عنوان مقاله [English]
At the time of contract design in multi - echelon supply chains, some important information about cost or demand may not be available. In such a situation, contract design with upstream and downstream, i.e., a supplier and a retailer, members of a supply chain becomes an important issue. In this research, a three- echelon supply chain, consisting of a supplier, a manufacturer, as contract designer, and a retailer, is considered. Due to different reasons, such as time- consuming supply process, it is assumed that the manufacturer has to place supply orders before the start of a selling season. The retailer prepares the final product for the selling season with stochastic demand. At the time of supply contract, the manufacturer has a continuous distribution from the retailers processing cost. However, uncertainty about the retailers cost is eliminates eliminated after a while. The manufacturers optimal supply order, according to an option contract, is investigated. The option contract helps the manufacturer to postpone some decisions until information uncertainty about retailers cost is eliminated. The manufacturer, firstly, decides about initial and option orders. Later, after realization of the retailers cost, the manufacturer decides about the exercised orders. Through exercised orders, the manufacturer can adjust initial orders. The optimal exercised orders, are calculated analytically. Also, it is established that the manufacturers objective function is concave in terms of initial and option orders, and thus, the optimal value of these variables can be found easily. The manufacturer also offers a coordinating buy-back contract to its downstream member, i.e., the retailer. The optimal values for the buy-back contract, whenever the manufacturer obtains a specific portion of the manufacturer-retailer system profit, are calculated. In the numerical experiments, it is investigated how each manufacturers contract with its upstream and downstream members affects each other. The numerical results show that the designed supply chain contract in each supply chain echelon, depends on the information and the contracts of the other echelons, and contracts should not be considered separately from each other.