Research on Two-Level Price-Fluctuation Supply Chain Ordering Strategy Problem

Algorithm 1

	Step 1: select suitable Copula functions according to the characteristics of price and demand fluctuation at each price level. First based on the experience, then the goodness-of-fit test is carried out. Specific Copula functions are selected as per [29, 30]. And the parameters of the selected Copula functions are set through historical data.
	Step 2: determine the marginal distributions of price and demand at each price level with the related parameters estimated through the historical data.
	Step 3: generate two pairs of random variables and , with marginal distributions satisfying uniform distribution in and the correlation in each pair satisfying the selected Copula function.
	Step 4: number pairs of random price and demand at each level are obtained by inverse transformation:
	Repeat Step 3-Step 4, enough number pairs of random price and demand are obtained for both price levels, which satisfy the given marginal distributions and Copula functions.
	Step 5: initialize parameters , , , , , , , , and the wholesale price set . According to the generated discrete data of price and demand, the joint probability distributions of price and demand at two price levels are calculated, denoted by , then the marginal distribution of demand at each level is obtained. The statistic demand intervals at the normal and the discount levels are and . Then, the order quantity interval is determined, denoted by , where and .
	Step 6: divide the order quantity interval into equal parts, where . Let .
	Step 7: calculate corresponding according to the discrete model (P4):
	Take indicator set: .
	Step 8: obtain the profit set of the supplier {} satisfying indicator set and calculate the approximate optimal order quantity which maximizes the profit of the supplier, i.e., , and the maximum profit of the supplier is calculated.
	Step 9: if , the algorithm terminates. The approximate optimal order quantity is , and the corresponding wholesale price is ; the supplier’s profit is . Otherwise, let , go to Step 6.