Integrated pricing and capacity decision for a telecommunication service provider

This paper studies a price and capacity decision for a telecommunications service provider that differentiates its products based on price and quality of service to maximize revenue. We assume the market is segmented into two customer classes. Time sensitive customers are willing to pay a price premium for a shorter service time, while price sensitive customers are willing to accept a longer service time in return for a lower price. The service provider offers products and services that differ only in their guaranteed service times and prices. We first develop a mathematical model to determine the optimal product price and optimal capacity necessary for maximizing total profit. We then consider a case where a service provider can marginally increase or decrease the capacity, and compute the optimal price and optimal capacity.     

The concert queueing game: to wait or to be late

We introduce the concert (or cafeteria) queueing problem: A finite but large number of customers arrive into a queueing system that starts service at a specified opening time. Each customer is free to choose her arrival time (before or after opening time), and is interested in early service completion with minimal wait. These goals are captured by a cost function which is additive and linear in the waiting time and service completion time, with coefficients that may be class dependent. We consider a fluid model of this system, which is motivated as the fluid-scale limit of the stochastic system. In the fluid setting, we explicitly identify the unique Nash-equilibrium arrival profile for each class of customers. Our structural results imply that, in equilibrium, the arrival rate is increasing up until the closing time where all customers are served. Furthermore, the waiting queue is maximal at the opening time, and monotonically decreases thereafter. In the simple single class setting, we show that the price of anarchy (PoA, the efficiency loss relative to the socially optimal solution) is exactly two, while in the multi-class setting we develop tight upper and lower bounds on the PoA. In addition, we consider several mechanisms that may be used to reduce the PoA. The proposed model may explain queueing phenomena in diverse settings that involve a pre-assigned opening time.     

Cloud Computing System Management Under Flat Rate Pricing

Success of cloud computing service depends on an acceptable pricing mechanism both by users and the service provider. Piece rate pricing by counting work load should be favorable for the service provider due to the QoS control and finite resource, such as computing and, communication powers. Though the pricing mechanism based on counting work load is reasonable and fair, the experiences learned from ADSL, 3G and Wi-Fi show a different story. The flat rate pricing mechanism is the winner all the way. This study proposes a flat rate pricing mechanism with congestion control, called FRPCC. In the cloud computing system, allocation of resources can be formulated as an optimization problem seeking to maximize the sum of the utility function of each user under the constraints of fairness. The piece rate pricing mechanism is easy to achieve the social welfare but is not easy to be acceptable for customers. Consequently, we propose a congestion control scheme to reach the same goal with a flat rate pricing mechanism. The proposed FRPCC approach can achieve social welfare in the cloud computing environment. Performance evaluations show efficacy of, FRPCC approach in providing social welfare under fairness and preventing congestion.     

The Effects of the Service Environment on Perceived Waiting Time and Emotions

Because customers’ experience of waiting for service may negatively affect their behavioral approach toward the service organization, improving the service environment may also improve their waiting experience. This study examined the different effects of environmental elements on the perceived waiting time route and the emotional route. We surveyed 326 customers of a leading fast‐food chain restaurant in Taiwan during rush hour. We found that the emotional route is a stronger predictor of customer approach behavior than the perceived waiting time route. Moreover, the explained wait and perceived crowding directly affect both the perceived waiting time route and the emotional route. The effect of the design factor on the customer behavior approach is significant in the emotional route, but it is not significant in the perceived waiting route. In addition, perceived crowding has the strongest effect on the perceived waiting time route, and the explained wait has the strongest effect on the emotional route.     

Two pricing mechanisms for a service provider when customers’ delay costs are value-related

In this paper, we study two pricing mechanisms for a provider that serves delay-sensitive customers, one is the uniform pricing and the other is the priority auction. The expected delay cost of a customer is assumed to depend on his value for the service (i.e. the unit delay cost is a strictly increasing function of his value) and the expected sojourn time caused by the number of customers in the system (and his payment-based position in the queue if auction is adopted). Hence, each customer reacts to the service provider’s pricing mechanism by deciding whether or not to enter the service system and how much he pays. This resulting problem is a Stackelberg game. When auction is adopted, by using of adverse selection, we derive a feasible scheme in which customers with higher value would like to pay more. We further compare the performance of these two pricing mechanisms. Our numerical examples show that auction performs better not only in terms of revenue making but also in terms of social welfare improvement. Interestingly, auction can also render more customer surplus in most instances, which differs from the common techniques in revenue management field.     

