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Fixed-charge transportation problem (FCTP) is an extension of classical transportation problem in which a fixed cost is incurred, independent of the amount transported, along with a variable cost that is proportional to the amount shipped. In this paper, FCTP is formulated using a mixed integer programming model, and transformed into a series of minimum cost maximum flow (MCMF) problems for solution. Based on MCMF algorithm, a heuristic algorithm, named FCTP-HA, is presented to solve FCTP. The theory, on which FCTP-HA is based, is strictly proved. FCTP-HA not only can find good heuristic even optimal solution to FCTP, but also has good performance in the sense of being implemented on computer, computational time and required memory for computation. Numerical experiments demonstrate that FCTP-HA is an efficient and robust method to solve FCTP.