The Browne–Yechiali single‐machine sequence is optimal for flow‐shops

An optimal polynomial time solution for minimum makespan on a single machine with linear job deterioration is known in the scheduling literature for about 20 years (Browne and Yechiali, 1990 ). An extension of this result to flow‐shop settings has not been published since then. In this note we provide this result: we show that the Browne–Yechiali sequence remains optimal for flow‐shops, i.e. we present a polynomial time $(O(n\log n))$ solution for minimum makespan on an m‐machine flow‐shop with linear job deterioration.