Multiple Types Of Customers Research Articles

A Critical-Level Dynamic Pricing Mechanism for Improving Supply Chain Inventory Policies With Multiple Types of Customers: An Integration of Rationing Policy and Dynamic Pricing

In today’s highly dynamic and competitive environment, an effective and practical inventory policy is critical for every supply chain and can dramatically affect its performance. When a supply chain faces multiple types of customers with different characteristics, management encounters even more challenges in making decisions about inventory policies. By integrating inventory rationing policies and dynamic pricing strategies, this study proposes a critical-level dynamic pricing (CLDP) mechanism associated with inventory ordering policies to address these challenges. Furthermore, to demonstrate the implementation and evaluate the effectiveness of the proposed policy, we develop a simulation model with the CLDP mechanism and apply it to a specific numerical case. The results show that the proposed inventory policy improves the total net profit by 12.58%. Finally, the conclusions and future research topics are discussed.

Supply Chain Inventory Optimization With Multiple Types of Customers and Equal Priorities: A Study Using Heuristic and Simulation Methods

In this study, the optimal inventory policies for a supply chain with multiple types of customers is investigated to minimize the total inventory cost. Each customer type has specific demand patterns in terms of ordering frequency and order quantity; moreover, there is no difference in priority among the customers. Due to the computational complexity of this optimization problem, we develop a reduced form of the original problem and propose a heuristic that is easily implementable by practitioners. In addition, a simulation model is developed on the same problem setting as a benchmark. To illustrate the implementation and the effectiveness of the proposed heuristic, a numerical example is studied, followed by a sensitivity analysis of the key parameters. The numerical results show that our heuristic provides a comparable performance as simulation-based optimization (a 2.6% difference), and the sensitivity analysis shows a reliable robustness of the model (less than 5.2% difference).

Subscription Pricing for Free Delivery Services

Many firms that offer home delivery of products purchased online now provide consumers the option of subscribing to a membership plan for free delivery of limited or unlimited number of orders instead of customers paying delivery charges for each order. This paper seeks to understand the benefits to firms and consumers of introducing such free-delivery subscription (FDS) plans to complement their traditional pay-for-delivery (PFD) option, characterize the firm's optimal FDS subscription pricing strategy, and study the effects of product, consumer, and market characteristics on the subscription fees and firm's profits. We develop and analyze an economic model that incorporates salient features of product delivery settings that prior models of subscription pricing do not fully capture. The features include simultaneous availability of PFD and FDS options, lift in a consumer's demand when she switches from PFD to FDS, the possibility of attracting new consumers when the firm introduces FDS, and order batching by customers due to per-order delivery charges and free-delivery order allowances. Our utility-based approach to model consumers’ purchasing choices incorporates consumer heterogeneity both in terms of their utility for the product and their shopping preference under the PFD option. For homogeneous consumers, we show that introducing a FDS plan raises the firm's profit, establish the optimality of offering unlimited free-delivery allowance, and analyze comparative statics. With multiple customer types, our analysis of two subscription pricing strategies for FDS plans—a single “Universal” plan and multiple “Tiered” plans with varying subscription fees and free-delivery limits—leads to several interesting insights on delivery pricing strategies, as well as drivers and sensitivity of the optimal policy, profits, and number of subscribers. We supplement this analysis with extensive computational experiments that reveal a substantial increase in profits when a firm adds one or more FDS plans to its PFD option even though the optimal subscription fee(s) only covers part of the firm's actual shipping costs. These results also permit us to gauge the influence and understand the trends in the profitability of the Universal and Tiered plans as various parameters change.

Admission Control of Double-Sided Queues With Multiple Customer Types

Admission Control of Double-Sided Queues With Multiple Customer Types

Distribution network voltage analysis with data-driven electric vehicle load profiles

The number of electric vehicles (EVs) is expected to increase significantly in the near future, which will affect the operation of future power networks. This study investigates the impact of EVs on the distribution network voltage profile by collecting measurements from residential, slow commercial, and fast public EV charging stations throughout the annual cycle. It is revealed from the data that annual utilization factors for residential, slow commercial, and fast public charging stations are 89%, 55%, and 24%, respectively. The optimal power flow solutions have been presented without the EV and with EV (home, commercial, and public) load profiles. Simulation results identify the voltage violation's extent, instant, and duration that may affect the future distribution grid. Most voltage violations happen in the evening, weekday afternoon, and midday for residential, slow commercial, and fast public EV charging stations, respectively. Furthermore, multiple enabling technologies have been demonstrated to reduce voltage violations, such as coordinated charging (reduced voltage violation by 50%), renewable charging (by 50%), and combinations of multiple types of customers (by 30%). This study presents some key insights into future power system operational scenarios with widespread EV charging stations that can be managed by multiple enabling technologies.

