First thing you need to do is find out if this person is actually being complacent; just because everyone else is running about like headless chickens, fighting fires and making a big fuss about how busy they are it doesn't mean that the person serenely sitting quietly and working is being complacent. They may just be being more efficient than everyone else! You need to look at actual output rather than activity. Only if the output is missing or flawed is there actual evidence of complacency.
Second thing you have to do is assess whether the complacency you find is consistent. Often you will find that someone is underperforming short term or only in a specific part of their role. This is not to say that you should allow or condone this; it still must be tackled, but you need to be able to be specific about the area of shortcoming rather than raising a 'blanket' matter. For instance, Dave doesn't do the final checks of the figures before sending them, rather than Dave is unreliable, or Dave didn't do the final checks last week, rather than Dave never does the final checks.
Now that you have actually identified and measured the complacent behaviour you need to investigate the underlying cause. Yes, you could just rely on the authority of your position to tell Dave to sort himself out or start walking, but that will present you with a heap of other problems that are worth avoiding at this point. By finding the cause you, or Dave, can manage it, if you don't find the cause the problem will simply come back, or worse, spread to others.
There is a little 'equation' that goes P=S+W. This is Performance = Skill + Will. Complacency is the Will part, so for the purposes of this article we aren't going to consider the option that Dave doesn't do the final checks because he lacks the Skill to do them, but simply because he is lacking the Will to do them (or to do them properly).
Often you will find that once a person realises that their complacency has been noticed and commented upon, they will start to improve their performance; in everyday circles this is the boss is watching, look busy response, in more scientific circles it is called the Hawthorne Effect.
If the cause of the apparent complacency is some element of genuine hardship; exhaustion caused by ill health or family problems for instance, then as a manager you may find that simply suggesting a couple of days off work might help the individual to sort out their problem and return to form.
If the person has no genuine and acceptable reason for being complacent then you can follow a simple 5 step process to get them back on track. It isn't heavy and it isn't legalistic; it is a quick and straightforward approach.
1. Clearly explain what you have seen that is not acceptable; be specific and be brief, for example, you have been late three times this month, on the 3rd, the 7th and the 11th. Each time by over 30 minutes.
2. Briefly explain why this is a problem...avoid just going for the mechanistic; Your contracted hours are 9 to 5 and you aren't doing them
Instead try to focus on the impact their complacency is having, for example,
By coming in late other people are having to cover for you and that is not fair on them
3. Tell them what changes you expect to see in their behaviour- don't beat around the bush; be blunt, be absolutely clear, make it measurable, for example
I'll expect to see you here on the dot of 9am every morning for the next month
If the response if the individual at this stage is contriteness and an assurance of improvement, skip to step 5
4. If, and only if, they still don't seem to be taking this seriously, explain the positive consequences of their improvement;
If you do this then I'll still be able to consider your request for leave. If that still doesn't seem to be getting through go for the negative consequences of failing to improve, for example,
If you are late again without a really good reason then I shall put you on a formal warning for dismissal
5. Set a review date; as Oscar Wilde said, "Nothing concentrates the mind so much as knowing you are to be hanged in the morning"
If the person repeats their unacceptable behaviour you need to instigate formal proceedings to get them out of the organisation; if you don't others will start to copy this behaviour. If they improve, thank them, and then don't mention it again!