随机需求环境下联产品系统价格与产量决策研究

基于固定比例生产技术和多产品随机需求的情形,研究了联产品制造商的两阶段产量和价格联合优化模型。通过反向倒推的优化求解,得到了联产品制造商的最优产量和价格决策以及变化规律。同时研究了需求服从均匀分布时,需求波动对均衡的影响。研究结果表明,在订货成本较低和一种产品的需求波动性较大时,当另外一种产品的波动增大,则该产品的最优订货量增大,同时价格下降。借助数值仿真,分析了价格敏感度和产出比例对最优决策和利润的影响。结果表明,在给定一种产品的价格敏感度时,另外一种的价格敏感度越大,那么该产品的价格就越低,制造商的订货量就下降。当一种产品的产出比例固定时,另一种产品的产出比例上升时,则该产品的价格下降,制造商的订货量下降,总利润上升。

Co-product’s joint pricing and quantity decisions with stochastic demand and fixed proportion technology

The co-production system refers to a system that can simultaneously generate multiple products in the same production process,and has a wide range of applications in practice.In the agro-processing industry,sugar cane processing can simultaneously produce edible sugar and animal feed;in the meat processing industry,beef can be processed to produce high-quality beef and ordinary beef at the same time;in the semiconductor processing industry,the wafer can be simultaneously processed into different grades of chips;and in the petroleum refining industry,crude oil is processed to produce both light and heavy oil.In a traditional production system,one raw material(production capacity)yields only one product.The manufacturer can determine the production quantity of each product according to the resource demand characteristics(i.e.,the input amounts of various raw materials);likewise,the co-production system yields a plurality of products according to a fixed ratio by processing the same raw material.Therefore,when considering the continued input of the same raw material(capacity),the manufacturer needs to comprehensively consider the demand characteristics of each terminal market and the costs of comparable production processes to make appropriate decisions.Research on the co-production system has significant practical and theoretical value.From a practical perspective,effective management of the system can not only greatly enhance enterprise profits,but also play an environmental role.From a theoretical perspective,the co-production system creates value through cost sharing,which is significantly different from the production risk-sharing effect.When the demand correlation increases,the effect of capacity sharing is diminished and the effect of cost sharing enhanced.In addition,the profit improvement through flexible pricing strategy and conversion flexibility strategy is greater than the impact of the final product replacement.Although the co-production system has a wide range of applications in various industries,few theoretical studies have been conducted on the system,many of which often overlook random factors that may influence the system.Based on fixed-scale production technology and multi-product random demand situations,the two-stage production and price joint optimization model of the joint production manufacturer was studied.Through the optimization of reverse pushback,the optimal yield,price decision,and change law of the co-production manufacturer are obtained.At the same time,the influence of fluctuating demand on the equilibrium is observed where the demand obeys the uniform distribution.Through numerical simulation,the influence of price sensitivity and the output ratio on optimal decision-making and profit is analyzed.The study yielded the following interesting conclusions.First,when the order cost is low and the demand fluctuation of Product 2 is large,the fluctuation of Product 1 will decrease,increasing its optimal order quantity and decreasing its price;on the contrary,when the demand fluctuation of Product 2 is less volatile,the increase in the volatility of Product 1 will result in a decrease in its optimal order quantity and an increase in its price.Second,given the price sensitivity of Product 1,the price sensitivity of Product 2 will rise,its price will drop,and its order quantity will decrease;at the same time,if the price of Product 1 is raised,the overall profit of the manufacturer will drop.Third,when the output ratio of Product 1 is fixed and the output ratio of Product 2 is raised,the price of Product 1 rises,and that of Product 2 falls,along with its order quantity;as a result,the total profit is higher.