劉 健，張 帥，趙洪款，李兆斌

服務(wù)機(jī)制設(shè)計(jì)與顧客分類服務(wù)定價(jià)研究

劉 健1，張 帥1，趙洪款1，李兆斌2

（1.南京理工大學(xué)經(jīng)濟(jì)管理學(xué)院，江蘇 南京 210094；2.南京航空航天大學(xué)經(jīng)濟(jì)管理學(xué)院，江蘇 南京 211106）

服務(wù)系統(tǒng)；排隊(duì)論；顧客分類；定價(jià)策略；目標(biāo)優(yōu)化

0 引言

2015年，服務(wù)業(yè)實(shí)現(xiàn)的稅收占全部稅收的比重達(dá)54.8%，是我國(guó)稅收主要?jiǎng)?chuàng)造者。服務(wù)業(yè)占比重持續(xù)上升，表明我國(guó)經(jīng)濟(jì)結(jié)構(gòu)正在發(fā)生重大變化，轉(zhuǎn)型升級(jí)已到了關(guān)鍵階段，中國(guó)經(jīng)濟(jì)由工業(yè)主導(dǎo)向服務(wù)業(yè)主導(dǎo)加快轉(zhuǎn)變，中國(guó)“服務(wù)化”進(jìn)程已不可逆轉(zhuǎn)，服務(wù)業(yè)已成為新常態(tài)下中國(guó)經(jīng)濟(jì)增長(zhǎng)的新動(dòng)力①2015年服務(wù)業(yè)引領(lǐng)國(guó)民經(jīng)濟(jì)穩(wěn)步發(fā)展，中央政府門戶網(wǎng)站，來(lái)源：統(tǒng)計(jì)局. http://www.gov.cn/xinwen/2016-03/10/content_5051710.htm。

排隊(duì)是服務(wù)提供中一個(gè)非常重要的問(wèn)題，其源于短時(shí)間內(nèi)供給與需求的不匹配。由于顧客的異質(zhì)性（即：顧客等待時(shí)間成本不同），為了提高排隊(duì)的效率和顧客滿意度，需要識(shí)別出顧客的異質(zhì)性并在實(shí)施服務(wù)機(jī)制（策略）時(shí)根據(jù)其異質(zhì)性進(jìn)行有效的區(qū)分。服務(wù)提供商通過(guò)相應(yīng)的排隊(duì)機(jī)制來(lái)獲取更多利潤(rùn)，這種針對(duì)顧客異質(zhì)性的區(qū)分通常利用在服務(wù)系統(tǒng)中設(shè)置優(yōu)先權(quán)（貴賓席）來(lái)實(shí)現(xiàn)。在服務(wù)系統(tǒng)中引入優(yōu)先權(quán)選項(xiàng)設(shè)置之前，需要評(píng)估其預(yù)期效果，因此需要考慮以下問(wèn)題：①優(yōu)先權(quán)的設(shè)置在當(dāng)前服務(wù)系統(tǒng)是否具有吸引力？②設(shè)置優(yōu)先權(quán)是否能夠增加企業(yè)收益？③應(yīng)該對(duì)優(yōu)先權(quán)加收多少服務(wù)費(fèi)？④是否應(yīng)該限制加入優(yōu)先權(quán)的顧客數(shù)量或比例？

顧客等待時(shí)間成本是回答本文研究問(wèn)題的關(guān)鍵，為了達(dá)到所述的研究目標(biāo)，需要用一種合適的方法找到不同顧客等待時(shí)間成本之間的互異性，但總體而言，顧客時(shí)間成本的分析是非常復(fù)雜的，到目前為止幾乎沒(méi)有可能找到一個(gè)完美建模方分布和指數(shù)分布的等待時(shí)間成本函數(shù)。文獻(xiàn)[4-5]通過(guò)將顧客的等待時(shí)間成本分割為不同的幾種類型（同種類型顧客之間等待成本相同），針對(duì)上述問(wèn)題進(jìn)行相應(yīng)研究，但作者并沒(méi)有考慮相應(yīng)的等待成本分布。

本文在研究過(guò)程中針對(duì)兩種不同情形的服務(wù)系統(tǒng)進(jìn)行分析：①壟斷型服務(wù)系統(tǒng)（顧客不可選擇退出或不能離開服務(wù)系統(tǒng)、產(chǎn)品替代性較弱、市場(chǎng)競(jìng)爭(zhēng)不激烈或無(wú)競(jìng)爭(zhēng)，顧客獲得服務(wù)價(jià)值無(wú)窮大等）（如：簽證受理服務(wù)等）；②非壟斷型服務(wù)系統(tǒng)（顧客根據(jù)通過(guò)服務(wù)獲得效用的大小來(lái)選擇離開服務(wù)系統(tǒng)或留在服務(wù)系統(tǒng)、產(chǎn)品替代性較強(qiáng)、市場(chǎng)競(jìng)爭(zhēng)激勵(lì)或顧客獲得的服務(wù)價(jià)值在一定范圍之內(nèi)等）（如：酒吧、餐廳或者游樂(lè)園等）。

