Research On Vending Machine Replenishment Problem Based On Multi-product Newsboy Model

Vending machine has brought a lot of convenience for modern life.In order to realize automatic operation and improve sales profit,this paper considers using historical sales data to model,better solve the replenishment problem of vending machine for business firms,and realize automatic operation.In order to solve the replenishment problem of vending machines,the demand distribution function of the next cycle is predicted according to the historical data.Then,it is used as model input and the multi-product newsboy replenishment model based on the aisle capacity constraint and the multi-product newsboy replenishment model built by service level and aisle capacity are built respectively.This paper builds three models: 1)Based on the historical sales data of vending machines,the ARIMA model is used to predict the fitting value,and then the regression prediction model is built with other external conditions to obtain the demand distribution prediction function of the next cycle.2)Because of the difference between vending machine and other traditional stores,each product has its own fixed aisle and its capacity is limited.Therefore,taking the demand distribution function as the input,a multi-product newsboy replenishment model based on the capacity constraint of the aisle is built,and the solution of the model is solved by Lagrange function and KKT condition.3)Considering that the frequent shortage of vending machines will lead to poor shopping experience and reduce customer loyalty,they will choose other purchasing channels instead.Therefore,we further study the impact of service level,and build a multi-product newsboy replenishment model based on the dual constraints of aisle capacity and service level.For the solution of the model,Lagrange function and KKT condition are used and binary search algorithm is combined to solve the problem.For the model built in this paper,the sales data of a certain brand vending machine in Shanghai Metro are used as an example.The results show that:1)On the basis of the time series forecasting model based on the simple historical sales data,the comprehensive forecasting model built by adding the holiday,temperature,weather and other factors can get higher forecasting accuracy.2)Compared with the original method of replenishing all aisles for vending machines at each replenishment time point,the multi-product Newsboy replenishment model based on the aisle capacity constraint and the multi-product newsboy replenishment model based on the dual constraints of aisle capacity and service level can bring more benefits,and the revenue difference increases with the increase in the transportation cost of each product.3)Considering the constraints of service level,there is a contrary relationship between the expected profit and service level.With the increase of service level,the decline rate of expected profit is relatively flat in the earlier stage,and sharply increases in the later stage.After adding the service level constraint,the expected profit decreases compared with the replenishment model with only the aisle capacity constraint.However,the model can not only bring more benefits than the original scheme of replenishing the aisle,but also ensure that the service level reaches the expected value.For enterprises,setting a higher level of service will lead to greater economic costs,so the enterprises need to choose a reasonable service level to control the cost at a lower level.