American Institute of Mathematical Sciences

Advanced
April  2016, 12(2): 403-430. doi: 10.3934/jimo.2016.12.403

An MILP approach to multi-location, multi-period equipment selection for surface mining with case studies

Christina Burt 1, , Louis Caccetta 2, , Leon Fouché 3, and  Palitha Welgama 3,

1. 

Department of Computing and Information Systems, University of Melbourne, Parkville, Australia
2. 

Western Australian Centre of Excellence in Industrial Optimisation, Curtin University of Technology, Bentley, Perth, Australia
3. 

Rio Tinto Technical Services, Perth, Australia, Australia

Received  March 2014 Revised  September 2014 Published  June 2015

In the surface mining industry, the Equipment Selection Problem involves choosing an appropriate fleet of trucks and loaders such that the long-term mine plan can be satisfied. An important characteristic for multi-location (multi-location and multi-dumpsite) mines is that the underlying problem is a multi-commodity flow problem. The problem is therefore at least as difficult as the fixed-charge, capacitated multi-commodity flow problem. For long-term schedules it is useful to consider both the purchase and salvage of the equipment, since equipment may be superseded, and there is the possibility of used pre-existing equipment. This may also lead to heterogeneous fleets and arising compatibility considerations. In this paper, we consider two case studies provided by our industry partner. We develop a mixed-integer linear programming model for heterogeneous equipment selection in a surface mine with multiple locations and a multiple period schedule. Encoded in the solution is an allocation scheme in addition to a purchase and salvage policy. We develop a solution approach, including variable preprocessing, to tackle this large-scale problem. We illustrate the computational effectiveness of the resulting model on the two case studies for large sets of equipment and long-term schedule scenarios.
Keywords: equipment selection., OR in natural resources, transportation logistics, integer programming, preprocessing.
Mathematics Subject Classification: 90C11, 90B06, 90B10, 90B9.
Citation: Christina Burt, Louis Caccetta, Leon Fouché, Palitha Welgama. An MILP approach to multi-location, multi-period equipment selection for surface mining with case studies. Journal of Industrial & Management Optimization, 2016, 12 (2) : 403-430. doi: 10.3934/jimo.2016.12.403
References:
[1]

S. Almutawa, M. Savsar and K. Al-Rashdan, Optimum machine selection in multistage manufacturing systems,, International Journal of Production Research, 43 (2005), 1109.  doi: 10.1080/00207540412331320544.  Google Scholar

[2]

M. Baxter, M. Brown and H.-S. Gan, A decision support tool for equipment replacement in forestry harvesting operations,, in Proceedings of the 45th Annual Conference of the ORSNA, (2010), 363.   Google Scholar

[3]

D. P. Bennett and C. A. Yano, A decomposition approach for an equipment selection and multiple product routing problem incorporating environmental factors,, European Journal of Operational Research, 156 (2004), 643.  doi: 10.1016/S0377-2217(03)00138-3.  Google Scholar

[4]

C. Burt and L. Caccetta, Equipment selection for surface mining: A review,, Interfaces, 44 (2014), 143.  doi: 10.1287/inte.2013.0732.  Google Scholar

[5]

C. Burt, L. Caccetta, P. Welgama and L. Fouché, Equipment selection with heterogeneous fleets for multiple period schedules,, Journal of the Operational Research Society, 62 (2010), 1498.  doi: 10.1057/jors.2010.107.  Google Scholar

[6]

C. N. Burt and L. Caccetta, Match factor for heterogeneous truck and loader fleets,, International Journal of Mining, 21 (2007), 262.  doi: 10.1080/17480930701388606.  Google Scholar

[7]

N. Çelebi, An equipment selection and cost analysis system for openpit coal mines,, International Journal of Surface Mining, 12 (1998), 181.   Google Scholar

[8]

T. Cebesoy, Surface mining equipment cost analysis with a developed linear break even model,, International Journal of Surface Mining, 11 (1997), 53.  doi: 10.1080/09208119708944060.  Google Scholar

[9]

M. Chen, A heuristic for solving manufacturing process and equipment selection problems,, International Journal of Production Research, 37 (1999), 359.  doi: 10.1080/002075499191814.  Google Scholar

[10]

K. Dagdelen, E. Topal and M. Kuchta, Linear programming model applied to scheduling of iron ore production at the Kiruna mine, Sweden,, in Mine planning and equipment selection 2000 : Proceedings of the Ninth International Symposium on Mine Planning and Equipment Selection /Athens/Greece/6-9 November 2000 (eds. G. Panagiotou and T. Michalakopoulos), (2000), 6.   Google Scholar

[11]

K. Dagdelen and M. W. Asad, Optimum cement quarry scheduling algorithm,, in Application of computers and operations research in the mineral industry (ed. S. Bandopadhyay), (2002), 697.   Google Scholar

