Lagrangian relaxation algorithms for real-time hybrid flowshop scheduling with finite intermediate buffers

Abstract

We investigate the problem of scheduling N jobs on parallel identical machines in J successive stages with finite buffer capacities between consecutive stages in a real-time environment. The objective is to find a schedule that minimizes the sum of weighted completion time of jobs. This problem has proven strongly NP-hard. In this paper, the scheduling problem is formulated as an integer programming model considering buffers as machines with zero processing time. Lagrangian relaxation algorithms are developed combined with a speed-up dynamic programming approach. The complication and time consumption of solving all the subproblems at each iteration in subgradient optimization motivate the development of the surrogate subgradient method, where only one subproblem is minimized at each iteration and an adaptive multiplier update scheme of Lagrangian multipliers is designed. Computational experiments with up to 100 jobs show that the designed surrogate subgradient algorithm provides a better performance as compared to the subgradient algorithm.

The hybrid flow shop scheduling problem

“…A regular HFS, this time with the sum of weighted completion times criterion, is approached with mathematical programming and lagrangian relaxation in [189]. The same problem and objective, but with the addition of limited buffers, is studied in [188]. A rescheduling problem that considers inventory constraints is dealt with in [166].…”

New Developments and Decision-makings in Production and Retailing

“…The third is dynamic programming (Roman 1971;Ibraki and Nakamura 1994;Lorigeon et al 2002;Choi et al 2004), which is also an enumeration technique used to search for an optimal solution among the possible solutions. And the fourth is the relaxation method (Narahari and Srigopal 1996;Zhang et al 2000;Hwang and Chang 2003;Tang and Xuan 2006) which allows a near-optimal solution to be reached with less computation.…”

Practical solutions for a dock assignment problem with trailer transportation

“…Many research articles related to flexible flow-shop scheduling are available, but most of these do not handle unequal ready times. Both approximation (see, e.g., Tang and Xuan 2006;Nichi et al 2010) and optimal approaches (for instance Kis and Pesch 2005;Haouari et al 2006) have been published.…”