In previous studies on the order allocation of the supply chain, suppliers involved in the order allocation are expected to accept orders passively. The strategic behaviours of functional logistics service providers (FLSPs), especially pre-estimate behaviour, have an important influence on the results of order allocation. First, this paper focuses on the pre-estimate behaviour and utility function of FLSPs, and attempts to determine the critical condition for FLSP participation in order allocation. Second, based on the rational expectations equilibrium (REE) between FLSPs and logistics services integrator (LSI), an order allocation optimisation model for LSI is proposed. Satisfying the constraints of FLSP participation in order allocation, the model considers three objectives, namely, minimising the cost of LSI, maximising the order satisfaction of FLSPs, and matching the different logistics capacities of FLSPs as much as possible. Numerical analysis is performed. The effects of order uncertainty, the expected discount coefficient, and the business reputation of FLSP on order allocation are discussed. The findings indicate that order allocation results taking the REE into consideration are better than those when the REE is not considered, implying that the LSI’s introduction of the rational pre-estimate behaviour of FLSPs into order allocation will improve the comprehensive performance of LSSC, as well as the order allocation process of the LSI. FLSPs should rationally put forward the expected discount coefficient according to their weights of quantity satisfaction and price satisfaction, thereby maximising the satisfaction of FLSPs. In addition, LSI should select the FLSP with better business reputation to maximise the comprehensive performance of the logistics service supply chain. Finally, this paper uses Tianjin Baoyun Logistics Company as an example to illustrate the application of model conclusions.