Mathematical Researches

In this paper, a two-level supply chain with one buyer and one producer with insufficient working capital is considered. If the buyer pays early, the manufacturer gives a percentage discount to the buyer for each day early. The buyer and the producer cover the lack of liquidity from short-term debt from financial institutions. The objective function in both levels of the supply chain is the profit and the decision variables of the both level are the discount percentage and early payment time. The analysis of the profit functions of the two level of the chain shows that these functions have a saddle (critical) point. Considering this issue, it is important to find the appropriate range of discount percentage and payment time, which is not worse than disagreement between buyer and producer. To determine this range, the manufacturer's profit is greater than or equal to the amount of profit when not discounting. In that range, the interest rate range of financing and the interest rate of the buyer's investment have been analyzed. The results show that there are conditions that created an agreement between the levels of the supply chain by using the dynamic discount mechanism.