Performance prediction of loss and delay Markovian queueing model with nopassing and removable additional servers

In this investigation, the loss and delay Markovian queueing system with nopassing is proposed. The customers may balk or renege with certain probability, on finding all servers busy on their arrival. To cope up with the balking and reneging behaviour of the customers, there is provision of removable additional servers apart from permanent servers so as to provide the better grade of service at optimal cost operating conditions. The customers are classified into two classes depending upon whether they can wait or lost when all servers are busy. The customers can also be categorized into two classes from service point of view. Type A customers have zero service time whereas type B customers have exponential service time. The explicit expressions for the average number of customers in the system, the expected waiting time for both types of customers, etc., are derived by using steady-state queue size distribution. Some earlier results are deduced by setting appropriate system parameters. The system behaviour is examined with the help of numerical illustrations by varying different parameters.Scope and purposeThe performance prediction of various systems in communication switching network, remote border security check post, jobs processing in computers, etc., are influenced by the customers behaviour, in particular, when nopassing constraints are prevalent. The incorporation of loss and delay phenomena is likely to bring about understanding whether the customers would like to wait in the queue or would be lost in case when all servers are busy. The provision of additional removable servers will be helpful in upgrading the service and to reduce the discouragement behaviour of the customers in such congestion situations.     

Optimal control of service for facilities holding inventory

This paper addresses the problem of optimally controlling service rates for an inventory system of service facilities. We consider a finite capacity system with Poisson arrivals and exponentially distributed leadtimes and service times. For given values of maximum inventory and reorder levels, we determine the service rates to be employed at each instant of time so that the long-run expected cost rate is minimized. The problem is modelled as a semi-Markov decision problem. We establish the existence of a stationary optimal policy and we solve it by employing linear programming. Several instances of a numerical example, which provide insight into the behaviour of the system, are presented.Scope and purposeIn this article we discuss the problem of inventory control of service parts at a service facility where there is only a limited waiting space for customers. If a customer enters the service facility and sees all the waiting spaces occupied he/she will leave the facility, which results in both intangible losses (loss of goodwill) and tangible losses (loss in profit). Hence, the service provider aims at obtaining an optimal rate at which service is to be provided by balancing costs due to waiting time and limited waiting spaces against costs due to ordering and overheads due to storing items. We develop an algorithm that controls the service rate as a function of the number of customers waiting for service.     

A new procedure to estimate waiting time in GI/G/2 system by server observation

Most GI/G/2 queueing formulae need the variance of inter-arrival time, which is in many cases more difficult to estimate than the other values used in the formulae such as the mean of inter-arrival time, mean of service time and variance of service time. This paper presents a new GI/G/2 queueing formula which uses a slightly different set of data easier to obtain than the variance of inter-arrival time. The key variables are the numbers of system busy periods and system idle periods. Also, it is shown, by simulation, that the waiting time estimation error from the new formula is far less than other popular queueing formulae which use the first two moments of service time and inter-arrival time over a wide range of coefficient of variation.Scope and purposeWaiting is very common in our daily life, and the estimation is sometimes very important for the design of service and manufacturing systems. If the number of barbers at a barber's shop is too small, customers frequently wait for the service too long. If the number of machines in a manufacturing shop is too small, the production lead time from order entry to product delivery can be very long.The waiting time is closely related not only to the average service requirement but also to the variability of it. If customers require service at the same time, the average waiting time of the customers will be longer than the average waiting time with even requests. Traditionally, the variance of inter-arrival time has been used to represent the variability; however, estimation of the variance needs observation of customer arrivals, which often needs much effort. This paper presents another procedure to estimate the waiting time. This procedure does not need the observation of customers. The estimation of waiting time for bank teller machines can be a good application example of this new procedure because the machines do not have the arrival data of the customers. The procedure presented here is for a two parallel server case.     

