Lean and agile principles have attracted considerable interest in the past few decades. Industrial sectors throughout the world are upgrading to these principles to enhance their performance, since they have been proven to be efficient in handling supply chains. However, the present market trend demands a more robust strategy incorporating the salient features of both lean and agile principles. Inspired by these, the leagility principle has emerged, encapsulating both lean and agile features. The present work proposes a leagile supply chain based model for manufacturing industries. The paper emphasizes the various aspects of leagile supply chain modeling and implementation and proposes a new Hybrid Chaos-based Fast Genetic Tabu Simulated Annealing (CFGTSA) algorithm to solve the complex scheduling problem prevailing in the leagile environment. The proposed CFGTSA algorithm is compared with the GA, SA, TS and Hybrid Tabu SA algorithms to demonstrate its efficacy in handling complex scheduling problems.