Take-away and sit-down service operations under inequity aversion

¹ Department of Mathematical Sciences of Tsinghua University, Beijing 100084, P.R. China
² School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P.R. China
³ College of Management and Economics, Tianjin University, Tianjin 300072, P.R. China

^* Corresponding author: xcsun@tju.edu.cn

Received: 21 May 2023
Accepted: 18 July 2024

Abstract

Profit contributed by take-away service has become an increasingly essential element of the restaurant operating revenue. Since take-away service usually relies on the third-party platform and there are many differences between the cost of take-away service and that of sit-down service. We focus on the restaurant which provides both sit-down service and take-away service, the service system is modeled as a two-stage tandem queueing system. We study the restaurant’s optimal capacity level for each stage. Besides, as there exist price/waiting time difference between the two services, inequity aversion is also investigated in our model. We study symmetrical and asymmetrical inequity aversion. We find that the optimal service capacity consists of two parts, base capacity and safety capacity. And the loss resulted from waiting time lag is equal to the waste of resources caused by fluctuations in arrival rate. Further, when customers really long for the restaurant, even if high price will lead to severe inequity aversion, restaurant can always earn more by raising the price in service channel with high revenue. While when customers are indifferent of the restaurant and the others, the price gap is meant to result in revenue decrease. In addition, reduction in customers’ susceptibility can help to enhance operation profit in general. Market environment plays a decisive role in choosing the optimal service level.