Yes, as Clio says.
Assuming you are having to lose some jobs, D, then its a pity that they super-dooper new kit you were given doesn't tell you about the process, as that is the most important part to get right.
There's some info here - suggest you nose around a bit in it.
http://www.businesslink.gov.uk/bdotg/action/de tail?r.l1=1073858787&r.l3=1074019927&r.lc=en&r .t=RESOURCES&type=RESOURCES&itemId=1073792400& r.i=1073792401&r.l2=1073876974&r.s=sc
You will find that you have a fair amount of flex in the criteria you use - just don't use just one criteria and think about whether the criteria you do choose might be automaticaly unfair to one group of workers.
You can use std of work performance and/or attendence records - these are often favourite because they are generally maintained by businesses and aren't easily challenged (at ET).
I agree that losing LIFO is a poor idea - indeed I often feel that FIFO would be far better but never seen an organisation bold enough to try it.
Make sure you define your pool for selection initially - in your department's case it is probably everyone.
Then consult, consult, consult. Employers usually get caught out because they fail to do the consult bit correctly - your new manual will presumably tell you that.