Based On Queuing Theory Optimization's Supermarket Working Hours' Problem

The supermarket store is a newly developed modern model of sales industry; it became the main formation of people's daily shopping place quickly because of its cheap running cost and highly effective serving performance. The supermarket store succeeds in marketing field because it can decrease the cost and let the customer gain more benefits. As the supermarket grew more and more large-scale, it began to get into a crag-fast. On one hand it faced the business profits lure, on the other it have to meet the public's efficiency need of the supermarket. In this two side choosing trouble problem, the checkout counter of the supermarket turned out to be a important role in supermarket business. Modern supermarket grew in large-scale and gathering aspect for a long time, it's customer population grew huge too. The efficiency of the trading server became a problem which both customer and the merchandise pay much attention on.Customers think the market counter provided the more the better so they can do shopping at any time. At the manager side, they hired the stuff as little as they can unless they lose customers so they can cut the cost of the business and earn more benefits. These two side quest problem can be concluded into one question that is how to manage the economic value and social value together, or how to save the customers shopping time mostly and maximize the economic value. This is a complicated optimization problem.This article is based on the problem and uses the queuing theory to analyses and optimizes the supermarket queuing problem. The supermarket queuing problem can be included into multi-counter random serve-system. This system accords with the parameters relationship in M/M/n/∞/∞theory demonstration. Based on the study in this demonstration we find the main character and common point in these counter serve-systems. According to the parameter relationship in the theory model we optimize the real queuing system, and find the academic theory. Then we study the further optimal detail: ascertain the worker's worktable in supermarket and the minimum of the works number. The analysis of the work-time table under the condition of the optimization of the queuing system is a multi-goal combinatory optimal problem and also a NP-hard problem. The answer of the goal function would grow by exponent-scale, so it's impossible to illustrate all the answers to compare and find the optimal answer. So we need to find a arithmetic to find the best answer. The Genetic-Arithmetic is a good arithmetic in this field, it is a fast- constringent arithmetic and has full-situation finding. Its optimization can dispart into four steps: 1.coding; 2.ascertain the parameter; 3.evolving and iterating; 4.analysing the result. This article utilizes the optimized result of the queuing theory to find the best answer in full-situation by the GA arithmetic. If the optimal answer meets the constringent condition in arithmetic then accept the answer as the best answer. At last decodes the answer by the coding scheme to get the real combinatory optimal answer.