兩個服務層級等候系統中，訂價問題之研究

Pricing for a Queueing Service System with Two Classes of Services

陳建宏(Cheng-Hung Chen)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2002年)

https://doi.org/10.6840/cycu200200277

摘要

摘要

服務系統假使沒有付費機制將使得顧客大量湧進服務系統中，造成服務系統塞暴現象產生。因此有效控制流量的最佳方法，即為制定最適訂價，使得顧客在接受服務的同時亦能獲得較好的服務品質。區別訂價(price discrimination)理論對於區分顧客群而言是重要的工具，系統管理者會因需求不同來設定不同價格供消費者做選擇，進而達到系統與顧客雙贏的局面。
本研究主要目的是探討在區別訂價策略下，顧客進入服務系統選擇服務層級完全依據顧客自行評量（perceived service value）各個服務等級所得之服務價值與服務成本的差最大來做決定。我們考慮的等候服務系統為兩個M/M/1的等候系統，系統內有兩個服務層級(較高服務層級和一般服務層級)，顧客到達率依據普瓦松(Poisson)分配，服務層級之服務速率依據指數(Exponential)分配。我們利用平衡方程式先求出平衡解 再尋求最佳解 。 為平衡狀態下較高服務層級顧客的邊際服務價值， 為平衡狀態下一般服務層級顧客的邊際服務價值。
我們求取等候服務系統最佳值的方法有二，1. 固定 值，改變 值以求得服務系統最佳收益2. 固定 值，改變 值以求得服務系統最佳收益。經由改變 或 值所產生的結果，一一探討與分析其現象。

關鍵字

區別訂價理論 ； 一般服務層級 ； 較高服務層級 ； 顧客自行評估值

並列摘要

Abstract

In queueing service system, the administrator provides different service quality and set different service price for customers who want to enter service system and accept service. Different customers may have radically different values for a service quality, so techniques for differential pricing become very important.
By providing multi-classes service system, we can not only classify the group of customers but also gain greater profit. The high service class provides fast service speed and high service quality to customers. The general service class provides ordinary service speed and ordinary service quality to customers. The different service class has different price for customers. The customers sort themselves into different groups according to their perceived service value. They have an incentive to join the service system if their perceived service value exceeds the service cost. The service cost includes an admission price and the expected delay cost. The expect delay cost can be estimated, based on the system parameters.
There is a difficult challenge for the system administrator to enable the customers enjoy the reasonable service quality while service system can gain more revenue under optimal price mechanism.
In this study, we consider the problem of two classes system selection of customers perceived service value and discuss pricing mechanism of the demand function. We use price discrimination to classify the groups of customers and find optimal price to gain optimum profit. The service classes can be classified three classes: high service class, general service class and not enter service system. The number of customers in each service class is according to different pricing mechanism.
Our demand function is different with the usual demand function of multi-classes service system. The customers are not divided into two groups enter service system in advance and they make their decisions individually not collusively. In our service system, the service costs for the customers are the service price plus the waiting cost in system. This may lead to a difference between the demand functions from the system’s point of view and from the customers’ point of view.
In this study, we discuss the problem of how to set service rate, how to set service price of each service class and the customers how to select service class. We now consider our service system as a queueing system with two service classes. There are three kinds of customers: high-class customers, general-class customers and not enter service system customers. We consider our service system as two M/M/1 queueing systems. We assume that the arrival stream is according Poisson processes with rate and the service classes is according to Exponential processes with service rate . In some condition, the customers who want to enter service system only come to high class. We will discuss the optimal service price of high class in order to gain optimum profit. Also, the customers can be classified two groups and receive service by themselves. We decide the service price of two classes in order to maximize the total profit too.

並列關鍵字

High service class ； Perceived service value ； Price discrimination ； General service class

參考文獻

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