Various recent scheduling literature has studied the so called customer order scheduling problem. In this class of scheduling problems, there are multiple customer orders, and each of them consists of several jobs. The order finishes and is ready to be shipped when the last job of the order finishes. In this paper, we consider the customer order scheduling problem in a permutation flow shop environment with machines. There are orders and each order has jobs. The objective is to minimize the total completion time of the orders. We present multiple problem properties and a MINLP formulation of the problem. Furthermore, four heuristics which follow the Iterated Greedy Algorithm are developed. In a computational experiment, we evaluated the four heuristics on their practicability. They showed good results in short calculation time when compared with the MINLP solution from a solver. Afterwards, we compared the four heuristics with each other for different problem sizes.