This paper is to get the cycle time of the vendor with minimum cost in an integrated production and inventory model of the single-vendor multi-buyers supply chain. The vendor is the manufacturer of the product and the buyers are retailers. The cycle time of the vendor is the elapsed time from the beginning time of the production to that of the next production. The mathematical model is represented with the cycle time of the vendor and the numbers of supply from manufacturer to the retailers during the cycle time of the vendor in a supply chain. The cost factors are the production setup cost and the inventory holding cost of the vendor, the ordering cost and the inventory holding cost of the retailers. The cycle time of the vendor that minimizes the cost in a supply chain is obtained with the cost of the manufacturer. The number of supply from manufacturer to the retailer is obtained with the ordering cost and inventory holding cost of retailer, and inventory holding cost of the manufacturer. The numerical examples are shown to analyze the cost difference between the vendor cost cycle method and the optimal solution. The effectiveness of the vendor cost cycle method is shown through the numerical examples.