本文創(chuàng)新之處：基于顧客時(shí)間成本均勻分布和收入函數(shù)分布，利用顧客效用函數(shù)，針對(duì)壟斷型服務(wù)系統(tǒng)與非壟斷型服務(wù)系統(tǒng)分析構(gòu)造相應(yīng)的服務(wù)定價(jià)函數(shù)、企業(yè)收益函數(shù)與服務(wù)系統(tǒng)總體顧客效用函數(shù)，從企業(yè)收益最大化視角，研究表明應(yīng)對(duì)顧客進(jìn)行分類服務(wù)來(lái)獲得更大收益，并解決了對(duì)顧客進(jìn)行服務(wù)分類的最優(yōu)服務(wù)費(fèi)用定價(jià)問(wèn)題及相應(yīng)顧客比例，在此基礎(chǔ)上從服務(wù)系統(tǒng)總體顧客效用最大化視角出發(fā)，針對(duì)兩種類型的服務(wù)系統(tǒng)研究表明應(yīng)取消顧客分類服務(wù)。

本文主要框架：第二部分首先構(gòu)建不同類型顧客的效用模型，然后對(duì)顧客效用模型選擇進(jìn)行分析，第三部分對(duì)企業(yè)收益進(jìn)行優(yōu)化分析，接下來(lái)在第四部分對(duì)顧客效用進(jìn)行優(yōu)化分析，第五部分對(duì)顧客等待時(shí)間成本為收入函數(shù)分布的情形進(jìn)行數(shù)值模擬?；谏鲜鰞蓚€(gè)優(yōu)化視角分別針對(duì)兩種服務(wù)系統(tǒng)的最優(yōu)定價(jià)策略進(jìn)行分析，并給出相應(yīng)結(jié)論和管理啟示。最后對(duì)本文的主要工作進(jìn)行歸納總結(jié)，并指出未來(lái)的研究方向。

1 模型構(gòu)建

1.1 效用模型

1.2 壟斷型服務(wù)系統(tǒng)顧客效用選擇

因此，顧客等待時(shí)間成本與顧客分類之間的關(guān)系如式(3)所示：

1.3 非壟斷型服務(wù)系統(tǒng)顧客效用選擇

根據(jù)上面3個(gè)不同的約束關(guān)系，進(jìn)行分析可知：

綜上所述，可知針對(duì)顧客能夠離開服務(wù)系統(tǒng)時(shí)存在下面兩種不同的情況。

針對(duì)非壟斷型服務(wù)系統(tǒng)，等待時(shí)間成本最高的顧客不論在哪種情況下都會(huì)選擇離開服務(wù)系統(tǒng)。針對(duì)非壟斷型系統(tǒng)存在的上述兩種情況，接下來(lái)將會(huì)分別對(duì)其進(jìn)行優(yōu)化分析，然后綜合比較，給出相應(yīng)的服務(wù)定價(jià)策略與最優(yōu)收益。

2 企業(yè)收益優(yōu)化分析

2.1 壟斷型服務(wù)系統(tǒng)

2.1.1企業(yè)收益函數(shù)

2.1.2 企業(yè)最優(yōu)收益求解

現(xiàn)實(shí)生活中，顧客進(jìn)入服務(wù)系統(tǒng)后，根據(jù)獲得服務(wù)價(jià)值，多數(shù)情形是可以自由選擇離開服務(wù)系統(tǒng)，這時(shí)企業(yè)如何設(shè)置最優(yōu)的優(yōu)先權(quán)服務(wù)費(fèi)用，是否應(yīng)該對(duì)顧客進(jìn)行分類服務(wù)，我們將在下一節(jié)對(duì)該情形進(jìn)行詳細(xì)闡述。

2.2 非壟斷型服務(wù)系統(tǒng)

2.2.1 服務(wù)系統(tǒng)存在兩種隊(duì)列企業(yè)收益函數(shù)

根據(jù)顧客類型與時(shí)間成本的關(guān)系式(4)可得：

2.2.2 企業(yè)最優(yōu)收益分析

根據(jù)上面的分析及表達(dá)式，針對(duì)非壟斷型服務(wù)系統(tǒng)中有兩種隊(duì)列（顧客）存在時(shí)，可得服務(wù)提供商的最大收益值和對(duì)顧客進(jìn)行分類服務(wù)的優(yōu)先權(quán)定價(jià)及不同類型顧客相應(yīng)的比例。

