The customer order scheduling problem (COSP) is defined as to determine the sequence of tasks to satisfy the demand of customers who order several types of products produced on a single machine. A setup is required whenever a product type is launched. The objective of the scheduling problem is to minimize the average customer order flow time. Since the customer order scheduling problem is known to be strongly NP-hard, we solve it using four major metaheuristics and compare the performance of these heuristics, namely, simulated annealing, genetic algorithms, tabu search, and ant colony optimization. These are selected to represent various characteristics of metaheuristics: nature-inspired vs. artificially created, population-based vs. local search, etc. A set of problems is generated to compare the solution quality and computational efforts of these heuristics. Results of the experimentation show that tabu search and ant colony perform better for large problems whereas simulated annealing performs best in small-size problems. Some conclusions are also drawn on the interactions between various problem parameters and the performance of the heuristics.