This paper is to analyze an integrated production and inventory model in a single-vendor multi-buyer supply chain. The vendor is defined as the manufacturer and the buyers as the retailers. The product that the manufacturer produces is supplied to the retailers with constant periodic time interval. The production rate of the manufacturer is constant for the time. The demand of the retailers is constant for the time. The cycle time of the vendor is defined as the elapsed time from the start of the production to the start of the next production, while the cycle times of the buyer as the elapsed time between the adjacent supply times from the vendor to the buyer. The cycle times of the vendor and the buyers that minimizes the total cost in a supply chain are analyzed. The cost factors are the production setup cost and the inventory holding cost of the manufacturer, the ordering cost and the inventory holding cost of the retailers. The cycle time of the vendor is investigated through the cycle time that satisfies economic production quantity with the production setup cost and the inventory holding cost of the manufacturer. An integrated production and inventory model is formulated, and an algorithm is developed. An numerical example is presented to explain the algorithm. The solution of the algorithm for the numerical examples is compared with that of genetic algorithm. Numerical example shows that the vendor and the buyers can save cost by integrated decision making.

This paper is to analyze the cycle time of the vendor in a single-vendor multi-buyers supply chain. The vendor is the manufacturer and the buyers are the retailers. The cycle time of the vendor is the elapse time from the beginning time of the production to the beginning time of the next production. The cycle time of the vendor that minimizes the total cost in a supply chain is analyzed. 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 times of the vendor obtained with the costs of the vendor is compared with those obtained with the costs of the vendor and the retailers. Various numerical examples are tested if the cycle times of the vendor for both methods are the same.