This paper is to get the cycle time of the vendor with minimum cost in an integrated production and inventory model of single-vendor multi-buyer multi-product supply chain. The vendor is the manufacturer of the product and the buyers are retailers. A manufacturer produces different kinds of products and supplies them to the retailers. The cycle time of the vendor is the elapsed time of two consecutive production start times. All product types have the same cycle time of the vendor. A mathematical model is represented with the cycle time of the vendor and the number of item supply from manufacturer to the retailers during the cycle time of the vendor in a supply chain. The cycle time of the vendor that minimizes the cost in a supply chain is obtained with the cost factors of the manufacturer. The number of item supply from the manufacturer to the retailer is obtained with the ordering cost and inventory holding cost of retailer and inventory holding cost of the manufacturer. A minimum cost solution method is suggested. A solution result is compared with the optimal solution and that of the genetic algorithm through a numerical example.