A fully polynomial approximation scheme for the problem of scheduling n deteriorating jobs on a single machine to minimize makespan is presented. Each algorithm of the scheme runs in O(n5L4/ε3) time, where L is the number of bits in the binary encoding of the largest numerical parameter in the input, and ε is required relative error. The idea behind the scheme is rather general and it can be used to develop fully polynomial approximation schemes for other combinatorial optimization problems. Main feature of the scheme is that it does not require any prior knowledge of lower and/or upper bounds on the value of optimal solutions.
