Optimal production and procurement decisions in a supply chain with an option contract and partial backordering under uncertainties

This paper considers a decentralized supply chain including one retailer and one manufacturer , where the manufacturer's production yield and the retailer's demand are both sto-chastic. At the beginning of the selling season, the retailer places an order and purchases an option contract with the manufacturer. After the selling season, the excess demand is partially backordered, and the retailer exercises his option order and then place an instant order for the backorders. The optimal ordering policy for the retailer and the corresponding production decision for the manufacturer are studied. Numerical examples are carried out to show the impact of the model parameters on the optimal policies. With the rapid development of science and technology, the lifecycles of products become shorter and shorter, and then more and more products have the attributes of fashion or seasonal goods. Therefore, in the past five decades, both researchers and practitioners have paid much attention to the important issues such as procurement, lot-sizing and inventory in operations management for newsvendor-type products. The earlier studies mainly focused on how to find the buyer's optimal ordering policies such that the buyer's expected profit (cost) is maximized (minimized) (see e. With the globalization of market and competition, supply chain management has become popular and many researchers have focused on coordination issues of the supply chain for newsvendor-type products (Pasternack [6], Emmons and Gilbert [7], Chen et al. [8], Seliaman and Ahmad [9], Zhou and Wang [10]). Our study is related to determining production and procurement with an option contract under uncertainties, so we confine ourselves in reviewing the related works as follows. Since option contracts are an efficient instrument to help hedge against the uncertainties and to reduce double marginalization in supply chains, they have attracted substantial attention in the area of supply chain management. Eppen and Iyer [11] considered a backup agreement between a catalog company and manufacturers, which is essentially an option contract. They showed that backup agreements have substantial effects on expected profit and committed quantity. An option model to quantify and price a flexible supply contract was studied by Cheng et al. [12], where the supplier decides the price of options as well as the exercise price according to the manufacturer's