In stratified deposits such as coal, lignite, and phosphate, the ratio of waste to ore is often very high and one of the major concerns relates to waste placement to in-pit or external dumps. Unless it is known which waste dump will be used for the extracted material, depending on the availability of the waste dumps (in-pit or external), the haulage cost can largely vary at different times. Hence it is crucial to incorporate the waste placement decisions into the pit scheduling problem for better planning. Ignoring the waste placement and thereby the different waste haulage costs at different times could lead to flawed results. Traditionally, the pit scheduling problem and dump scheduling are studied in isolation with a few exceptions in the literature. Our aim is to fill the research gap in pit scheduling of stratified deposits with in-pit waste dumping and haulage road options. This paper focuses on the integration of pit and dump scheduling including in-pit dumping strategy. This strategy requires a factor of the lag to be considered with the working face. In this paper, we also demonstrate how to maintain a lag space with the dynamically changing mining face and consider waste rock placements in correct dumping (in-pit or external) locations.