Pricing and ordering under trade promotion, brand competition, and demand uncertainty

In practice, many manufacturers offer trade promotion to retailers to induce demand. it is also common for a retailer to sell products of competing manufacturers. this paper considers a two-echelon supply chain where two manufacturers provide a trade promotion to a retailer, and the retailer faces uncertain and price-dependent demand. in the model, the manufacturers determine wholesale prices and the retailer determines retail price and order quantity to maximize their own profits. an algorithm based on non-linear optimization is provided to solve the problem. we compare three trade promotions under brand competition: off-invoice, scan-back, and buy-back policies, and discuss the effects of trade promotions on decisions and profits. the results indicate that the manufacturers and retailer prefer the buy-back policy over the off-invoice and scan-back policies. the retailer's profit will increase and the manufacturers' profits will decrease as the brand substitution effect increases. also, the manufacturers will raise their wholesale prices, but the retailer will reduce the retail price and order quantity when the brand substitution rate increases.