We introduce the Monte-Carlo based heuristic with first-come-first-served approximation for future optimal strategy (MC-FCFS) in order to maximize profit in a network revenue management problem. Like the randomized linear programming (RLP) model, one purpose of the MC-FCFS heuristic is to have information about displacement costs, considering the full probability distribution of future demands instead of a simplified degenerate distribution as in the deterministic linear programming (DLP) model. However, this information is conveyed by applying the FCFS heuristic as a future strategy rather than using the optimal ex-post profits as in the RLP heuristic. We show that MC-FCFS performs approximately as well as the RLP heuristic at a much lower computational cost and much better than the DLP heuristic at maximizing profit in a multi-night hotel booking setting with or without planned upgrades.