of the class-specific service level estimations. As long as expected lead times are identical, we also show empirically the near-insensitivity of the effect of the type of lead time distribution and the lead time variability on the achieved service levels. The CTMC approximation works well under variety of system parameters and lead time distributions. For the cases considered in the constant lead time scenarios with service levels which we expect to see in practice (with fill rate requirements at least 60 % and 90 % for the low-priority and high priority customer classes, respectively), the average absolute errors for the CTMC approximations are calculated as 0.09 % (for the low-priority class fill rate) and 0.05 % (for the high-priority class fill rate); while the maximum absolute errors for the CTMC approximations are calculated as 0.37 % (for the low-priority fill rate) and 0.18 % (for the high-priority fill rate). The CTMC approach also provides quality approximations for the Erlang, lognormal and gamma distributed lead times.

Advance Service Reservations with Heterogeneous Customers

We study a fundamental model of resource allocation in which a finite number of resources must be assigned in an online manner to a heterogeneous stream of customers. The customers arrive randomly over time according to known stochastic processes. Each customer requires a specific amount of capacity and has a specific preference for each of the resources with some resources being feasible for the customer and some not. The system must find a feasible assignment of each customer to a resource or must reject the customer. The aim is to maximize the total expected capacity utilization of the resources over the horizon. This model has application in services, freight transportation, and online advertising. We present online algorithms with bounded competitive ratios relative to an optimal off-line algorithm that knows all stochastic information. Our algorithms perform extremely well compared with common heuristics as demonstrated on a real data set from a large hospital system in New York City. This paper was accepted by Yinyu Ye, optimization.

Choices for competing service providers with heterogeneous customers: Traditional versus opaque sales modes

Competing service providers have been conducting opaque sales widely by cooperating with an intermediary, such as Priceline.com and Hotwire.com, to increase capacity flexibility, realise price discrimination and create a new channel for customers. Whether competing service providers should collaborate with an intermediary when facing heterogeneous customers and how a contract design can be made between service providers and the intermediary are two challenging research problems. Recent advances in opaque sales have focused on homogeneous customers, whereas the revenue sharing mechanism for heterogeneous customers has remained unexplored. This study considers two competing service providers that collaborate with an intermediary in a heterogeneous market with leisure and business customers. Styled models are built to capture the traditional and opaque sales modes. The contracting strategies are derived by comparing the profit of the two modes. Considering the simultaneous arrivals of two kinds of customers, we find that the decisions of service providers relate to two factors: the market structure and the revenue sharing mechanisms. In a high-pricing strategy market, service providers may collaborate with an intermediary. Conversely, in a low-pricing strategy market, service providers may not collaborate with an intermediary. In both situations, service providers should strive for a balance between the profit derived from the intermediary and the potential profit loss from opaque sales.

Naor’s model with heterogeneous customers and arrival rate uncertainty

This paper examines an extension of Naor’s observable queueing model in which the arrival rate is not known with certainty by either customers or the system manager. Further, customers are heterogeneous in terms of their service valuation and waiting time cost. We analyze the stability of the system and properties of the revenue maximizing fee and socially optimal fee.

Competition Between Offline and Online Retailers with Heterogeneous Customers

We consider the spatial competition between two traditional physical (or offline) retailers and an Internet (or online) retailer where the efficiency of the latter differs from that of the former. We assume that consumers are heterogeneous across two dimensions: (1) the costs of traveling to either of the offline retailers; and (2) the costs of purchasing from the online retailer. Both dimensions depend on the spatial location of consumers and are independent of each other. We show that the online retailer maximizes its profit at an intermediate level of the consumer disutility of online purchase when its efficiency is low.

Pricing Ancillary Service Subscriptions

We investigate heterogeneous customer choice behavior in the presence of main products—ancillary services with options of pay-per-use and subscription—and outside option. The willingness to pay for a service subscription is derived as a closed-form expression, which enables us to characterize the optimal pricing strategy and the impact of service subscriptions on customer surplus. Analytical results and numerical experiments show that offering service subscriptions may result in “win-win,” “win-win-win,” “win-win-lose,” or “lose-lose-win” scenarios or in other situations for the firm, competitors, and customers in a variety of monopolistic and duopolistic scenarios. The advantages of service subscription still remain with heterogeneous customers differing on multiple dimensions including the nominal utility, uncertainty in the need of ancillary service, and purchase frequency. We find that if the product quality for both firms, measured by nominal utility, is not significantly different, more fierce price competition by offering a service subscription may result in a higher customer surplus, compared with that without a service subscription. Ancillary service subscription can help firms to better price-discriminate heterogeneous customers through different subscription decisions and subsequent purchase behavior. This paper was accepted by Gad Allon, operations management.

