The 2-valued case of makespan minimization with assignment constraints

Authors:
Stavros G. Kolliopoulos;Yannis Moysoglou
Affiliations:
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Panepistimiopolis Ilissia, Athens 157 84, Greece;Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Panepistimiopolis Ilissia, Athens 157 84, Greece
Venue:
Information Processing Letters
Year:
2013

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Abstract

We consider the following special case of minimizing makespan. A set of jobs J and a set of machines M are given. Each job j@?J can be scheduled on a machine from a subset M"j of M. The processing time of j is the same on all machines in M"j. The jobs are of two sizes, namely b (big) and s (small). We present a polynomial-time algorithm that approximates the value of the optimal makespan within a factor of 1.883 and some further improvements when every job can be scheduled on at most two machines.