Minimization of the maximal penalty in the case of preemption of jobs

For a class of structural sets of penalty functions={_i} _i=1 ⁿ with lower quasiconvex functions _i defined for sets of jobs={_i} _i=1 ⁿ , one gives an algorithm for solving the problem n /1/ preemp ¦ max, having order 0(np), where n is the number of jobs _i and p is the total length of the completion of all jobs of the set.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 102, pp. 61–67, 1980.In conclusion, the author expresses her gratitude to K. V. Shakhbazyan for his interest in this paper.