This paper presents the scientific framework underpinning the resource valuation and optimisation model (RVOM). The RVOM is a partial differential equation based real options software package, which helps mine owners optimally plan their operations, understand their project risks, and make defensible valuations. This is achieved in the presence of both financial and physical uncertainty, as well as processing capacity constraints. The RVOM can be applied to any multi-ore mine, open pit or otherwise, where the block-order of extraction has already been planned using existing software tools such as the Gemcom Whittle strategic mine planning package. The RVOM can also take account of multiple commodities within a single mine, and multiple forms of price behaviour. The three key outputs from the RVOM are: valuation, optimal decision and probability of decision. Adecision takes account of upfront costs, and can include an unlimited number of transitions between: normal operation, expanded operation, care and maintenance and abandonment (and variants thereof). The RVOM then employs stochastic process theory to determine the probability of reaching these decisions. This gives the mine operators clear indications as to where their risks lie, aiding their mine planning. A clear example of the RVOMs usage to a case-study gold mine is presented, demonstrating its broad applicability, the added value it can create and how users can easily make use of the RVOM's state-of-the-art algorithmic engine.