Single machine scheduling with a variable common due date and resource-dependent processing times

Authors:
C. T. Daniel Ng;T. C. Edwin Cheng;Mikhail Y. Kovalyov;S. S. Lam
Affiliations:
Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Minsk 220012, Belarus;School of Business & Administration, The Open University of Hong Kong, Homantin, Kowloon, Hong Kong
Venue:
Computers and Operations Research
Year:
2003

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Abstract

The problem of scheduling n jobs with a variable common due date on a single machine is studied. It is assumed that the job processing times are non-increasing linear functions of an equal amount of a resource allocated to the jobs. The due date and resource values can be continuous or discrete. The objective is to minimize a linear combination of scheduling, due date assignment and resource consumption costs. The resource consumption cost function may be non-monotonous. Algorithms with O(n2 log n) running times are presented for scheduling costs involving earliness/tardiness and number of tardy jobs. Computational experiments show that the algorithms can solve problems with n= 5,000 in less than a minute on a standard PC.