A best possible online algorithm for minimizing the total completion time and the total soft penalty cost

Green high-performance concrete is widely adopted in the construction industry to reduce building energy consumption and enhance quality. Prompt delivery of green high-performance concrete is vital for successful project completion because the processes relating to green high-performance concrete are the critical path in most cases, namely that the project delay will occur if the works involving green high-performance concrete are delayed caused by late delivery of green high-performance concrete. This research proposes an online scheduling model, which takes into account the idle time of green high-performance concrete in manufacturing, that is the time from release until start, in order to improve prompt delivery of green high-performance concrete. Formally, there are irrelevant jobs arriving online over time and the fundamental knowledge of each job J_j is not declared until it is released at time r_j . Our objective is to minimize the total completion time plus the total soft penalty cost of all jobs, where “soft penalty” cost of job J_j is α (S_j-r_j) with soft penalty coefficient α > 0 , S_j and r_j are starting processing time and release date of job J_j , respectively. For this problem, by applying the technique “Peeling Onion”, it is explicitly derived that the classic online algorithm DSPT is best possible with competitive ratio 2+α .