2.2.3 服務(wù)系統(tǒng)存在一種隊(duì)列企業(yè)收益函數(shù)

顯然，當(dāng)顧客比例為固定數(shù)值時(shí)，企業(yè)的最大收益也為固定值，如式(12)所示：

2.2.4 兩種情況分析

服務(wù)供應(yīng)商采取兩種隊(duì)列（兩種顧客）還是一種隊(duì)列（僅有普通顧客），關(guān)鍵取決于哪種情形獲得的收益更大。根據(jù)公式(10)與(12)中的企業(yè)最大收益值，可得下面的不等關(guān)系式：

管理啟示2：針對(duì)非壟斷型服務(wù)系統(tǒng)，服務(wù)供應(yīng)商應(yīng)仍然應(yīng)對(duì)顧客進(jìn)行分類服務(wù)（兩種隊(duì)列）來(lái)獲得更大收益。

3 顧客效用優(yōu)化分析

3.1 壟斷型服務(wù)系統(tǒng)

3.2 非壟斷型服務(wù)系統(tǒng)

在定義域邊界點(diǎn)處，顧客最大效用值滿足如下等式關(guān)系

服務(wù)提供商取消顧客分類僅保留普通隊(duì)列與服務(wù)提供商采取顧客分類但取消分類費(fèi)用此時(shí)所有顧客都進(jìn)入優(yōu)先權(quán)隊(duì)列，這兩種情形下系統(tǒng)中顧客的效用是相同的。

管理啟示3：從顧客效應(yīng)最大化出發(fā)，在兩種服務(wù)系統(tǒng)（壟斷型服務(wù)系統(tǒng)或非壟斷型服務(wù)系統(tǒng)）下，服務(wù)提供商都應(yīng)取消顧客分類服務(wù)，僅保留普通顧客或者采取分類服務(wù)但不收取分類費(fèi)用，此時(shí)所有顧客都進(jìn)入優(yōu)先權(quán)隊(duì)列，與此同時(shí)，在這兩種情形下，企業(yè)最大收益都是完全相同的。

4 基于等待時(shí)間成本為收入分布函數(shù)的服務(wù)機(jī)制分析

針對(duì)優(yōu)先權(quán)顧客的最優(yōu)比例，企業(yè)最大收益值和獲取優(yōu)先權(quán)服務(wù)的最優(yōu)定價(jià)值，如表1所示。

表1 非壟斷型顧客數(shù)值模擬最優(yōu)結(jié)果數(shù)據(jù)表

總之，從顧客效用最大化視角，我們得到與第4部分一致結(jié)論：服務(wù)提供商應(yīng)取消顧客分類服務(wù)或采取分類服務(wù)但不收取分類服務(wù)費(fèi)用。

5 結(jié)論

本文基于顧客等待時(shí)間成本均勻分布和收入分布，對(duì)壟斷型服務(wù)系統(tǒng)與非壟斷型服務(wù)系統(tǒng)的機(jī)制設(shè)計(jì)與顧客分類服務(wù)定價(jià)問(wèn)題，從企業(yè)收益和顧客效用兩個(gè)視角出發(fā)進(jìn)行優(yōu)化分析，并提出相應(yīng)的管理啟示。

本文主要做了四個(gè)方面的工作：①針對(duì)壟斷型服務(wù)系統(tǒng)與非壟斷服務(wù)系統(tǒng)分別構(gòu)造了的服務(wù)定價(jià)函數(shù)與企業(yè)收益函數(shù)。②針對(duì)壟斷型服務(wù)系統(tǒng)和非壟斷型服務(wù)系統(tǒng)，解決了企業(yè)收益最大時(shí)，對(duì)顧客進(jìn)行分類服務(wù)（獲取優(yōu)先權(quán)服務(wù)）的最優(yōu)定價(jià)值及相應(yīng)的優(yōu)先權(quán)顧客與普通顧客比例。③從顧客效用最大化視角，針對(duì)上述兩種服務(wù)系統(tǒng)，研究表明系統(tǒng)中僅保留一種隊(duì)列（取消顧客分類服務(wù)僅保留普通顧客或取消顧客分類服務(wù)費(fèi)用讓所有顧客都進(jìn)入優(yōu)先權(quán)）時(shí)顧客效用最大。④當(dāng)顧客等待時(shí)間成本為收入分布時(shí)，服務(wù)提供商仍然采取完全相同的策略。

根據(jù)本文研究，從企業(yè)收益（盈利性企業(yè)）角度出發(fā)應(yīng)對(duì)顧客進(jìn)行分類服務(wù)，從服務(wù)系統(tǒng)顧客總體效用（非盈利企業(yè)）最大出發(fā)應(yīng)取消顧客分類服務(wù)僅保留一種隊(duì)列。本文的主要工作可歸納為表2中內(nèi)容。

