Abstract: Service quality becomes more and more important as after-sale service competitions become fierce in modern business. Scholars usually consider the joint decisions of warranty length and product price. In this paper, service quality decisions based on traditional warranty length and price optimization researches are concerned. Better service quality and warranty length can promote sales and raise the price. These three dimensions have dynamic relationship in product lifecycle, but few scholars consider them jointly. The market of consumer goods and developed optimal control problems including cost models, demand models and profit model were investigated in this paper. Manufactures' profit is optimized by choosing optimal service quality, price and warranty length jointly. The maximum principle method is used to obtain solutions. The optimal policies for static market were further investigated and Lingo11 was used to do some numerical tests for dynamic market. This research can help manufactures make better warranty policy and give consumers better warranty service.

Key words: warranty, service quality, warranty length, price, repeated purchase, static and dynamic market, maximum principle