We consider a single batch machine on-line scheduling problem with delivery times. In this paper on-line means that jobs arrive over time and the characteristics of jobs are unknown until their arrival times. Once the processing of a job is completed it is delivered to the destination. The objective is to minimize the time by which all jobs have been delivered. For each job J
j
, its processing time and delivery time are denoted by p
j
and q
j
, respectively. We consider two restricted models: (1) the jobs have small delivery times, i.e., for each job J
j
, q
j
≤p
j
; (2) the jobs have agreeable processing and delivery times, i.e., for any two jobs J
i
and J
j
, p
i
>
p
j
implies q
i
≥q
j
. We provide an on-line algorithm with competitive ratio (√5+1)/2 for both problems, and the results are the best possible.
