A branch-and-bound procedure for a single-machine earliness scheduling problem with two agents
This paper addresses a two-agent scheduling problem on a single machine where the objective is to minimize the total weighted earliness cost of all jobs, while keeping the earliness cost of one agent below or at a fixed level Q. A mixed-integer programming (MIP) model is first formulated to find the optimal solution which is useful for small-size problem instances. To solve medium- to large-size problem instances, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is then provided to derive the optimal solution. A simulated annealing heuristic algorithm incorporating with a heuristic procedure is developed to derive the near-optimal solutions for the problem. A computational experiment is also conducted to evaluate the performance of the proposed algorithms.
single-machine scheduling two-agent total weighted earliness cost