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

Abstract

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 Jj is not declared until it is released at time rj. Our objective is to minimize the total completion time plus the total soft penalty cost of all jobs, where “soft penalty” cost of job Jj is α(Sj- rj) with soft penalty coefficient α> 0 , Sj and rj are starting processing time and release date of job Jj, 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.