Two-agent scheduling with linear deteriorating jobs on a single machine.

*(English)* Zbl 1148.90324
Hu, Xiaodong (ed.) et al., Computing and combinatorics. 14th annual international conference, COCOON 2008, Dalian, China, June 27–29, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-69732-9/pbk). Lecture Notes in Computer Science 5092, 642-650 (2008).

Summary: 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.

##### MSC:

90B35 | Scheduling theory, deterministic |