An analysis of the role of order quantity in supply chains with uncertainties from demand and/or supply

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We study the role of order quantity in supply chains when uncertainty exists in demand and/or supply. We consider a supply chain model consisting of one supplier and one buyer. It is widely known that order quantity is a tool used by the buyer to deal with the potential supply shortage or supply surplus due to the uncertainties in supply and/or demand. However, it is unclear how the decision makers use order quantity to hedge against different types of uncertainties. In addition, to comprehensively explore the role of order quantity, we analyze the impact of order quantity on coordinating contract design. In the model with demand uncertainty only, order quantity is a tool applied to hedge against the uncertainty in both of the decentralized system and the centralized system, and the buyer’s incentive for order quantity in the decentralized system is lower than that in the centralized system. To achieve coordination, the buyer’s ordering strategy has to be conservative in both demand and supply, i.e., order quantity is the same as the supply and less than the maximal demand. In the model with supply uncertainty only, the order quantity is used as a tool to hedge against the uncertainty but not in the centralized system. To achieve coordination, the buyer’s ordering strategy has to be conservative in supply but aggressive in demand, i.e., order quantity is less than the maximal supply but higher than the maximal demand. Furthermore, compared to the demand uncertainty, the supply uncertainty makes it more difficult to design a quantity-based coordinating contract. This can be seen from two facts. Finally, in the hybrid model with both uncertainties, the role of the order quantity and the design of the quantity-based coordinating contracts are similar to the model with supply uncertainty only. These results imply that the supply uncertainty seems to have a more significant impact on the application of order quantity than the demand uncertainty.