The successful implementation of Just-in-time (JIT) production in today's supply chain environment requires a new spirit of cooperation between the buyer and the vendor. An integrated inventory model with such a consideration is based on the total cost optimization under a common stock policy and business formula. However, the supposition of known annual demand in most related literature may not be realistic. This paper proposes the inclusion of fuzzy annual demand and/or the production rate, and then employs the signed distance, a ranking method for fuzzy numbers, to find the estimate of the common total cost in the fuzzy sense, and subsequently derives the corresponding optimal buyer's quantity and the integer number of lots in which the items are delivered from the vendor to the purchaser. Numerical examples are provided to illustrate the results of proposed models.