Dynamic and Pareto-improving swapping of vehicles to enhance integrated and modular mobility services

Efficiency of many mobility services depends on effective matching of service vehicles and customers over time and space. New technologies, such as those related to service integrators and modularized autonomous vehicle platforms (i.e., chassis with built-in power and control systems), further allow pooling of vehicles from traditionally separate service operators to flexibly serve multiple types of customers (e.g., passengers and freight). Dynamic matching systems, if not carefully managed, suffer from the so-called wild goose chase (WGC) phenomenon, which describes an inefficient system equilibrium with a large number of vehicles trapped in unproductive deadheading. This paper proposes a new dynamic vehicle swap strategy that can be used to enhance system efficiency by reducing the expected waiting/deadheading time. This strategy can not only mitigate the WGC and reduce the needed fleet size, but also ensure that the vehicle swap achieves a Pareto improvement for each involved participant. Approximate analytic formulas are derived from a series of differential equations and spatial probability models to estimate the expected system performance in the steady state. This system of nonlinear equations can be solved numerically to yield the equilibrium points and the associated system performance metrics. Agent-based simulations are used to verify the accuracy of the derived formulas, and to demonstrate the effectiveness of the proposed dynamic and Pareto-improving swap strategy in a variety of application contexts (e.g., taxi, service integrator, or pooled modular chassis).

Admission and routing control of multiple queues with multiple types of customers

We study the routing and admission control problem in a parallel queueing system with heterogeneous servers serving multiple types of customers. The system makes admission decision regarding whether to admit a customer upon arrival as well as routing decision of the queue to which the admitted customer is assigned. The objective is to maximize the expected profit, which includes customer-dependent revenues and holding cost and server-dependent cost. We first characterize the structure of the optimal policy for the case with two servers and two types of customers that have the same holding cost. We show that the optimal admission and routing policy has a complex non-monotone structure; however, we show that this non-monotone structure is the result of overlapping of three pairwise dominant policies that have a monotone structure. Utilizing the above structure, we propose three heuristics for the general case of multiple servers and multiple types of customers. Through a numerical study, we demonstrate the effectiveness of our heuristics, and provide conditions under which each heuristic performs well. Lastly, we provide insights on the effect of holding cost on customer rejection and the effect of fixed production cost on capacity allocation.

Stability of a stochastic ring network

In this paper we establish a necessary and sufficient stability condition for a stochastic ring network. Such networks naturally appear in a variety of applications within communication, computer, and road traffic systems. They typically involve multiple customer types and some form of priority structure to decide which customer receives service. These two system features tend to complicate the issue of identifying a stability condition, but we demonstrate how the ring topology can be leveraged to solve the problem.

On the optimality of a maintenance queueing system

We consider a finite single-server maintenance queue with multiple types of customers. The difference between customers' types is defined by the offered rewards. We show that the optimal admission control policy for maximizing the long-run average reward per unit time has a trunk reservation structure. Meanwhile, if the equipment is off, there exists a threshold of the queue length, above which the optimal repair speed is increasing in the queue length and below which the optimal repair speed is 0.

Capacity Allocation of an Integrated Production and Service System

Manufacturing servitization has become a major trend in industry that is implemented by so called integrated production and service systems (IPSSs) to offer not only products but also their associated services. In this study, we explore the capacity allocation policy for an IPSS that consists of a manufacturing facility and a service center. The IPSS serves two classes of customers, each demanding a specific product produced at the manufacturing facility and, subsequently, the associated service offered by the service center. We formulate this problem of resource allocation as a Markov decision process. Our analysis suggests that it is optimal to serve the customer with the larger cost saving rate and slower service rate, where the cost saving rate equals service rate times the sum of holding cost and waiting cost. Then we explore production control policies coupled with optimal service ones. We demonstrate that, with light service traffic, the system under the optimal production policy becomes similar to a make‐to‐stock system. Such a system can effectively hedge the system uncertainty. Therefore, the optimal production policy for the IPSS is also a hedging point policy. Under this policy, switching and idling curves split the state space into three regions: one without any production, the two others for production of two type products, respectively. We also discuss the optimal control policies of the two extensions of the IPSS (one with multiple types of product and customers, and the other with a single product and two classes of customers) and find that the characters of the optimal production and service policy still hold. Finally, we develop three heuristic integrated scheduling policies. Numerical experiments show that one is very effective.

