Quantity Discount and Its Combined Contract for Global Supply Chain under Uncertain and Price- Dependant Demand

Abstract

Quantity discount contract is widely used in practical management and is paid much attention by management research. Until now, there is a lack of research on the quantity discount contract for supply chain under uncertain and price-dependant demand. On the other hand, when formulating contract the global supply chain contract should take some international finance and/or trade factors into account, in addition to the usual factors of the supply chain in one country. So far, those international finance and/or trade factors are ignored by nearly all related researches on supply chain contract. Products with short life cycle but long production time has uncertain demand and their demand depends on selling price. This paper investigates the quantity discount and its combined contract for global supply chains based on the theory of interest rate parity. For the additive demand case, which random variable obeys uniform distribution, the quantity discount contract for supply chains is developed from two aspects. Firstly, the contract with quantity discount is developed under uncertain and price-dependant demand. Also, the combined contract with quantity discount and the transfer payment are designed to coordinate the supply chain. Secondly, the paper pays attention to the global supply chain which takes exchange rate, international transport cost and tariff into account. In this paper, four decision models are proposed: decentralized decision-making with no contract, centralized decision-making, quantity discount, the combined contract with quantity discount, and transfer payment. On the basis of the results of Nicholas, the optimal selling price, the optimal order quantity, and the expected profit of each party of the supply chain are obtained for each decision-making model. The results are shown as follows:(1) For the random demand in the additive form, which is subject to uniform distribution, the optimal selling price and the optimal order quantity are obtained. The contract with quantity discount, that is(d *, p* dinate global supply chains.(2) Although the optimal selling price and the optimal ordering quantity of the d, q*d), is prescribed to coorseller with the quantity discount contract, i.e.(d *, p*, *d qd), is respectively equal to the optimal selling price and the optimal order quantity with centralized decision-making, and the maximum profit for the system of the supply chain can also be obtained. However, the supply chain is not coordinated with only quantity discount. The profit of the supplier becomes less seriously.(3) With the combined contract with quantity discount and transfer payment, i.e.(d *, p* profit for the system of the supply chain is obtained, but also the profit of the seller and that of the supplier are also improved. d, q*d, ?), not only the maximumSo, the supply chain is coordinated.(4) For the combined contract with quantity discount and transfer payment, i.e.(d *, p*, q*d d,?), the discount rated *is affected by the sharing ratio of the international transport cost and the tariff rates, but has nothing to do with the exchange rate e. The other parameters are affected by these three factors.(5) To the product with short life cycle but long production time, the parameters of the combined contract are determined by the parties of the global supply chain if the long term exchange rate is forecasted by the theory of interest rate parity. The profit of the global supply chain system is further improved by the combined contract on the basis of the profit without considering changes in exchange rate. The coordination result is nearly close to that of the global supply chain with practical exchange rate. Therefore, the global supply chain is coordinated more perfectly.