A polynomial-time algorithm for a flow-shop batching problem with equal-length operations

A flow-shop batching problem with consistent batches is considered in which the processing times of all jobs on each machine are equal to p and all batch set-up times are equal to s. In such a problem one has to partition the set of jobs into batches and to schedule the batches on each machine. The processing time of a batch Bi is the sum of processing times of operations in Bi and the earliest start of Bi on a machine is the finishing time of Bi on the previous machine plus the set-up time s. Cheng et al. [2] provided an O(n) pseudopolynomial-time algorithm for solving the special case of the problem with two machines. Mosheiov & Oron [3] developed an algorithm of the same time complexity for the general case with more than two machines. Ng and Kovalyov [9] improved the pseudopolynomial complexity to O ( √ n). In this paper we provide a polynomial-time algorithm of time complexity O ( log n ) .