Single-machine scheduling with deteriorating jobs under a series-parallel graph constraint

Authors:
Ji-Bo Wang;C. T. Ng;T. C. E. Cheng
Affiliations:
Department of Science, Shenyang Institute of Aeronautical Engineering, Shenyang 110136, People's Republic of China and Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowl ...;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Logistics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
Venue:
Computers and Operations Research
Year:
2008

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Abstract

This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series-parallel graph. It is shown that for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too.