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The Nurse Rostering Problem (NRP) is one of the NP-hard problems that are difficult to solve for optimality. NRP deals with the distribution of working shifts to the staff nurses at healthcare organizations under given rules. Normally, NRP aims at generating a duty roster that satisfies all of the hard constraints (mandatory) and as many soft constraints (optional) as possible. This work introduces a greedy constructive heuristic algorithm, based on building two patterns of two-week's duration that satisfies all of the hard constraints and several soft constraints. The first pattern is designed mainly to fulfill the night shift coverage whilst the second pattern is concerned with morning and evening shifts only. If the solution is not feasible (for example the coverage is not met), a repairing mechanism algorithm is applied until a feasible solution is reached. Simulated Annealing (SA) is then used to improve the constructed solution. A real dataset from Universiti Kebangsaan Malaysia Medical Center (UKMMC) is used in this work to test the proposed approach. Currently, the duty roster at UKMMC is still constructed manually. Promising results have been obtained and presented in this paper.