Data-Driven Sports Ticket Pricing for Multiple Sales Channels with Heterogeneous Customers

Problem Definition: We develop a framework to study purchase behavior from distinct segments of heterogeneous customers, and to optimize prices for different policies in a sports ticket market with multiple sales channels. Academic/Practical Relevance: Sports teams face challenges maintaining or increasing ticket sales levels. With the growth of analytics, they aim to implement data-driven pricing techniques to improve gate revenues; however they do not have state-of-the-art demand estimation and price optimization tools that take into account the range of valuation across different seat sections and opponent match-ups. Methodology: Partnering with a college football team, we develop a data-driven pricing tool which: (1) segments customers in two sales channels using transaction-level data and anonymous customer profiles; (2) explores the decision-making process of different customers within these segments using the Multinomial Logit and Mixed-Multinomial Logit frameworks; and (3) decides optimal or near-optimal prices subject to some business constraints enforced by the team management. In addition, our method takes the sequential arrivals of customers and the capacity constraints of seat categories into account. Results: Our estimation results show that customers differ significantly in their sensitivities to price and distance to the field within each segment, in addition to the differences across segments. We also observe that customers become less likely to choose a seat category as its remaining inventory falls below a certain point. Managerial Implications: By analyzing different policies, we show that price optimization could increase revenue by as much as 7.6%. In addition, better categorization of games and further refinement of seat category differentiation and related pricing may help further boost this figure up to 11.9%

Robust Product Positioning Considering Customer Preferences

This paper investigates the product-positioning problem for a monopolist developing of a new product. The majority of the literature on product positioning assumes that the consumer choice model and parameters are both precisely known. In reality, however, the marketer may be uncertain about the model structure or the parameters due to incomplete information, small sample data size, etc. In this paper, we investigate a robust product-positioning problem based on the multinomial logit model to account for parameter uncertainty. We first establish a nominal product-positioning model, in which valuation parameters are assumed to be known. Then, we investigate a static robust product-positioning problem with the multinomial logit model to obtain the maximin revenue. We also propose a two-period dynamic robust model. For each setting, we consider both homogeneous and heterogeneous customers' preferences. Finally, numerical experiments are presented to compare the nominal model with the static robust model, and to compare the static robust model with the dynamic robust model. The experiments show that when facing uncertain parameters, the robust model obtains more stable revenue than the nominal model; the dynamic robust model obtains higher revenue than the static robust model.

Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience

We consider a queuing network with single-server nodes and heterogeneous customers. The number of customers, which can obtain service simultaneously, is restricted. Customers that cannot be admitted to the network upon arrival make repeated attempts to obtain service. The service time at the nodes is exponentially distributed. After service completion at a node, the serviced customer can transit to another node or leave the network forever. The main features of the model are the mutual dependence of processes of customer arrivals and retrials and the impatience and non-persistence of customers. Dynamics of the network are described by a multidimensional Markov chain with infinite state space, state inhomogeneous behavior and special structure of the infinitesimal generator. The explicit form of the generator is derived. An effective algorithm for computing the stationary distribution of this chain is recommended. The expressions for computation of the key performance measures of the network are given. Numerical results illustrating the importance of the account of the mentioned features of the model are presented. The model can be useful for capacity planning, performance evaluation and optimization of various wireless telecommunication networks, transportation and manufacturing systems.

A supply chain network economic model with time-based competition

This paper presents an integrated model for time-cost competition between supply chains with heterogeneous customers. The firms in our model can offer various time options for their production/service to time-sensitive customers. This gives rise of a new concept of time-based supply chain, which we call T-chain, to be the basic element in the competition and extends the inter supply chain competition to a new dimension of time. Assuming the customers are heterogeneous in time-cost bi-criteria decision making, we integrate the discrete choice theory into supply chain network competition and formulate the equilibrium conditions as a multinomial logit based variational inequality problem. Numerical examples are presented for model illustration and managerial insights such as profit maximization for a firm who participates in this supply chain network.

