Summary: An optimal solution is derived for the procedure proposed by V. L. Tong [Ann. Math. Stat. 40, 1300-1324 (1969; Zbl 0184.41702)] for the problem of simultaneously partitioning the test population means \(\mu_ i\) (1\(\leq i\leq k)\) as being less than \(\mu_ 0+\delta\) \(*_ i\) or being greater than \(\mu_ 0+\delta\) \(*_ 2\) where \(\mu_ 0\) denotes the control population mean and \(\delta\) \(*_ 1\), \(\delta\) \(*_ 2\) \((\delta\) \(*_ 1<\delta\) \(*_ 2)\) are preassigned constants. The tables of the optimal design constants are provided for implementing the procedure which guarantees a specified probability of making a correct decision regardless of the true values of the \(\mu_ i\). Savings associated with this optimal solution are illustrated numerically.