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