MANAGING PRICE AND SERVICE RATE IN CUSTOMER-INTENSIVE SERVICES UNDER SOCIAL INTERACTIONS

This paper investigates the price and service rate decisions in a customer-intensive service in an M/M/1 queue system under the influence of social interactions, where a higher value of the service is perceived if more customers purchase the service. The customer-intensive nature of the service requires a low service speed to maintain its quality, which may increase the congestion of the system. Two cases where customers are either homogeneous or heterogeneous in terms of the customer intensity are considered. It is found that social interactions can always benefit the service provider as more expected revenue can be achieved, and potential profits would be lost if the influence of social interactions is ignored. For the case with heterogeneous customers, the optimal price and service rate decisions are solved with or without considering social interaction effect. The study finds the proportions of high and low sensitive customers and the social interaction intensity are critical to the operational decisions and the market coverage strategies. These results offer a better understanding on the interplay between the quality-speed conundrum and the influence of social interactions in customers’ purchase behaviour in managing customer-intensive services.

Learning to live within your (water) budget: Evidence from allocation-based rates

As allocation-based rates (ABR) become more widely adopted in the residential water sector, it is important to determine whether consumers interpret the water budget as a target for water use, or if they simply respond to the increasing block design. This paper exploits a natural experiment created when ABR were adopted by a California water district, that allows us to identify households with high water use as a treatment group. We find evidence of heterogeneous customer responses, and policy-induced behavioral changes that imply customers adjust their target level of water use based on the information signal provided by the water budget.

On-Demand Service Sharing with Collective Dynamic Pricing

This paper designs a dynamic allocation and pricing mechanism for an on-demand platform that can provide individual or shared services. Time-sensitive customers arrive stochastically onto the platform with heterogenous willingness to pay. The mechanism optimizes at what time, to which customers and at what price to provide services. This environment creates inter-agent and inter-temporal dependencies. We decompose the platform's problem into a dynamic program, based on the novel notion of collective virtual value --- defined as the total surplus that the platform can extract from all customers. The optimal mechanism in this complex environment follows a simple, easily-implementable index rule: service is provided each time the collective virtual value exceeds a threshold, which decreases with the number of available suppliers. Service sharing thus leads to temporal discrimination: as opposed to the classical problem of dynamic pricing with commitment, customers may receive an immediate service or a delayed service --- based on their own willingness to pay and the system's dynamics. Ultimately, service sharing is not exclusively governed by cost-minimization and demand-supply management objectives, but also by discriminatory incentives: it provides an additional degree of freedom to offer differentiated service levels across heterogenous customers.

Learning to Rank an Assortment of Products

We consider the product ranking challenge that online retailers face when their customers typically behave as window shoppers: they form an impression of the assortment after browsing products ranked in the initial positions and then decide whether to continue browsing. We design online learning algorithms for product ranking that maximize the number of customers who engage with the site. Customers' product preferences and attention spans are correlated and unknown to the retailer; furthermore, the retailer cannot exploit similarities across products owing to the presence of subjective, stylistic elements and the fact that products may not be substitutes. We develop a class of online learning-then-earning algorithms that prescribe a ranking to offer each customer, learning from preceding customers' clickstream data to offer better rankings to subsequent customers. Our algorithms balance product popularity with diversity: the notion of appealing to a large variety of heterogeneous customers. We prove that our learning algorithms converge to a ranking that matches the best-known approximation factors for the offline, complete information setting. Finally, we partner with Wayfair - a multi-billion dollar home goods online retailer - to estimate the impact of our algorithms in practice via simulations using actual clickstream data, and we find that our algorithms yield a significant increase (5-30%) in the number of customers that engage with the site.

Collaborative R&D and Pricing Policy of Supply Chain under the Selection Behavior of Heterogeneous Customer

Considering that a manufacturer and its core part supplier make collaborative R&D on serial products of 3 grades, high-, mid-, and low-grade, and their core parts according to costumers’ preference for the performance, or intrinsic value, of products, we propose a collaborative R&D model based on costumers’ selection behavior to study the collaborative R&D policy and pricing policy of the supply chain. Then we establish a bargaining game model to study how they allocate the profit they earned. We obtain the optimal policies through theoretic and experimental analysis, and we use Apple iPhone case to illustrate the models and conclusions of this paper. It is found that if the aim of the supply chain is only to maximize its total profit, it should only develop the high-grade product and make its price half of its intrinsic value; if the aim of the supply chain is to maximizing profit while increasing the sales and market shares of the serial products, it should at least develop the high-grade and low-grade product; the ratio of price between the higher grade and the lower grade should be greater than the corresponding ratio of the intrinsic value, while the difference of price between higher grade and the lower grade should be less than the corresponding difference of the intrinsic value.

