Abstract: Nowadays the logistics outsourcing is the important factor in the competition and revolution of retailer's omni-channel, facing end customers who are sensitive to both retail price and logistics service, we consider the retailer who outsources the logistics to multiple symmetric TPLs who compete on price and service level. The retailer allocates demand to the TPLs using a MNL (Multinominal Logit Model) choice function while the retailer chooses her price and allocation parameter to maximize his profits. Under symmetric information, a game-theoretic framework is applied to obtain the equilibrium solutions for every entity in single-sourcing, dual-sourcing and multisourcing, the comparison of equilibrium price, service level and retailer's profit in different scenarios was presented. An interesting result shows that both the price and service level of TPLs decrease when the retailer outsources demand to more than one TPL, which makes the retailer difficult to determine the outsourcing strategy. We found that the advantage of single-sourcing versus multisourcing depends on the sensitivity of market demand to retail price and logistics service. For maximized her profits, the retailer prefer to single-sourcing when the sensitivity parameter is high, however, when the sensitivity parameter is low, retailer would rather choose dual-sourcing. Furthermore, we studied the impact of the number of TPLs on the retailer's performance in the competitive setting, we found that while service level decreases as the number of TPLs increases, but the equilibrium logistics price does not change. Overall, the retail's profit is decreasing with the number of TPLs, suggesting that the retailer prefer to dual-source instead of multisourcing. In addition, we considered the problem that the retailer decides how to allocate demands between the TPLs in order to foster competition on both logistics price and service, the optimal parameter of allocation function is given for the dual-sourcing and multisoucing. Finally, the numerical simulation shows the effect that market demand sensitivity and the values which weight the logistics service relative to price have on the retailer's profits. These useful conclusions can provide supports for enterprise managers to make decisions.

Key words: logistics of retailers, outsourcing, competition, double decline effect