AbstractThe paper discusses mathematical properties of the well‐known Bellman‐Johnson 3 ×nsequencing problem. Optimal rules for some special cases are developed. For the case min Bi≥ maxAjwe find an optimal sequence of the 2 ×nproblem for machinesBandCand move one item to the front of the sequence to minimize (7); when minBi≥ maxCjwe solve a 2 ×nproblem for machinesAandBand move one item to the end of the optimal sequence so as to minimize (9).There is also given a sufficient optimality condition for a solution obtained by Johnson's approximate method. This explains why this method so often produces an optima