The environmental protection concerns and legislation are pushing companies to redesign and plan their activities in an environmental friendly manner. This will probably be done by constraining companies to emit less than a given amount of carbon dioxide per product that is being produced and transported. In addition, some companies may volunteer to reduce their carbon footprint. Consequently, companies will face new constraints that force them to reduce carbon emissions while still minimizing production and transportation costs. Transportation is at the heart of logistics activities and is one of the leading sources of greenhouse gas emissions. The emitted carbon dioxide through transportation activities is accounting for almost 80% of the total greenhouse gas emissions. The need to implement Just-In-Time (JIT) strategy for transporting small batch sizes seems to beagainst environmental concerns. The JIT principles favor small and frequent deliveries by many small rush transports with multiple regional warehouses. Although several attempts have been made to analyze green supply chain networks, little attention has been paid to develop JIT distribution models in carbon constrained environment. Incorporation of environmental objectives and constraints with JIT distribution will generate new problems resulting in new combinatorial optimization models. In addition, these objectives and constraints will add to the model complexities. Both areas require to be investigated. In this research, a bi-objective carbon-capped logistic model was developed for a JIT distribution that takes into account different carbon emission constraints. The objectives include minimization of total costs and carbon cap. Since the studied problem is Non-deterministic Polynomial-time Hard (NP-Hard), a nondominated sorting genetic algorithm-II (NSGA-II) was employed to solve the problem. For validation and verification of the obtained results, non-dominated ranking genetic algorithm (NRGA) was applied. Then, Taguchi approach was employed to tune the parameters of both algorithms; their performances were then compared in terms of some multi-objective performance measures. For further improvements of NSGA-II, a modified firefly algorithm as local searcher was applied. Seven problems with different sizes of small, medium, and large were designed in order to simulate the different cases. The findings have significant implications for the understanding of how varying carbon cap could significantly affect total logistics costs and total carbon emission. More specifically, the results also demonstrated devising policies that enable companies to decide when and how to fulfill the required carbon cap could let firms fulfill these caps at significantly lower costs with lower carbon emission. In addition to these findings, the performance of the proposed solution methodology demonstrated higher efficiency particularly in terms of less CPU time usage by 6.62% and higher quality of obtained solutions by 5.14% on average for different sizes of the problem as compared to the classical NSGA-II
