This thesis considers a nonpreemptive single-machine clustered job scheduling problem where the objective is to minimize maximum lateness subject to ready times and due dates. Problems with lateness minimization measure are known NP-complete. However, polynomial time algorithms are possible if jobs are clustered. Thus, a polynomial time algorithm is derived for the problem by use of dominant solution properties. And a heuristic approach is tried for jobs which are not clustered. Numerical examples are tested for the algorithm illustration.