Revenue maximization in service systems with heterogeneous customers

In this paper, we consider revenue maximization problems for service systems with heterogeneous customers. To extract meaningful insights, we consider a simplified two queue system where each server charges an admission price to its customers. The customers differ in their cost for unit delay and this customer heterogeneity is modeled as a random variable with distribution F. On arrival, the customers must choose a server that offers the lowest sum of admission price and the expected delay cost.Given the admission prices at the two servers and the explicit knowledge of the distribution F, we first characterize the Wardrop equilibrium routing for the heterogeneous customers. We then consider a monopoly system where both the servers belong to a single operator. For this system we characterize the revenue maximizing program for the monopoly operator and outline its properties. We then consider the duopoly problem where each server competes with the other server to maximize its revenue rate. For the special case when the servers have identical service capacity, we obtain the necessary condition for existence of symmetric Nash equilibrium prices.For the analysis of the monopoly and the duopoly problem, the heterogeneity distribution F is assumed to be explicitly known. However, for most practical scenarios, the functional form of F may not be known to the system operator and in such cases, the revenue maximizing prices cannot be determined. In the last part of the paper, we provide an elementary method to estimate the distribution F. This method relies on suitably varying the admission prices based on the properties of the Wardrop equilibrium. We also illustrate this method with some suitable numerical examples.

A generic two-stage fuzzy inference system for dynamic prioritization of customers

This paper presents a fuzzy expert system for prioritization of heterogeneous customers with different needs. In this way, it is possible to improve the average waiting cost of a queuing system and enhance customer satisfaction as the basic component of organizations. Each customer has his own specific characteristics and demands and expects the system to understand his value and provide the best service. In this study, a two-stage Mamdani fuzzy inference system (FIS) was applied as a decision-making approach to prioritize customers based on Service Duration, Service Value, Customer Loyalty, Maximum Toleration, and Waiting Time. For this purpose, an expert system was developed that can be applied in various fields perfectly. To evaluate and analyze the performance of Fuzzy Prioritization System (FPS), the proposed model is compared with the First-In-First-Out (FIFO) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods as common approaches for prioritizing customers. The results of numerical experiments revealed the efficiency of the proposed system compared to these two methods.

Service Center Staffing with Cross‐Trained Agents and Heterogeneous Customers

We model a real‐world service center with cross‐trained agents serving customer requests that are heterogeneous with respect to complexity and priority levels: High priority requests preempt low priority requests and low‐skilled agents can only serve less complex requests, while high skilled agents can serve all requests. Our main aim is to dynamically assign requests to agents considering the priority and complexity levels of requests. We model this system as a Markov chain that is infinite in multiple dimensions and thus is not amenable to exact analysis. We therefore apply approximation and bounding techniques to develop a tractable, novel algorithm using the Matrix Analytic Method. Our algorithm closely approximates the operations of the real‐world service system under a simple but effective threshold‐based request‐assignment policy. Extensive computational results demonstrate the usefulness of our algorithm to minimize costs given an existing staffing configuration, as well as in helping to make long‐term staffing decisions. In addition, our algorithm also has at least two orders of magnitude shorter computation times than each replication of simulation. Hence, it is both fast and accurate.

When to Triage in Service Systems with Hidden Customer Class Identities?

In service systems with heterogeneous customers, prioritization with respect to the relative importance of customers is known to improve certain performance measures. However, in many applications, information necessary to determine the importance level of a customer may not be available immediately but can be revealed only through some preliminary investigation, which is sometimes called triage. This triage process is typically error-prone and may take substantial amount of time, and hence, it is not always clear if and when it should be implemented for purposes of priority assignment. To provide insights into this question, we study a stylized queueing model with a single server and two types of customers with hidden type identities and different rates of waiting costs. By means of a Markov decision formulation, we first show that the optimal dynamic policy on triage is characterized by a switching curve: if the number of unclassified customers is sufficiently large, then the server triages an unclassified customer; otherwise, the server skips triage and directly serves an unclassified customer. We also identify a mathematical condition under which triage should never be considered, which depends on the classification power of triage, mean triage and service times, and the heterogeneity of customers. Based on all our numerical and analytical results, we conclude that triage for purposes of prioritization should not be considered if it takes a significantly large amount of time in comparison to the actual service but if it is sufficiently fast, then implementing a policy that triages some or all customers can significantly reduce long-run average costs of waiting. In these cases where there is benefit to using triage, a policy that triages all arrivals can be used if the triage time is substantially short and the probability that a customer is classified into a higher priority is large; otherwise, a policy that triages customers dynamically depending on the system state would perform significantly better than the triage-all policy, especially when the traffic is heavy.