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In this paper we consider the problem of scheduling n jobs such that makespan is minimized. It is assumed that the jobs can be divided into K job-classes and that the change-over time between two consecutive jobs depends on the job-classes to which the two jobs belong. In this setting, we discuss the one machine scheduling problem with arbitrary processing times and the parallel machines scheduling problem with identical processing times. In both cases it is assumed that the number of job-classes K is fixed. By using an appropriate * Corresponding author. 1integer programming formulation with a fixed number of variables and constraints, it is shown that these two problems are solvable in polynomial time. For the one machine scheduling case it is shown that the complexity of our algorithm is linear in the number of jobs n. Moreover, if the problem is encoded according to the high multiplicity model of Hochbaum and Shamir, the time complexity of the algorithm is shown to be a polynomial in log n. In the parallel machine scheduling case, it is shown that if the number of machines is fixed the same results hold. 2 Scope and PurposeOne of the key problems in manufacturing operations is to determine the assignment of jobs to machines and the sequence of the jobs on each machine. In this paper we consider an environment in which the machines are identical, change-over times in between the processing of two consecutive jobs are job-dependent and the objective is to maximize the utilization of the machines which is equivalent to minimizing the makespan. Unfortunately, such problems fall into the strongly N P-hard category. However, it is the purpose of this paper to show that the computational complexity drastically improves if the jobs are divided into a small number of groups where each group consists of "similar" jobs. Such situations can be found in applications where the jobs in a group are identical or the jobs in a group require a similar state of the machine, like e.g. color for a painting machine or toolloading in flexible manufacturing systems. We give fast algorithms for the one-machine problem and the problem with multiple machines and identical processing times.