Public bus transit service (PBTS) is recognized as a highly effective mode of transportation, offering accessibility, affordability, and adaptability that contribute to its critical role in transportation networks. The extensive literature on PBTS encompasses various aspects, with mathematical programming emerging as a widely employed methodology to tackle the public bus transit network design and operations planning problem (PBTNDP&OPP). In this paper, first, we employ the critical path method (CPM) to visually map the development of existing literature on the application of mathematical programming in PBTND&OPP by focusing on manuscripts published in top-tier journals. The objective is to identify key subproblems extensively studied in the literature and recently emerging topics. Then, we conduct a comprehensive review of recent applications of mathematical programming in PBTND&OPP, encompassing sustainable and green practices, as well as emerging

transportation technologies and modes within PBTS. These two sub-problems have been identified as recently emerged and hot topics in the literature of mathematical programming and PBTND&OPP, based on the provided CPM in the first step. Selected papers for each sub-problem are examined, providing insights into problem formulation, objective functions, decision variables, demand patterns, network structures, and key findings. Based on the literature review, we systematically identify research gaps in each sub-problem and offer directions and suggestions for future studies. While there is a considerable body of literature that has applied mathematical programming to investigate these two emerging topics, our review highlights that the existing literature is still in the early stages of development. Hence, numerous problems relating to these topics remain ripe for exploration

through mathematical programming. Examining the effects of sustainable development policies or the introduction of emerging technologies on the reliability and long-term performance of PBTSs represents a significant gap in current research. On the methodological side, the main gap in the literature is the absence of efficient hybrid approaches, where mathematical programming is integrated with other approaches to provide more robust results and to capture the dynamics of PBTSs. Our work aims to advance knowledge in the field of PBTND&OPP and inspire further research endeavors.