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In supply-chain management, the constrained shortest path problem in a network has wide applications. In this paper, the optimality and algorithm of the shortest path with fuzzy constraints (noted as SPFC) is studied. Introducing the fuzzy objective weight of a path into the objective function, an integer fuzzy optimization model is established for the SPFC problem. Then a simulated annealing algorithm is given to solve the problem. And the numerical simulation of example demonstrates the feasibility and effectiveness of the approach.