A single-machine scheduling problem with two agents and decreasing linear deteriorating jobs

This paper deals with the two-agent scheduling problem with decreasing linear deteriorating jobs on a single machine, where the goal is to minimize the total completion time of the first agent with the restriction that the maximum cost of the second agent cannot exceed a given upper bound. Two agents compete to perform their respective jobs on a common single machine, and each agent has his own criterion to optimize. We introduce a decreasing linear deterioration model into the two-agent single-machine scheduling where the processing times of jobs are defined as a decreasing linear function of their starting times. We propose the optimal properties and present the optimal polynomial time algorithm to solve the scheduling problem.