Study Of The Effect Of Yield Uncertainty On The Newsvendor Modles Based On The Stochastica Comparsion

The goal of the traditional newsvendor model is to find the optimal order quantity to maximize the expected profit or minimize the cost under stochastic demand conditions.The production process is susceptible to personnel, machinery, raw materials, processes,and environmental aspects. When the manufacturer inputs the same, it is not necessary to obtain the same amount of homogeneous product, which means the product yield is uncertain. The yield uncertainty universally exists in agricultural products,semiconductors, some daily consumer goods and other processing industries. Under the condition of stochastic yield environment, enterprises with integrated production and marketing can reduce the losses caused by under-production or over-production through emergency purchase or low-cost sales in the secondary market. Enterprises should consider both the demand uncertainty and the output uncertainty. Therefore, it is of great theoretical and practical significance to study the effect of yield uncertainty on the newsvendor model with stochastic demand and emergency purchase and low-cost sales on the secondary market.Firstly, the background, purpose and meaning of the problem research, the framework, the content and the innovation point are given. Secondly, it summarizes the research status of the newsvendor model, the uncertainty of demand, the uncertainty of the yield, the secondary market and the stochastic comparison. Under the condition of the different stochastic demand function structures, the newsvendor model with constant secondary market price and the secondary market price dependent yield are established respectively. Through comparison theory, the effect of the yield rate and yield error of random on the optimal selling price,the optimal order quantity and the expected sales profit have been discussed. And by the comparative analysis, the validity of the newsvendor model with the stochastic demand and the random output and the secondary market price dependent yield are obtained. Finally, the summary and prospect are made. Based on stochastic comparison theory, this paper studies the effect of yield uncertainty on newsvendor model. The main research work and innovationare as follows:(1)In this paper the effect of yield uncertainty on the newsvendor model with the price-dependent additive demand is studied. Newsvendor models with the price-dependent additive demand and the constant unit price of emergency purchase and salvaged sale is established. By using the theory of stochastic comparisons, it shows that in the in-house production case, a less variable yield rate and a stochastically larger yield rate lead to a lower optimal price and a higher expected profit, while a less variable yield error leads to a higher expected profit, and a stochastically larger yield rate leads to a higher optimal order quantity and a higher expected profit. In the pure procurement case, a less variable yield rate (error)leads to a lower optimal price and a higher expected profit, and the effect of the stochastically larger yield rate (error)on the optimal price, optimal order quantity,expected profit are not universal. The upper and lower bounds of the expected sales profit under the error of the output with a less variable yield rate (error) and a stochastically larger yield rate (error) have been gained.The results are simulated and analyzed by numerical examples, which is different from the results of the previous studies which focus on the effect of yield uncertainty on the newsvendor model with the product demand and the demand-dependent price.(2)In this paper the effect of yield uncertainty on the newsvendor model with the additive-multiplicative price-dependent demand is dicussed. Newsvendor models with the price-dependent additive-multiplicative demand and the constant unit price of emergency purchase and salvaged sale has been established. By using the theory of stochastic comparisons, it shows that in the in-house production case, a less variable yield rate and a stochastically larger yield rate lead to a lower optimal price and a higher expected profit, while the effect on the optimal order quantity is uncertain. And a stochastically larger and a less variable yield error lead to a higher expected profit,while a stochastically larger yield rate lead to a higher optimal order quantity. In the pure procurement case, a less variable yield rate (error) leads to a lower optimal sale price and a higher expected profit .The results are simulated and analyzed by numerical examples, which is different from the results of the previous studies which focus on the effect of yield uncertainty on the newsvendor model with the multiplicative demand and the demand-dependent price. It shows that the two models are suitable for different types of products of the newsboy problem.(3)In this paper the effect of yield uncertainty on the newsvendor model with the price-dependent demand and yield dependent secondary market price is studied. The newsvendor models with the price-dependent multiplicative demand and yield dependent secondary market price has been established. By using the theory of stochastic comparisons,it shows that when emergency purchase is non increasing random function and meets some additional conditions, a less variable yield rate or error leads to a higher expected profit, but the effect on the optimal order quantity and the optimal selling price are both uncertain, when emergency purchase is non increasing random function while a stochastically larger yield rate leads to a lower optimal price,while the effect of a stochastically larger yield erro on the optimal sale price is uncertain,the effect of a stochastically larger yield rate or error on the optimal order quantity are uncertain.The theoretical analysis and practical significance are simulated and analyzed by numerical examples, which is different from the results of the previous studies which focus on the effect of yield uncertainty on the newsvendor model with constant secondary market price and the demand-dependent price, and a less variable is represented by the convex order.(4)In this paper the effect of yield uncertainty on the newsvendor model with the price-dependent and sale effort demand and yield dependent secondary market price is dicussed. The newsvendor model with the price-dependent and sale effort additive demand and yield dependent secondary market price has been established. By using the theory of stochastic comparisons, it shows that when emergency purchase is non increasing random function and meets some additional conditions, a less variable yield rate or erro leads to a higher expected profit, but the effect on the optimal order quantity, the optimal selling price and sale effort are all uncertain, when emergency purchase is non increasing random function while a stochastically larger yield rate leads to a lower optimal price and sale effort, while the effect of a stochastically larger yield erro on the optimal sale price and sale effort are uncertain,the effect of a stochastically larger yield rate or erro on the optimal order quantity are uncertain. The theoretical analysis and practical significance are simulated and analyzed by numerical examples,which is different from the results of the previous studies which focus on the effect of yield uncertainty on the newsvendor model with yield dependent secondary market price and the demand-dependent price, Compared with the newsvendor model with the price-dependent and yield dependent secondary market price,it shows that the newsvendor model with the price-dependent and sale effort demand and yield dependent secondary market price is more general and practical.According to the stochastic comparison theory, comparing the stochastic profits of newsvendor model such as in sence of monotonically increasing convex order will be studied. Besides, the effect of demand uncertainty or yield uncertainty on the newsvendor model with the punishment outage and risk aversion and the yield dependent secondary market price will be considered. Furthermore, the optimization problem and other aspects of the problem of the generalized newsvendor models can be discussed.