Abstract:

The time gap between advertising exposure and its effect is a common universal phenomenon， which provokes the manager's thoughtful consideration. The main reason for this phenomenon is the delayed effect. In this paper， the advertising decision and coordination problem are explored for a supply chain in the finite horizon planning when product goodwill is affected by the delayed effect. By establishing the product goodwill as a delay differential equation of brand advertising investment， an advertising decision model with finite horizon constraint is firstly constructed for a supply chain. Later， the finite horizon optimal control theory for the time-delay system is utilized to derive the optimal advertising strategies， product goodwill， and supply chain profits under the decentralized and centralized decision scenarios. Then， the equilibrium results can be compared and analyzed， including the optimal advertising effort， product goodwill， and profits. Finally， a demand-dependent compound contract is designed to coordinate the supply chain perfectly based on the centralized supply chain as a benchmark. It can be pointed out that， unlike the infinite horizon planning situation， the optimal advertising effort level of the manufacturer is time-dependent in the finite horizon planning and follows the principle of “gradual reduction-early termination.” A longer advertising period and a shorter advertising delayed time can stimulate the advertising investment of the manufacturer， improve the accumulation of product goodwill and obtain more profits. Even if the delayed effect occurs in the finite horizon planning， the centralized decision is always the best decision-making mechanism in the supply chain. The research results will provide some theoretical guidance for the marketing practice of supply chain enterprises.

Key words: finite horizon planning, delayed effect, advertising strategy, contract coordination