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mining by open pit and underground methods and transition from open pit to underground mining are among the most important challenges in mining engineering, and have been recently considered in many research investigations. Different researchers have attempted to solve these problems and presented solutions based on empirical, heuristic, and mathematical programming methods. In these works, the transition problem has been examined in three modes: (1) optimizing transition from open pit to underground mining, (2) determining the point, depth, or limit of transition from open pit to underground operation, and (3) determining the time of transition. Bakhtavar, Shahriar, and Mirhasani (2012) reviewed the solutions proposed for the transition problem, a summary of which is given in Table I, together with the most recent solutions. It can be seen from Table I that few of the solutions have an empirical basis, ultimately leading to only an estimated response. The main weaknesses of the empirical solutions are ignoring the time value of money, production planning, and uncertainties. Most of the solutions for the transition problem have a heuristic basis and follow a similar process by use of the cash flow solution introduced by Nilsson (1982). They make an economic comparison among different options, including open pit and underground mining. Some other heuristic solutions, such as the algorithms proposed by Bakhtavar and Shahriar (2007) and Shahriar (2007) and Bakhtavar, Shahriar, and Oraee (2008a, 2008b) are based on an economic comparison of open pit and underground mining methods at different levels of an ore deposit. The main drawback of the heuristic solutions is their complete dependence on the optimization algorithms of surface and underground mining. For this reason, they cannot solve the transition problem independently. Another deficiency of the heuristic solutions, excluding the research presented by Opoku and Musingwini (2013), is failure to consider uncertainty. This deficiency leads to the small difference between their responses and the reality. The working steps of the solution presented by Opoku and Musingwini (2013) are mostly similar to the solution by Visser and Ding (2007), except that Opoku and Musingwini emphasized uncertainties during geological simulation (in kriging) and prepared production planning and economic models employing conventional mining software. Among the solutions for the transition problem, studies by Bakhtavar, Shahriar, and Mirhasani (2012), Newman, Yano, and Rubio (2013), Chung, Topal, and Ghosh (2016), and MacNeil and Dimitrakopoulos (2017) have a mathematical basis and are more stable than others. These methods can be considered a foundation and then developed or modified to achieve an optimum solution to the transition problem, similar to the development of the optimization models of final pit limits and production planning. A stochastic mathematical model for determination of transition time in the non-simultaneous case of surface and underground mining by E. Bakhtavar*, J. Abdollahisharif†, and A. Aminzadeh*