A Novel Pricing Algorithm Based on Reward-Punishment Mechanism for Supply and Demand Balancing

Demand response (DR) is a powerful tool to maintain the stability of the power system and maximize the profit of the electricity market, where the customers engage in the pricing scheme and adjust their electricity demand proactively based on the price. In DR programs, most existing works are based on the assumption that the prediction of the electricity demand from customers is always accurate and trustworthy, which will lead to high cost and fluctuation of the electricity market once the prediction is obeyed. In this paper, we design a reward and punishment mechanism to constrain customers’ dishonest behaviors and propose a novel pricing algorithm based on the reward and punishment mechanism to relax the assumption, which guarantees the total electricity demands of all customers are within a secure range and obtain the maximum profit of the supplier. Meanwhile, we obtain the optimal demand and provide a upper and lower bound of the proposed price for the electricity market. In addition to a single type of customer, we also consider multiple types of customers, each of whom has different characteristics to prices. Extensive simulation results are constructed to demonstrate the effectiveness of the proposed algorithm compared with other pricing algorithms. It also shows that the average electricity consumption of a whole community is mostly affected by the residents’ electricity consumption and the balance of the supply and all types of customers is achieved under the proposed pricing algorithm.

Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs

For a queueing system with multiple customer types differing in service-time distributions and waiting costs, it is well known that the cµ-rule is optimal if costs for waiting are incurred linearly with time. In this paper, we seek to identify policies that minimize the long-run average cost under nonlinear waiting cost functions within the set of fixed priority policies that only use the type identities of customers independently of the system state. For a single-server queueing system with Poisson arrivals and two or more customer types, we first show that some form of the cµ-rule holds with the caveat that the indices are complex, depending on the arrival rate, higher moments of service time, and proportions of customer types. Under quadratic cost functions, we provide a set of conditions that determine whether to give priority to one type over the other or not to give priority but serve them according to first-come, first-served (FCFS). These conditions lead to useful insights into when strict (and fixed) priority policies should be preferred over FCFS and when they should be avoided. For example, we find that, when traffic is heavy, service times are highly variable, and the customer types are not heterogenous, so then prioritizing one type over the other (especially a proportionally dominant type) would be worse than not assigning any priority. By means of a numerical study, we generate further insights into more specific conditions under which fixed priority policies can be considered as an alternative to FCFS. This paper was accepted by Baris Ata, stochastic models and simulation.

Equilibrium Queueing Strategies of Three Types of Customers in A Single Queue

Different types of customers have different revenue and waiting costs per unit time. Although in queuing economics, research on customer equilibrium strategies has achieved fruitful results, most of these are based on a single customer type. Research on multiple types of customers is rare. We consider a single queue with three types of customers. We analyse system stationary distribution and obtain the equilibrium balking strategy of each type customers. In addition, the social benefit is discussed under the reward-cost structure in the full observable.

Optimization strategy of price‐based demand response considering the bidirectional feedback effect

Time of use pricing strategy can not only reduce the load fluctuation but also improve the power system reliability. Generally, before carrying out a time of use pricing optimization, it needs to perform a period partition optimization for dividing peak-valley periods. In existing researches, however, the period partition optimization and the time of use pricing optimization are implemented independently. Although the output of period partition optimization is used as the input of time of use pricing optimization, the bidirectional feedback effect between period partition optimization and time of use pricing optimization is not considered, which will lead to the existing time of use pricing optimization may not be the globally optimal solution. Therefore, this paper investigates a new optimization method for time of use pricing optimization with the consideration of bidirectional feedback effect, establishes a comprehensive customer satisfaction degree model considering the customer load proportion coefficient, and defines an elastic cofactor to describe the electricity price response difference of multiple types of customers. The Roy Billinton test system is used to verify the correctness and effectiveness of the proposed method in this paper.

Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs

For queueing systems with multiple customer types differing in service time distributions and costs for waiting, it is known that giving priority to one type over others minimizes the long-run average waiting costs when waiting is penalized linearly in time. However, when waiting costs are nonlinear, which is typically a more reasonable depiction of reality, it is not clear whether policies that ignore the type information such as the first-come-first-serve policy (FCFS) should be replaced with type-based priority policies. To shed some light on to this problem, we study a single-server queueing system with two types of customers under static queueing policies that use information on customers’ types and order of arrival. Our main theorem ranks the type-based priority policies and FCFS according to their long-run average waiting costs under nonlinear cost functions. We then apply this result to polynomial cost functions and generate insights into when prioritization is advantageous. For example, we find that when customers are similar in terms of their service time distributions, then the parameter region where FCFS is more preferable over type-based priority policies under quadratic costs increases with traffic intensity. We also conduct a numerical study to compare the best static policy with a well-known dynamic policy that requires information on the current waiting times of customers. We find that the best static policy performs comparably with (sometimes even better than) this dynamic policy except when the traffic is heavy and it is not clear which type should receive priority.

