Two machines flow shop with reentrance and exact time lag

¹ University of Algiers 3, Faculty of Economics and Management sciences, 2 street Ahmed Waked, Dely Brahim, Algiers, Algeria.
amrouche-karim@hotmail.com
² RECITS laboratory, Faculty of Mathematics, USTHB University, BP 32 Bab-Ezzouar, 16111 El-Alia, Algiers, Algeria.
mboudhar@usthb.dz

Received: 6 September 2013
Accepted: 1 June 2015

Abstract

This paper considers a reentrant flow shop with two machines and exact time lag L, in which each task may be processed in this order M₁,M₂,M₁ and there is an identical time lag between the completion time of the first operation and the start time of the second operation on the first machine. The objective is to minimize the total completion time. We prove the NP-hardness of a special case and we give some special subproblems that can be solved in polynomial time.