# Help on Minelib

## Minelib Description

Similar to the mixed-integer programming library (MIPLIB), we present a library of publicly available test problem instances for three classical types of open pit mining problems: the ultimate pit limit problem and two variants of open pit production scheduling problems.

Minelib initiative has been developed by:

## Block-model and Precedences files

Minelib include a block-model & precedences file for each mine. Block file is a text file with one line per block, providing different information in each case. See each instance for details.  Precedence files provide the information for each block of which blocks that should be extracted previously.  These two files provide all the basic information about each instance, and can be used for different purpose, not only the three problems defined in the document.

## Preprocessed Model Classes

From the block file information, we provide preprocessed files for three particular problem classes, the Ultimate Pit Problem (UPIT), the Constrained Pit Limit Problem (CPIT) and the more general Precedence Constrained Production Scheduling Problem (PCPSP).  We describe here the mathematical formulation of this three problems.

### Notations

Indices and sets:

• : set of time periods t in the horizon
• : set of blocks b
• : set of blocks b' that are predecessor blocks for block b
• : set of operational resource types r
• : set of destinations d

Parameters:

• : profit obtained from extracting (and processing) block b (at time period t and/or sending it to destination d)
• α: discount rate used in computing the objective function (profit) coefficients
• : the amount of operational resource r used to extract and, if applicable, process, block b (when sent to destination d)
• : minimum availability of operational resource r in time period t
• : maximum availability of operational resource r in time period t
• : arbitrary constraint coefficients on general side constraints
• , : arbitrary lower and upper bounds, respectively, on general side constraints (vectors with the number of rows equal to that in A)

Variables:

• = 1 if block b is in the final pit design, 0 otherwise
• = 1 if we extract block b in time period t, 0 otherwise
• :  fraction of block b sent to destination d in time period t