Decentralized Makespan Minimization for Uniformly Related Agents

We consider a set of indivisible operations and a set of uniformly related agents, i.e., agents with different speeds. Our aim is to develop a task allocation algorithm that minimizes the makespan in a decentralized manner. To achieve this, we first present the Operation Trading Algorithm. We show that the algorithm guarantees a worst case approximation factor of 1.618 for the 2 agent case and \frac1+\sqrt4n-32 for the general n agent case. Further, we prove that the algorithm guarantees a near-optimal makespan for real-life scenarios with large number of operations under the assumption of a fully connected network of agents. The algorithm also guarantees an approximation factor less than 2 for any number of identical agents. Following this, we present a Decentralized random Group Formation protocol which enables the agents to implement OTA(n) in a decentralized manner in presence of communication failures. Finally, using numerical results, we show that the algorithm generates near optimal allocations even in the presence of communication failures. Additionally, the algorithm is parameter free and allows fast re-planning, making it robust to machine failures and changes in the environment.