《1998 Efficient Lagrangian relaxation algorithms for industry size job-shop scheduling problems》.pdfVIP

IIE Transactions (1998) 30, 1085-1097 Efficient Lagrangian relaxation algorithms for industry size job-shop scheduling problems CHRISTOS A. KASKAVELIS and MICHAEL C. CARAMANIS* *Department of Manufacturing Engineering, Boston University, 15 St. Mary b Street, Boston MA 02215, USA E-mail: mcaraman@bi.edu Received September 1995and accepted January 1998 1 1 We improve thejob specificdecomposition Lagrangian relaxation algorithm applied to industry sizejob shop scheduling problems 0 2 with more than 10000 resource constraints. We introduce two new features in the Lagrange multiplier updating procedure. First, y l the usual solution of all subproblemsfollowed by dual cost estimation and update of multiplier values is replaced by the estimation u J of a surrogate dual cost function and a more frequent update of multipliers is implemented after each subproblem solution. 7 0 Second, an adaptive step size in the subgradient based multiplier update is introduced. Asymptoticproperties of the surrogate dual 7 5 cost function are obtained and the proposed algorithmic improvements are evaluated in extensive numerical examples including : 3 published data used by other researchers, as well as extensive real industrial scheduling system data. 0 t a ] y t 1. Introduction algorithm can both reduce tardiness and shorten cycle i s r times. e v i Job-shop scheduling is essential for on-time manufac- This paper does not claim major theoretical contribu- n U n turing and has been widely investigated [1,2]. This paper tions to the Lagrangian relaxation literature.