Parallel machine scheduling to maximize the weighted number of just-in-time jobs

Parallel machine scheduling problem of maximizing the weighted number of just-in-time jobs was investigated. The problem was NP complete in the strong sense, for which finding an optimal solution had been considered very unlikely. The performances of 4 greedy heuristic algorithms (WO1, WO2, DO1 and DO2) dev-eloped for solving the Pm|| Σ wј xiј problem were analysed. Two approaches adopted for assigning jobs to the machines were according to the earliest start time, and according to difference between latest due date and the job processing time. The time complexity of each algorithm was O(nmlogn). The heuristics WO2 and DO2 were suitable for certain number of machines and number of jobs, while WO1 and DO1 out classed the other two.