| We study a supply chain with one manufacturer and two retail channels, where an online retailer offers a lower price and free-rides a brick-and-mortar retailer's sales effort. The free riding effect reduces brick-and-mortar retailer's desired effort level, and thus hurts the manufacturer's profit and the overall supply chain performance. To coordinate the efforts, we design and compare several supply chain contracts: a selective rebate contract with price match, a revenue sharing contract with price match, and a target rebate contract with price match, as well as a wholesale price contract with price match. We study the contract performance under both deterministic and stochastic demands. Under deterministic demand, the analysis goes with two cases: the online channel is owned by or independent of the manufacturer.;We show that the selective rebate contract coordinates the supply chain in both cases. It can also allocate the system profit arbitrarily between the supply chain players. Furthermore, in the case that the manufacturer owns the online channel, there exists a solution regime on the Pareto-optimal frontier in which both the manufacturer and the brick-and-mortar retailer are better off from the baseline case. We also show that the manufacturer's optimal rebate only depends on the manufacturer's marginal profit and the consumers' sales effort sensitivities. The optimal rebate is independent of the market size and retail prices. In addition, we show that the revenue sharing contract with price match is equivalent to the selective rebate contract. Under stochastic demand, we show that the selective rebate contract outperforms all other contracts by improving supply chain efficiency. |