Benefits of providing amenities to impatient waiting customers

This paper proposes an OR modelling approach to study the effect of managing queue reneging by providing amenities to improve customers’ queueing experience. We evaluate quantitatively the changes in the servers’ utilization and customers’ satisfaction when the size and quality of the amenities are varied. We find that when the size of the amenities is increased to cover more and more customers, the incremental return in benefits will eventually diminish. So is the case when the quality of the amenities is improved to higher and higher standards for systems with sufficiently heavy workload. However, for systems with light workload, the models show that improving the quality of the amenities has an increasing incremental return in benefits.Scope and purposeReneging, the phenomenon of customers leaving a service system before finishing service, represents loss in revenues and goodwill to the service provider. Very often companies provide amenities to alleviate waiting customers’ discomfort so that they would be willing to wait for longer period of time. However, there is the trade-off between investing in amenities and generating more revenue from customers. Our work investigates the optimal balance for this trade-off and the most effective approach for setting up amenities.     

需求依赖库存且短缺量部分拖后的促销商品库存模型

促销商品是商场吸引顾客前往购买消费的一种重要手段,它可以有效带动其他商品的销售从而提高商场销售收入。考虑促销商品在缺货期间价格和时间对顾客等待行为的影响,构造了一个与销售价和等待时间相关的短缺量拖后率,建立了多次订货下两阶段存货影响需求和顾客等待的促销商品库存模型,并利用仿真方法分析价格和时间敏感因子、存货影响需求临界点、销售价格对销售商订货策略和系统总利润的影响。结果表明：价格和时间敏感因子对各周期服务水平影响显著,存货影响需求临界点对订货次数影响较大;当销售价在一定范围时,销售商只需调整各周期服务水平,而当销售价过高或过低时,销售商则需同时调整各周期服务水平和订货次数     

A tandem queue with general bulk service and servers' “vacation”

This paper analyses two queueing models consisting of two units I and II connected in series, separated by a finite buffer of size N. In both models, unit I has only one exponential server capable of serving customers one at a time and unit II consist of c parallel exponential servers, each of them serving customers in groups according to general bulk service rules. When the queue length in front of unit II is less than the minimum of batch size, the free servers take a vacation. On return from vacation, if the queue length is less than the minimum, they leave for another vacation in the first model, whereas in the second model they wait in the system until they get the minimum number of customers and then start servicing. The steady-state probability vector of the number of customers waiting and receiving service in unit I and waiting in the buffer is obtained for both the models, using the modified matrix geometric method. Numerical results are also presented.     

政府补贴和增值税退税政策的闭环供应链决策

基于政府补贴和增值税退税政策,通过Stackelberg博弈方法,建立由制造商、回收商和消费者组成的4种闭环供应链决策模型,得出相应的最优价格、补贴和退税政策.进一步,比较并分析4种不同模型下的回收价格、回收量、企业利润以及社会福利,得出政府和企业的最优决策选择.研究发现:1)4种情形下的社会福利均随着消费者环保意识的增加而递增.对政策制定者而言,若消费者环保意识较低,则政府补贴政策最优;若消费者环保意识较高,则政府补贴和增值税退税并存政策最优.2)在绿色消费者市场上,制造商选择高低两种不同定价策略受绿色细分市场规模和政府政策力度大小两方面因素的影响.     

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

A finite source multi-server inventory system with service facility

In this article, we study a continuous review retrial inventory system with a finite source of customers and identical multiple servers in parallel. The customers arrive according a quasi-random process. The customers demand unit item and the demanded items are delivered after performing some service the duration of which is distributed as exponential. The ordering policy is according to (s, S) policy. The lead times for the orders are assumed to have independent and identical exponential distributions. The arriving customer who finds all servers are busy or all items are in service, joins an orbit. These orbiting customer competes for service by sending out signals at random times until she finds a free server and at least one item is not in the service. The inter-retrial times are exponentially distributed with parameter depending on the number of customers in the orbit. The joint probability distribution of the number of customer in the orbit, the number of busy servers and the inventory level is obtained in the steady state case. The Laplace–Stieltjes transform of the waiting time distribution and the moments of the waiting time distribution are calculated. Various measures of stationary system performance are computed and the total expected cost per unit time is calculated. The results are illustrated numerically.     

