Decentralization cost in two-machine job-shop scheduling with minimum flow-time objective

A decentralized two-machine job-shop system is considered, where each machine minimizes its own flow-time objective. Analyzing the system as a non-cooperative game, we investigate the Decentralization Cost (DC), the ratio in terms of the system flow-time between the best Nash equilibrium and the centralized solution. Settings generating significant inefficiency are identified and discussed. We provide bounds on the maximal DC, and prove they are tight for two-job problems. For larger problems, we use a cross entropy meta-heuristic that searches for DC maximizing job durations. This supports the tightness of the proposed bounds for a flow-shop. Additionally, for a flow-shop, a simple, scheduling-based mechanism is proposed, which always generates efficiency.