Decentralization Cost in Two-Machine Job-shop Scheduling with Minimum Flow-time Objective

Scheduling problems naturally arise in supply chains, ranging from manufacturing and business levels in a single firm through multi-organizational processes. In these environments, jobs are served by various resources. As scheduling choices are often decentralized, an inferior system solution may occur. In this paper we investigate a decentralized job-shop system, where jobs are processed utilizing two resources, each of which is minimizing their own flow-time objective. Analyzing the system as a non-cooperative game, we investigate the decentralization cost (DC), the ratio between the best Nash equilibrium and the centralized solution in terms of the system flow-time. We show that, even when both the system manager and each resource manager aim at minimizing the same (flow-time) objective, inefficiency can occur for small as well as large instances. For flow-shop settings we provide tight bounds on the maximal DC and insights regarding settings that lead to significant DC values. We name such settings as flow-shop misaligned. For job-shop settings, we present a typical structure of jobs that leads to large values of DC. We conclude that managers within such decentralized systems should implement strategies that overcome the inherent inefficiency. A simple mechanism is proposed to reduce the DC value, and its useful effectiveness is analyzed numerically.