The correct answer is "had proved" because it is in the past perfect form, which is used to describe an action that was completed before another action or point in time in the past. In this sentence, the action of proving to be more cost-effective was completed before the company's decision to outsource the customer service department.

Option "proved" is incorrect because it is in the past simple form, which is used to describe an action that was completed in the past with no reference to another action or point in time in the past.

Option "has proved" is incorrect because it is in the present perfect form, which is used to describe an action that was completed at an unspecified time in the past or that began in the past and continues to the present.

Option "was proved" is incorrect because it is in the passive voice past simple (and not perfect) form.