Stope boundary optimization for an underground copper deposit using mixed integer linear programming based algorithm

Optimal ore body boundary and production area geometry (Stope) are essential to maximize the profit from an underground mining project subject to inherent physical, geotechnical and geological constraints. Number of researches have been introduced for stope boundary optimization but true optimal solution in three dimensional spaces is still out of reach. This article proposed a computer programming based optimization model using mixed integer linear programming based algorithm that incorporate stope boundary optimization with varying cost of mining and selling price of the metal. An actual ore body model was taken as case study to implement the algorithm in real mining scenario. In validation study, it is observed that, by using proposed model, the profit can be increased by 10% - 15% as compared to the present stoping practice. Simulating the optimal stope boundary by changing the various cost and price parameters helps to opt the best possible option for a given mining scenario to make most realistic plan.

Download Full-text

A mixed integer linear programming framework for optimising the extraction strategy of open pit – underground mining options and transitions

International Journal of Mining Reclamation and Environment ◽

10.1080/17480930.2019.1701968 ◽

2019 ◽

Vol 34 (10) ◽

pp. 700-724

Author(s):

Bright Oppong Afum ◽

Eugene Ben-Awuah ◽

Hooman Askari-Nasab

Keyword(s):

Linear Programming ◽

Integer Linear Programming ◽

Mixed Integer Linear Programming ◽

Underground Mining ◽

Open Pit ◽

Mixed Integer ◽

Programming Framework

Download Full-text

Minimum Spillage from Reservoirs using Mixed Integer Linear Programming

Journal of Engineering Research ◽

10.36909/jer.v9iicrie.11663 ◽

2021 ◽

Vol 9 (ICRIE) ◽

Author(s):

Kamel A. Almohseen ◽

Keyword(s):

Linear Programming ◽

Integer Linear Programming ◽

Simplex Method ◽

Mixed Integer Linear Programming ◽

Optimal Solution ◽

Mixed Integer ◽

Integer Variables

The use of the traditional linear programming is not possible when an if-condition is to be imposed on the model unless some modifications are made. The difficulty arises due to the fact that the inclusion of if-condition to the generic formulation of the linear programming and its mechanism called "simplex method" is not a trivial task. The mixed integer linear programming seems to be a good candidate to achieve this goal. However, two issues should be satisfied beforehand if one would like to minimize the spill. 1. the reservoir should be full up to the spillway crest level in order for the spillage to occur. 2. the next state of the reservoir after the spill has been occurred should be full as well. Adding binary integer variables to the model helps in achieving the optimal solution in terms of minimum sum of spillage without violating any of the underlying constraints. When the input to the model being altered, the results showed that the model can cope with the uncertainty inherent in any natural inflow process in terms of spillage minimization.

Download Full-text

Analysis of Mixed-Integer Linear Programming Formulations for a Fuel-Constrained Multiple Vehicle Routing Problem

Unmanned Systems ◽

10.1142/s2301385017500091 ◽

2017 ◽

Vol 05 (04) ◽

pp. 197-207 ◽

Cited By ~ 6

Author(s):

Kaarthik Sundar ◽

Saravanan Venkatachalam ◽

Sivakumar Rathinam

Keyword(s):

Linear Programming ◽

Vehicle Routing ◽

Integer Linear Programming ◽

Vehicle Routing Problem ◽

Mixed Integer Linear Programming ◽

Optimal Solution ◽

Branch And Cut ◽

Mixed Integer ◽

Computational Results ◽

Routing Problem

This paper addresses a fuel-constrained, multiple vehicle routing problem (FCMVRP) in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where [Formula: see text] vehicles are stationed. The vehicles are allowed to refuel at any refueling station, and the objective of the problem is to determine a route for each vehicle starting and terminating at the depot, such that each target is visited by at least one vehicle, the vehicles never run out of fuel while traversing their routes, and the total travel cost of all the routes is a minimum. We present four new mixed-integer linear programming (MILP) formulations for the problem. These formulations are compared both analytically and empirically, and a branch-and-cut algorithm is developed to compute an optimal solution. Extensive computational results on a large class of test instances that corroborate the effectiveness of the algorithm are also presented.

Download Full-text