Relationship between common objective functions, idle time and waiting time in permutation flow shop scheduling

This paper focuses on two components of idle time and waiting time, namely core idle time, ∑CITi, and core waiting time, ∑CWTj. Both measures are relevant indicators of the efficiency of production systems, since they are directly related to machine utilization and to the flow of jobs, and they can be used as scheduling criteria if no-idle and no-wait constraints do not have to be strictly enforced. However, they have been scarcely considered in the literature, and their relationship with other objectives in the permutation flowshop literature (makespan or Cmax and total completion time or ∑Cj), has not been studied. To bridge this gap, the alignment between ∑CITi and ∑CWTj, and the classical scheduling criteria is studied. First, it is shown that ∑CWTj (∑CITi) is tantamount to ∑Cj (Cmax) for some special cases. Secondly, the general case with randomly generated processing times is computationally analysed using exact methods. Results show alignment between ∑CWTj and ∑Cj and between ∑CITi and Cmax, being the alignment stronger for the first pair of objectives. Based on the analysis, conclusions about the possibilities for the permutation flowshop problem with these new objectives are established.