Two-Agent Scheduling with Linear Deteriorating Jobs on a Single Machine

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This paper considers the two-agent scheduling problems with linear deteriorating jobs to be processed on a single machine. By a deteriorating job we mean that the processing time of the job is a function of its starting time. Two agents compete for the usage of a common single machine and each agent has his own criterion to optimize. There are four objective functions: makespan, maximum lateness, maximum cost, and total completion time. Some basic properties of two different scheduling problems to minimize the objective function for one agent with a constraint on the other agent’s objective function are proved. Based on these properties, the optimal algorithms with polynomial time are presented for two different scheduling problems, respectively.

This work is supported by NSFC (Grant No. 70425003 and Grant No. 60674084), National 863 High-Tech Research and Development Program of China through approved No.2006AA04Z174 .