For the cell part scheduling(CPS) problem with transportation capacity constraint, an integer nonlinear programming(INLP) model is formulated to allocate the machines and automated guided vehicles(AGVs), and to schedule all parts. A reasonable transportation mode is presented, and an auction-based heuristic approach is proposed to solve the problem. An improved disjunctive graph model is developed to optimize the feasible solutions obtained by using auction-based approach. The auction consists of two aspects: Auction for AGV and auction for machine. Auctions can be used to evaluate the value of resources in different periods of time properly, so as to improve the utilization of resources and reduce the total production time. In both auctions, AGVs and machines act as auctioneers respectively, and parts act as bidders. Numerical experiments are conducted to test the auction-based approach and improved disjunctive graph model. The results demonstrate the effectiveness of proposed auction-based approach and improved disjunctive graph model, also indicate the influence of the capacity of AGV on scheduling parts.