表2 兩種類型服務(wù)系統(tǒng)在兩個(gè)不同視角下的最佳服務(wù)策略及分類服務(wù)定價(jià)值

本文研究過(guò)程中沒(méi)有考慮排隊(duì)過(guò)程中顧客的心理行為對(duì)顧客效用的影響，同時(shí)如何借助大數(shù)據(jù)技術(shù)準(zhǔn)確刻畫顧5BA2的時(shí)間成本分布函數(shù)，是我們未來(lái)需要深入研究的內(nèi)容。

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Service mechanism design and service pricing for customers segmentation

LIU Jian1, ZHANG Shuai1, ZHAO Hongkuan1, LI Zhaobin2

(1. School of Economics and Management, Nanjing University of Science and Technology, Nanjing 210094, China; 2. School of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China)

Matching capacity with demand is a central theme in service operations management. Waiting occurs when capacity-demand mismatch happens, either due to insufficient long-term capacity or short-term fluctuations in-service load. Queuing is a significant issue in the service operation. There is a limited server capacity, and customers are heterogeneous in their waiting queue. The service provider usually segments customers into different classes and provides prioritized services based on this classification. Customers segmentation (classification service of customers) will reduce some customers’ waiting times and further improve satisfaction to extract the maximum revenue. How to design a scientific queuing mechanism for heterogeneous time-sensitive customers to extract the maximum revenue and customers’ utility for the service provider?

In this paper, we exact analysis of a non-preemptive M/M/1 queue problem based on the customers’ waiting cost (the time value of customers) follow a uniform distribution. We study both a monopoly service system (customers cannot leave the system) and a non-monopoly service system (customers are allowed free to leave the system and choose not to join any of the queues), respectively. From the perspective of revenue maximization and utility maximization, we study, analyze and explore when it’s optimal for the service provider to charge for priority service, and when it’s optimal for the service provider to provide only one type of service and not prioritize.

In the first part, by comparing the total utility of customers joining different queues, we will build the corresponding relationships between waiting costs and queues for customers. On this basis, the function of the priority fee for customer segmentation is constructed. Then, we will also obtain the function of the firm’s revenue and optimize it to get the optimal results. The results indicate that the service provider should take customers segmentation by charging a priority service fee and keeping two queues in both service systems to gain maximum revenue.

Then, we will get the optimal priority service fee for customers segmentation, the optimal proportion of priority customers and regular customers, and the optimal maximum revenue. Later, we build the corresponding function of the customers’ utility in two kinds of service system. Next, from the perspective of customer utility maximization, our study shows that in the above two kinds of service systems (monopoly service system and non-monopoly service system), the service provider should cancel the classification service of customers. Also, this study suggests that the company keep regular customers only in the queue or cancel the priority fee for customers classification and make all customers join the priority queue to obtain the maximum utility of customers.

Finally, we extend our research and study the customer's waiting costs follows a Burr distribution according to numerical simulation. We will get similar conclusions and insights in the above two kinds of service systems from the revenue and utility perspectives. The optimal priority pricing fee may be different under two waiting costs distribution, but it is completely consistent with the conclusion that the service provider should adopt customers segmentation (two queues) or not (one queue).

In summary, our results indicate that the service provider should approach this service design question differently depending on the different perspectives. Some original and interesting propositions are drawn based on our research, which will give important, scientific, and useful management insights into the corresponding service provider on service mechanism and pricing.

Service system; Queuing theory; Customer segmentation; Pricing strategy; Objective optimization

2016-12-31

2017-11-16

Supported by the National Natural Science Foundation of China (71671092, 71301075), the Natural Science Foundation of Jiangsu Province (BK20130770), theInternational Postdoctoral Exchange Fellowship Program (21040072) and the Jiangsu Postdoctoral Research Funding Program (1501040A)

F224

A

1004-6062(2020)01-0086-008

10.13587/j.cnki.jieem.2020.01.010

2016-12-31

2017-11-16

國(guó)家自然科學(xué)基金資助項(xiàng)目（71671092、71301075）；江蘇省自然科學(xué)基金資助項(xiàng)目（BK20130770）；中國(guó)博士后國(guó)際交流計(jì)劃派出項(xiàng)目（21040072）；江蘇省博士后科研資助計(jì)劃項(xiàng)目（1501040A）

劉?。?982—），男，山東淄博人；南京理工大學(xué)管理科學(xué)與工程系副教授，博士（后）；主要從事排隊(duì)論研究。

中文編輯：杜 ??；英文編輯：Charlie C. Chen