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1. Put the customer on hold for an indefinite amount of time and play some music until someone is free to accept his call. But I would risk that he hangs up and never calls again.
2. Put the customer directly on answering machine and ask him to leave his number so we can call him back.
3. Put the customer on hold, but limit the on hold time (For example to three minutes). And if after the time set nobody is free to accept his call, redirect the call to the answering machine and ask him to leave his number.
I am wondering which option I should chose.
You're addressing the wrong problem. If all your lines are busy and someone calls in, the problem to fix is not what to do with that person under those conditions, it's to fix the conditions that leave you with all lines busy. You need more staff or some other similiar solution.
In our office, our admin people answer the phone first, if it rings twice and it's not answered (because they're on the phone), then I answer the phone. And if rings about the 3rd time, the sales reps are charged with picking up the phone and at least taking a personal message. The only way someone gets put on hold or to voicemail is if everyone in the office is on the phone, or there's nobody here. Otherwise, you get a person greeting you.
And if you get transferred over to someone who's not available, the call gets transferred back to the first person almost immediately, who takes a message by hand.
If they're calling about "A" they push one and get directed to A's box.
If they're calling about "B", they push two and get B's box.
Four different aspects of my company and each has it's own box.
If I had a staff I'm quite sure I'd do this differently. I can't afford a staff though. Hell, I can barely afford me.
Interesting thoughts. Most of the time these days when someone in the office asks to take a message, the person on the other end incredulously asks why we don't have voice mail.
I'm old school that way, but it's very deliberate. You call, you speak to someone, not a phone system.
Remember the old "telephone game" where 1 person told something to person number 2, who repeated it to person #3, etc. By the time the last person said the message, it was almost always completely different from the original message.
Voice mail scenario-
Caller: "My name is John Smith and I am trying to reach Mr. West about our order of widgets. Please call me at 888-555-1234."
Recipient hears: "My name is John Smith and I am trying to reach Michael West about our order of widgets. Please call me at 888-555-1234."
Other scenario-
Phone answerer, who is annoyed at having her tweeting interrupted by having to answer the phone: "Yes?"
Caller: "My name is John Smith and I am trying to reach Mr. West about ordering some widgets. Please call me at 888-555-1234."
PA: "OK, I'll give him the message."
PA writes: "Mike- Mr. Snitch wants to know where his widgets are. Call ASAP- 888-555-123<scribble>."
PA then leaves the message on her desk and gets back to her Tweeting, meaning to give the message to Michael West at some point. Later, she can't remember if the message was for Michael West or Michael Reston. So she give it to Michael Reston and hopes for the best.