AbstractConsider anm‐machine flow shop withnjobs. The processing time of jobj,j= 1,…,n, on each one of themmachines is equal to the random variableXjand is distributed according toFj. We show that, under certain conditions, more homogeneous distributionsF1,…,Fnresult in a smaller expected makespan. We also study the effect of the variability of distributionFjon the expected waiting costs of thenjobs and on the job sequencing which minimizes this total expected waiting cost. We show that the smallest (largest) variance first rule minimizes the total expected waiting cost on a single machine when the waiting cost function is increasing convex (concave). We also show that the smallest variance first rule minimizes, under given conditions, the total expected waiting cost in anmmachine flow shop when the waiting cost function is increasing convex. Similar results are also obtained for the two‐machine job shop. Similar results cannot be obtained when the processing times of jobjon the various machines are i.i.d. and distributed accordi