面向在线客服系统的调度算法研究

Different from traditional customer service systems, online customer service systems offer business services for multiple customers simultaneously, which makes the adaptation and scheduling between service providers and customers a big challenge. Based on the characteristics of online customer service, this paper proposes a scheduling model for online customer service systems. The scheduling model is composed of three constituents: a multi-priority customer queue, the states of the scheduling system and the transition relations between them, and the correspondence between scheduling strategies and states of the system. Its scheduling algorithm is designed. Experiments verify the rationality of the scheduling model and the effectiveness of the scheduling algorithm. In comparison to the operating customer service system, the algorithm can not only considerably reduce the average waiting time of customers, but also achieve load balancing among service providers, when guaranteeing high quality of services.     

Modeling,analysis, and evaluation of a carbon tax policy based on the emission factor

This paper studies a tax policy based on the emission factor, which is used as an intensity measure. Specifically, the paper models a situation where policy makers set a limit on the production emission factor of a regulated industry and require firms to pay tax if they exceed that target. The efficiency of the policy is evaluated against other existing environmental policies using a social welfare mathematical programming model. A case study is built within the context of the cement industry and is used to carry out the analysis. The results show that the intensity-based carbon tax achieves the highest consumers’ surplus and production quantities and the lowest prices. The policy is found to be effective in reducing CO₂ emissions with little impact on social welfare.     

Regulating an M/G/1 queue when customers know their demand

Customers do not necessarily join a queue at a socially optimal rate. Hence, queueing systems may call for regulation. For customers in an M/G/1 unobservable (not necessarily FCFS) queue and homogeneous with respect to waiting costs and service rewards, we show how queueing systems can be regulated by imposing an entry fee, a holding fee (based on time in the system), or a service fee (based on the required service time) when customers know their service requirements. We start with a unified approach and state the socially optimal fees. We show that customers are always worse off under a flat entry fee in comparison with holding and service fees. As for holding vs. service fees, the answer depends on the queueing regime and/or the service length itself. For example, under FCFS, service fees are preferred by all. Details are given on some common service regimes. We also review the case where customers know only the common distribution of service times, but not their actual requirements.     

基于用户行为的分时电价时段划分和价格制定

以往分时电价的时段划分仅考虑负荷曲线的数值变化,忽视了时段划分对分时电价的制定和对用户行为的影响,使得分时电价优化受限,需求侧响应不能达到最优的效果。为此提出了基于用户行为的分时电价时段划分和价格制定模型,首先通过模糊聚类法初步制定峰段、平段、谷段,然后将峰谷时段的起始时间和终止时间设为待优化的变量,并根据消费者心理学建立用户电价电量响应行为模型,最后以用户满意度和电网收益最大化为目标,同时对分时电价和时段划分进行优化。仿真结果显示,与直接根据FCM模糊聚类分析方法划分时段相比,该模型更能针对负荷特性激励用户响应分时电价,促使用户响应曲线更加平滑,进一步降低调峰成本,验证了该模型通过优化时段划分方法提高社会福利的有效性。     

弹性效用价格竞争博弈的纯策略寡占均衡

讨论了具有弹性效用的并行路径网络的多个服务提供商之间的价格竞争博弈问题。如果每个拥有链路的服务提供商的目的是设定使自己利润最大化的价格,而用户依据Wardrop原理选择自己的传输流量和传输路径。当每个用户的效用函数为凹函数且其一阶导数也是凹函数,网络链路的延迟函数为线性函数时,则证明了这种多个服务提供商之间的价格竞争博弈存在纯策略寡占均衡。     

Pay‐as‐you‐throw versus recycling fund system in closed‐loop supply chains with alliance recycling

This paper develops closed‐loop supply chain models with alliance recycling under two financing systems for recycling used products, that is, pay‐as‐you‐throw (PAYT) and recycling fund (RF). The primary goal behind analytic formulation is to investigate the differences between the two financing systems and determine which one performs better, and to examine the impact of target recycling rate and competition between recycling alliances (RAs) on channel decisions. We find that the PAYT system is always more beneficial to customers and the retailer, while the RF system increases the social welfare. If there is no competition between RAs, which system performs better for the RA depends on the baseline of subsidy fee, while which system performs better for manufacturers depends on their shares. However, if there is competition between RAs, the RF system is favored by the disadvantaged RA. Moreover, the restriction on target recycling rate has an effect on channel decisions.