In this study we address several two-agent problems in which the measure criterion is to minimize the maximum cost or total weighted completion of all the jobs, while subject to an upper bound on the maximum cost of agent A. In term of minimizing the maximum cost of all the jobs subject to an upper bound on the maximum cost of agent A, we discuss some optimal properties and propose polynomial time solution algorithm to solve it. In term of minimizing the total weighted completion of all the jobs subject to an upper bound on the maximum cost of agent A, we analyze the complexity, show that this problem is NP-hard, and discuss it under special cases. In addition, for minimizing the total weighted completion of all the jobs subject to an upper bound on the makespan of agent A, we derive some dominance rules to be used in a branch-and-bound method and propose a heuristic for finding the optimal and nearoptimal solution, respectively. A computational simulation is also provided to determine the performance of the proposed algorithms.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.