Multi-agent heterogeneous parallel machines scheduling problem with energy cost and just-in-time jobs

In the classic models of scheduling problems, researchers mostly concentrate on the objectives considering jobs completion time. Due to the relation among economy, energy and environmental concerns, attention to the energy use of machines have been considered by researchers in the field of scheduling in recent years. Also, In the literature of scheduling problems, it is mostly assumed that one agent try to optimize the problem. But, occasionally there are several agents that each has their own jobs and they must use a series of common resources to process them. In this study, a two-agent heterogeneous parallel-machines scheduling problem is studied in which the process speed of each job on each machine is adjustable. Since there is a direct link between the energy used in machines and process speed, the used energy costs affect on scheduling problem. In this study, the first agent is tried to minimize total tardiness penalty as well as energy costs of production machines and the second agent is tried to minimize total tardiness and earliness. The suitable schedule should be considered to allocate and sequence jobs of agents to the common resources to optimize appropriately the agent’s objective functions. Since the proposed problem is Np-hard, in order to solve it in large scale problems, a Memetic algorithm is developed and to verify the performance of this algorithm, we take into comparison the results of Memetic algorithm with the results of GAMS software and of another meta-heuristic algorithm.