An efficient heuristic for total flowtime minimisation in no-wait flowshops

Abstract

In this paper, we address the problem of scheduling jobs in a no-wait flowshop with the objective of minimising the total completion time. This problem is well-known for being nondeterministic polynomial-time hard, and therefore, most contributions to the topic focus on developing algorithms able to obtain good approximate solutions for the problem in a short CPU time. More specifically, there are various constructive heuristics available for the problem [such as the ones by Rajendran and Chaudhuri (Nav Res Logist 37:695–705, 1990); Bertolissi (J Mater Process Technol 107:459–465, 2000), Aldowaisan and Allahverdi (Omega 32:345–352, 2004) and the Chins heuristic by Fink and Voβ (Eur J Operat Res 151:400–414, 2003)], as well as a successful local search procedure (Pilot-1-Chins). We propose a new constructive heuristic based on an analogy with the two-machine problem in order to select the candidate to be appended in the partial schedule. The myopic behaviour of the heuristic is tempered by exploring the neighbourhood of the so-obtained partial schedules. The computational results indicate that the proposed heuristic outperforms existing ones in terms of quality of the solution obtained and equals the performance of the time-consuming Pilot-1-Chins.