Application of the Queueing Theory for Optimization of Number of Cashiers: A Case Study

Abstract

This work intends to show how the Queueing Theory may be used to predict the optimized number of cashiers is required at a certain time to attend the demand of a store. The research's object is the reality of a store with a great number of customers, and which uses the single line system for cashiers. In order to calculate the optimized number, this work adopts as starting point the condition that the probability of a customer to exceed a pre-determined average time in line is small. Through sample studies, a quantitative model of line type M/M/c (Exponential, Exponential, c service channels) was proposed for the case under analysis. Currently, the considered store adopts a system named Agifila to control the number of customers at the cashier’s single line. This work compares the proposed model, based on predictions, with the Agifila system, which is grounded on momentary control, in order to clarify both the model efficiency and the referenced system.