Process planning is an important decision-making task in manufacturing that serves as a bridge between design and manufacturing. It is used to determine the most efficient and economical way to manufacture a part based on resource availability and their technological capabilities by satisfying various precedence constraints between manufacturing operations. Process planning involves a number of steps to transform a raw material into a finished part, including selection of operations, machines, cutting tool and operation sequences. These decisions are crucial, as they directly impact the carbon emissions associated with machining processes. Operation sequencing in process planning generates the optimal order of machining operations by reducing the production time and cost. In today's highly competitive environment, manufacturers strive to produce economically viable products, often exploring a wide range of techniques—sometimes at the expense of environmental sustainability. The surge in industrial activities within rapidly developing economies, such as USA and India, has rendered it imperative to align productivity with environmental sustainability. It is estimated that the manufacturing industry accounts for 54% of total energy consumption and 20% of global carbon emissions. Experts predict a 17% increase in global manufacturing emissions between 2024 and 2050. To mitigate these challenges, we propose an approach that focuses on carbon-conscious operation sequence optimization in machining while minimizing production costs. Very few studies have so far examined process planning with an emphasis on environmental impact. Specifically, a need is felt for exploring operation sequence optimization by balancing economic and environmental considerations. This is also anticipated to help in reducing non-productive time and cost with better utilization of resources while minimizing waste. So, our study proposes a multi-objective operation sequence optimization that minimizes simultaneously the carbon emission as well as total production cost in machining. Firstly, the required operations for the machinable features of a part are selected based on part design specification and process capabilities, and carbon emissions are quantified for individual processing operations. Secondly, a multi-objective optimization model for operation sequencing is developed with the objectives of minimal carbon emissions and reduction of production costs. Due to its NP-hard nature of the search for an optimal solution, the operation sequence optimization problem is often challenging and time-consuming while solving it using exact mathematical modeling techniques. However, metaheuristic approaches offer the potential to obtain the near-optimal solution in a reasonable time frame. To solve the proposed models, we aim to implement standard meta-heuristic algorithms like Non-dominant Sorting Genetic Algorithm II (NSGA-II), Multi-objective Particle Swarm Optimization (MOPSO) and Multi-objective Ant colony Optimization (MOACO). Finally, case studies will be used to validate the performance of the above optimization models, and to perform comparison to verify the effectiveness of proposed techniques in providing low-carbon emissions with cost-effective machining operation sequences. The research work reported in this paper seeks to provide essential insights into the future of sustainable manufacturing process planning by balancing the trade-off between carbon emissions and production economics. This study also allows the administrators to effectively and accurately understand the concentration areas of carbon emissions and assists operators in managing carbon emissions data.