Buyback and price postponement in a decentralized supply chain with additive and price-dependent demand

Abstract

We examine buyback contracts in a dyadic supply chain where a retailer orders from a supplier before observing the random demand and sets a retail price after observing it (a.k.a. price postponement). We focus on the case with linear additive demand, which is well known to be less tractable than the case with linear multiplicative demand. With mild conditions on the distribution of demand uncertainty, we derive the supplier's optimal buyback contract and show the following results. The supplier strictly prefers buyback contracts to wholesale price-only contracts if and only if the unit production cost is lower than a threshold that depends on the dispersion of demand uncertainty; the optimal buyback rate is decreasing in the unit production cost; the profit allocation within the supply chain and channel efficiency depend on the dispersion of demand uncertainty. These results are in stark contrast to those in the case with linear multiplicative demand. Nevertheless, the relation between the operational decisions under the optimal buyback contract and those under the optimal wholesale price-only contract is consistent with the case of multiplicative demand. We further extend the analysis to two related scenarios. On one hand, our results continue to hold in a supply chain where one supplier sells to two competing retailers. On the other hand, when the retailer does not postpone retail pricing decisions, we establish three distinctive properties of the optimal buyback contract: the supplier strictly prefers buyback contracts to wholesale price-only contracts if and only if the unit production cost is intermediate; the optimal buyback rate is increasing in the unit production cost in the region where the supplier strictly prefers buyback contracts to wholesale price-only contracts; price postponement benefits both the retailer and the supply chain but does not always benefit the supplier. The above analysis shows that the supplier's preference between buyback and wholesale price-only contracts can swing either way when the retailer starts to practice price postponement.