Cloud computing, a novel and promising methodology in the distributed computing domain, provides a pay-per-use framework to solve large-scale scientific and business workflow applications. These workflow applications have a constraint that each of them must completed within the limited time (deadline constraint). Therefore, scheduling a workflow with deadline constraints is increasingly becoming a crucial research issue. However, many analytical reviews on scheduling problems reveal that existing solutions fail to provide cost-effective solutions and they do not consider the parameters like CPU performance variation, delay in acquisition and termination of Virtual Machines (VMs). This paper presents a Cost-Effective Firefly based Algorithm (CEFA) to solve workflow scheduling problems that can occur in an Infrastructure as a Service (IaaS) platform. The proposed CEFA uses a novel method for problem encoding, population initialization and fitness evaluation with an objective to provide cost-effective and optimized workflow execution within the time limit. The performance of the proposed CEFA is compared with the state-of-the-art algorithms such as IaaS Cloud-Partial Critical Path (IC-PCP), Particle Swarm Optimization (PSO), Robustness-Cost-Time (RCT), Robustness-Time-Cost (RTC), and Regressive Whale Optimization (RWO). Our experimental results demonstrate that the proposed CEFA outperforms current state-of-the-art heuristics with the criteria of achieving the deadline constraint and minimizing the cost of execution. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.