Two-stage, Multiple-lot, Lot Streaming Problem for a 1 + 2 Hybrid Flow Shop

In this paper, we address a multiple-lot lot streaming problem for a two-stage hybrid flow shop, which consists of one machine at Stage 1 and two parallel (identical) machines at Stage 2. Each item of a lot requires for its processing only one of the machines at Stage 2 after its processing at Stage 1. A lot can be split into sublots where the items in a sublot are processed together. The problem is to determine an optimal sequence in which to process the lots, number of sublots for each lot, sublot sizes, and the allocation of sublots to the machines at the second stage so as to minimize two objectives: makespan, and the sum of the completion times of all the lots. We exploit some basic results derived for the single-lot problem in order to develop mathematical programming-based heuristic methods for the solution of both problem instances. Our computational investigation reveals the efficacy of these methods.