The problem of minimizing the maximum delivery times while scheduling jobs on the single processor is a classical combinatorial optimization problem. Each job has a release time, processing time and a delivery time. The objective is to minimize the time, by which all jobs are delivered. This problem is denoted by 1 | r _j, q _j| C _max, has many applications, and it is NP-hard in strong sense. The problem is useful in solving flowshop and jobshop scheduling problems. The goal of this paper is to propose a new 3/2—approximation algorithm, which runs in O(nlog n) times for scheduling problem 1 | r _j, q _j| C _max. We present an example which shows that the bound of 3/2 is tight. To compare the effectiveness of proposed algorithms we tested random generated problems of up to 5000 jobs.