Optimality of admission control in a repairable queue

We study a repairable M∕M∕1∕N queueing system with multiple types of customers. The difference between customers’ types is defined by the offered rewards. Once customers are admitted to the system, they have the same service rate. We show that under the average reward criterion, all optimal (deterministic) stationary policies have the trunk reservation form. We then prove the uniqueness of the bias optimal policy.

Design heuristic for parallel many server systems

We study a parallel queueing system with multiple types of servers and customers. A bipartite graph describes which pairs of customer-server types are compatible. We consider the service policy that always assigns servers to the first, longest waiting compatible customer, and that always assigns customers to the longest idle compatible server if on arrival multiple compatible servers are available. For a general renewal stream of arriving customers, general service time distributions that depend both on customer and on server types, and general customer patience distributions, the behavior of such systems is very complicated. Key quantities for their performance are the matching rates, the fraction of services for each pair of compatible customer-server. Calculation of these matching rates in general is intractable, it depends on the entire shape of service time distributions. We suggest through a heuristic argument that if the number of servers becomes large, the matching rates are well approximated by matching rates calculated from the tractable bipartite infinite matching model. We present simulation evidence to support this heuristic argument, and show how this can be used to design systems with desired performance requirements.

Technical Note—Capacitated Assortment Optimization Under the Multinomial Logit Model with Nested Consideration Sets

We study capacitated assortment problems when customers choose under the multinomial logit model with nested consideration sets. In this choice model, there are multiple customer types, and a customer of a particular type is interested in purchasing only a particular subset of products. We use the term consideration set to refer to the subset of products that a customer of a particular type is interested in purchasing. The consideration sets of customers of different types are nested in the sense that the consideration set of one customer type is included in the consideration set of another. The choice process for customers of different types is governed by the same multinomial logit model except for the fact that customers of different types have different consideration sets. Each product, if offered to customers, occupies a certain amount of space. The sale of each product generates a certain amount of revenue. Given that customers choose from among the offered products according to the multinomial logit model with nested consideration sets, the goal of the assortment problem is to find a set of products to offer to maximize the expected revenue obtained from a customer, while making sure that the total space consumption of the offered products does not exceed a certain limit. We show that this assortment problem is NP-hard, even when there is no limit on the total space consumption of the offered products. Motivated by this complexity result, we give a fully polynomial time approximation scheme for the problem. The online appendix is available at https://doi.org/10.1287/opre.2017.1672 .

Large-scale heterogeneous service systems with general packing constraints

Abstract A service system with multiple types of customers, arriving according to Poisson processes, is considered. The system is heterogeneous in that the servers can also be of multiple types. Each customer has an independent, exponentially distributed service time, with the mean determined by its type. Multiple customers (possibly of different types) can be placed for service into one server, subject to `packing' constraints, which depend on the server type. Service times of different customers are independent, even if served simultaneously by the same server. The large-scale asymptotic regime is considered such that the customer arrival rates grow to ∞. We consider two variants of the model. For the infinite-server model, we prove asymptotic optimality of the greedy random (GRAND) algorithm in the sense of minimizing the weighted (by type) number of occupied servers in steady state. (This version of GRAND generalizes that introduced by Stolyar and Zhong (2015) for homogeneous systems, with all servers of the same type.) We then introduce a natural extension of the GRAND algorithm for finite-server systems with blocking. Assuming subcritical system load, we prove existence, uniqueness, and local stability of the large-scale system equilibrium point such that no blocking occurs. This result strongly suggests a conjecture that the steady-state blocking probability under the algorithm vanishes in the large-scale limit.

Large-Scale Bundle Size Pricing: A Theoretical Analysis

Bundle size pricing (BSP) is a multi-dimensional selling mechanism where the firm prices the size of the bundle rather than the different possible combinations of bundles. In BSP, the firm offers the customer a menu of different sizes and prices. The customer then chooses the size that maximizes his surplus and customizes his bundle given his chosen size. While BSP is commonly used across several industries, little is known about the optimal BSP policy in terms of sizes and prices along with the theoretical properties of its profit. In this paper, we provide a simple and tractable theoretical framework to analyze the large-scale BSP problem where a multi-product firm is selling a large number of products. The BSP problem is in general hard as it involves optimizing over order statistics, however we show that for large numbers of products, the BSP problem transforms from a hard multi-dimensional problem to a simple multi-unit pricing problem with concave and increasing utilities. Our framework allows us to identify the main source of inefficiency of BSP that is the heterogeneity of marginal costs across products. For this reason, we propose two new BSP policies called clustered BSP'' and assorted BSP'' that significantly reduce the inefficiency of regular BSP. We then utilize our framework to study richer models of BSP such as when customers have budgets and when there exists multiple customer types.