A best possible algorithm for an online scheduling problem with deteriorating effect in steel box girder section production

The paper focuses on an online scheduling problem with the effect of deterioration to minimize the maximum delivery time in steel box girder sections. This deterioration is considered in terms of job processing and delivery. Specifically, the processing time of job Jj is defined by an increasing function of its starting time t, i.e., pj = alpha j(A + Bt), where alpha j > 0 is the processing deterioration rate of job Jj. Moreover, the delivery time of job Jj is determined with an increasing function of its completion time, i.e., qj = bjCj, where bj > 0 is the delivery deterioration rate of job Jj. For this problem, we prove the property of optimal scheduling and show that the performance ratio of any deterministic online algorithm is not less than 2+ B alpha max. Furthermore, we provide a best possible online algorithm LDDR with a competitive ratio of 2 + B alpha max. And then a concise computational simulation study is presented to show that our algorithm performs very well in practice.