Research On Mathematical Model Of Vertical Cooperative R&D Investment Strategy In Supply Chain

With the rapid development of the global economy,the competition between enterprises has gradually intensified.More and more enterprises realize that improving their research and development ability through investment is crucial to maintain the competitive advantage of products.Enterprises’ research and development investment is mainly divided into quality investment to improve the product quality level,cost reduction investment to reduce the production cost by improving the production process,and green investment to improve the product green level,etc.But the high cost of investing in research and development makes it difficult for many companies to sustain.Therefore,vertical R&D investment cooperation between upstream and downstream enterprises becomes an inevitable choice for enterprises.Research shows that vertical R&D investment cooperation between upstream and downstream enterprises can bring higher profits to supply chain members and achieve a win-win situation.To this end,this paper will study the supplier’s decision on quality investment and production strategy of key components,the supplier and two competing manufacturers’ decision on production cost reduction investment cooperation strategy,and the two competing manufacturers’ decision on green investment strategy based on quality investment,and establish mathematical models based on different investment types and cooperation modes.The analytical solution is obtained by using optimization method,and the optimal decision of investment cooperation among supply chain members is obtained by analysis and comparison.The main research results are as follows.Firstly,a mathematical model of investment cooperation based on quality investment and cost sharing was put forward to study the supplier’s optimal production strategy of key components from the perspective of R&D investment efficiency and production cost.The analytical solution is obtained by using optimization method and backward recursion method.By comparing and analyzing the profits of supply chain members,it is found that if the production cost is lower,the supplier chooses to develop and produce the component.If the production cost is higher,the supplier chooses to develop and produce the component when the investment efficiency is higher.When the investment efficiency is lower,the supplier chooses to develop but not to produce the component.In addition,the mathematical model proposed and the conclusions obtained will provide the mathematical theoretical basis and management suggestions for the decision-making of production strategy of relevant supply chain enterprises.Secondly,aiming at the decision problem of investment cooperation strategy of production cost reduction between suppliers and two competing manufacturers,a mathematical model of investment cooperation based on production cost reduction investment and wholesale price discount is proposed,and the optimal decision of investment cooperation between suppliers and two competing manufacturers is studied from investment efficiency and wholesale price discount degree.By comparing and analyzing the profit of suppliers and manufacturers,it is found that when the wholesale price discount is low,the wholesale price discount contract and technology investment can improve the profit of supply chain members.Secondly,when the discount of wholesale price is low,or when the discount of wholesale price and the efficiency of technological investment are both high,the supplier is willing to accept the technological investment of the two manufacturers,and the two manufacturers are also willing to make technological investment to the supplier.When the model is extended to the asymmetric potential market size,the conclusion of the optimal cooperation strategy between the supplier and the two competing manufacturers does not change,which confirms the robustness of the model.In addition,the mathematical model proposed and the conclusions obtained will provide mathematical theoretical basis and management suggestions for the decision of cost reduction investment cooperation between related enterprises.Finally,aiming at the decision problem of green investment strategy of two competing manufacturers based on quality investment,a mathematical model based on quality investment and green investment was proposed,and the optimal decision of green investment of two competing manufacturers was studied from the point of difference between product quality.By comparing and analyzing the profits of manufacturers and retailers,it is found that when the quality difference between products is large,both manufacturers will not make green investment.When the quality difference between products is small,both manufacturers will make green investment.Furthermore,when the degree of quality difference between products is small,green investment by two manufacturers can enable both manufacturers and retailers to achieve a “win-win-win”.The extended model shows that the main conclusions do not change under the condition of endogenous wholesale price,which verifies the robustness of this conclusion.In addition,the mathematical model proposed and the research conclusions obtained will provide the mathematical theoretical basis and management suggestions for the green technology investment decision of related enterprises.