Two-machine No-wait Flowshop Scheduling With Deteriorating Effect And Convex Resource-dependent Processing Times

In classical scheduling theory, it is assumed that the job processing times fixed and constant values. In practice, however,we often encounter settings in which job processing times may be subject to change due to the phenomenon of deterioration.Job deterioration appears, for instance, in the steel production where the temperature of an ingot drops below a certain level while waiting to enter a rolling machine, which requires reheating of the ingot before rolling.Similar situations will also occur in scheduling maintenance tasks, national defense or cleaning assignments, where any delay in processing a job is penalized by incurring additional time for accomplishing the job.In this study,we consider scheduling problems with convex resource dependent processing times and deteriorating jobs,in which the processing time of a job is a function of its starting time and its convex resource allocation.The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately.This paper focus on the single-machine problems with objectives of minimizing a cost function containing makespan,total completion time,total absolute differences in completion times and total resource cost,and a cost function containing makespan,total waiting time,total absolute differences in waiting times and total resource cost,and a cost function containing makespan,total waiting times and total resource cost.It shows that the problems remain polynomially solvable under the proposed model.