A survey of scheduling problems with uncertain interval/bounded processing/setup times

Scheduling plays an important role in service and manufacturing environments for the delivery of reliable products on time. The scheduling literature reveals that the vast majority of the investigated scheduling problems are for the deterministic case where all parameters of jobs are known in advance and are fixed. However, in some real-world environments, the assumption of fixed parameters of jobs is not valid since job parameters are uncertain. An uncertain parameter can be modelled as having a probability distribution, or it can be modelled as a fuzzy number, or it can be modelled as a random variable within some interval with lower and upper bounds, distribution free. If the uncertain parameter, e.g., processing time, is modelled as a random variable within some lower or upper bounds, it is called interval or bounded processing time. The objective of this paper is to survey the investigated scheduling problems with interval or bounded processing/setup times. The scheduling literature is reviewed, the addressed problems are analyzed, and classified based on shop environments (single machine, parallel machine, flowshop, job shop), performance measures, the approach taken in the papers to solve the considered problem, and interval/bounded processing times or setup times. Some future research opportunities with interval/bounded processing/setup times are presented.