The customer order scheduling problem has received much attention recently due to its relevance to real world applications. In this study, the minimization of the total completion time of customer orders is studied in a dedicated machine environment, i.e. each order consists of one job on each machine. Two iterated greedy algorithms are presented that make use of problem properties and apply a new local search as well as a new construction function. In a computational experiment, both algorithms outperform two state-of-the-art approaches and prove their suitability to solve the customer order scheduling problem with dedicated machines.