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

Authors:
Peng Liu;Lixin Tang
Affiliations:
The Logistics Institute, Northeastern University, Shenyang, China;The Logistics Institute, Northeastern University, Shenyang, China
Venue:
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Year:
2008

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Abstract

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.