Abstract:

The external environment the market facing is becoming increasingly complex， and unexpected events occur frequently， which makes the price change at any time and makes the marginal profit fluctuate. In this ever-changing environment，if manufacturers and retailers cooperate in advertising，there will be some delay in advertising andprice competition among manufacturers. At this time， how to make decisions among members of the supply chain has become an urgent problem to be solved.In this paper， the influence of advertising delay degree on the optimal decision-making of supply chain members is studied based on marginal profit fluctuation and price competition among manufacturers.The concrete research ideas are as follows. Firstly， under the background of non-competition， the differential equation of brand goodwill and the profit equation of marginal profit fluctuation considering the effect of advertising delay are built. By applying differential game，the optimal wholesale price， optimal retail price， optimal advertising investment， optimal advertising sharing rate， brand goodwill and profit are found out. Secondly， the corresponding differential equations are constructed to obtain the optimal wholesale price， optimal retail price， optimal advertising investment， optimal advertising sharing rate， brand goodwill andprofit under the background of price competition among manufacturers. Finally， the influence of delay time on the optimal path of each decision parameter is verified by an example simulation and the comparison between the results obtained under the condition of competition among manufacturers with those obtained of non-competition is made. And based on above information， it can be conduded that the optimal retail price， optimal wholesale price， brand goodwill and profit are positively related tothe delay degree of national advertising and alsotothe delay degree of local advertising. The optimal advertising investment of manufacturersis only positively correlated with the delay degree of national advertising， while the optimal advertising investment of retailersis only positively correlated with the delay degree of local advertising. Meanwhile， the optimal sharing rate is aconstant， which has nothing to do with advertising investment and advertising delay. When manufacturers compete in price， the optimal wholesale price， the advertising input of manufacturers and retailers are alllow. The retail price of manufacturers incompetition is slightly lower than that innon-competition，but there is little difference. Price competition among manufacturers will damage the profits of manufacturers， but it will help retailers togethigher profits.In this study， it aims to explore the internal operation and evolution law of the dynamic optimization of the delayed cooperative advertising supply chain under the condition of marginal profit fluctuation， enrich the supply chain management theory， and provide scientific basis for the decision-making behavior of the supply chain and its members under the condition of price competition among manufacturers.

Key words: price fluctuation, manufacturer price competition, lagged effect, differential game