[12]

D. Edwards, H. Malekzadeh and S. Yisa, A linear programming decision tool for selecting the optimum excavator,, Structural Survey, 19 (2001), 113.  doi: 10.1108/EUM0000000005628.  Google Scholar

[13]

S. Erçelebi and C. Kirmanli, Review of surface mining equipment selection techniques,, in Mine planning and equipment selection 2000: Proceedings of the Ninth International Symposium on Mine Planning and Equipment Selection /Athens/Greece/6-9 November 2000 (eds. G. Panagiotou and T. Michalakopoulos), (2000), 6.   Google Scholar

[14]

M. Hassan, G. Hogg and D. Smith, A construction algorithm for the selection and assignment of materials handling equipment,, International Journal of Production Research, 23 (1985), 381.  doi: 10.1080/00207548508904715.  Google Scholar

[15]

A. Jayawardane and F. Harris, Further development of integer programming in earthwork optimization,, Journal of Construction Engineering and Management, 116 (1990), 18.   Google Scholar

[16]

T. B. Johnson, K. Dagdelen and S. Ramazan, Open pit mine scheduling based on fundamental tree algorithm,, in Application of computers and operations research in the mineral industry (ed. S. Bandopadhyay), (2002), 147.   Google Scholar

[17]

M. Kumral and P. Dowd, A simulated annealing approach to mine production scheduling,, Journal of the Operational Research Society, 56 (2005), 922.  doi: 10.1057/palgrave.jors.2601902.  Google Scholar

[18]

A. Michiotis, D. Xerocostas and N. Galitis, A new integrated system for selecting mining equipment,, Computers industrial engineering, 34 (1998), 391.  doi: 10.1016/S0360-8352(97)00164-2.  Google Scholar

[19]

S. H. L. Mirhosseyni and P. Web, A hybrid fuzzy knowledge-based expert system and genetic algorithm for efficient selection and assignment of material handling equipment,, Expert Systems with Applications, 36 (2009), 11875.  doi: 10.1016/j.eswa.2009.04.014.  Google Scholar

[20]

B. Morgan, Optimizing truck-loader matching,, in Mine Planning and Equipment Selection 1994 : Proceedings of the third International Symposium on Mine Planning and Equipment Selection, (1994), 18.   Google Scholar

[21]

S. Rajagopalan, Capacity expansion and equipment replacement: A unified approach,, Operations Research, 46 (1998), 846.  doi: 10.1287/opre.46.6.846.  Google Scholar

[22]

D. Raman, S. Nagalingam, B. Gurd and G. Lin, Quantity of material handling equipment - a queuing theory based approach,, Robotics and Computer-Integrated Manufacturing, 25 (2009), 348.   Google Scholar

[23]

S. Ramazan and R. Dimitrakopoulos, Production scheduling optimisation in a nickel laterite deposit: MIP and LP applications and infeasibility in the presence of orebody variability,, in Twelfth International Symposium on Mine Planning & Equipment Selection MPES 2003 (eds. M. D. Kuruppu and P. A. Lilly), (2003), 3.   Google Scholar

[24]

S. D. Smith, G. S. Wood and M. Gould, A new earthworks estimating methodology,, Construction Management and Economics, 18 (2000), 219.  doi: 10.1080/014461900370843.  Google Scholar

[25]

E. Topal and S. Ramazan, A new MIP model for mine equipment scheduling by minimizing maintenance cost,, European Journal of Operational Research, 207 (2010), 1065.  doi: 10.1016/j.ejor.2010.05.037.  Google Scholar

[26]

D. Webster and R. Reed, A material handling system selection model,, AIIE Transactions, 3 (1971), 13.  doi: 10.1080/05695557108974781.  Google Scholar

show all references

References:
[1]

S. Almutawa, M. Savsar and K. Al-Rashdan, Optimum machine selection in multistage manufacturing systems,, International Journal of Production Research, 43 (2005), 1109.  doi: 10.1080/00207540412331320544.  Google Scholar

[2]

M. Baxter, M. Brown and H.-S. Gan, A decision support tool for equipment replacement in forestry harvesting operations,, in Proceedings of the 45th Annual Conference of the ORSNA, (2010), 363.   Google Scholar

[3]

D. P. Bennett and C. A. Yano, A decomposition approach for an equipment selection and multiple product routing problem incorporating environmental factors,, European Journal of Operational Research, 156 (2004), 643.  doi: 10.1016/S0377-2217(03)00138-3.  Google Scholar

[4]

C. Burt and L. Caccetta, Equipment selection for surface mining: A review,, Interfaces, 44 (2014), 143.  doi: 10.1287/inte.2013.0732.  Google Scholar

[5]

C. Burt, L. Caccetta, P. Welgama and L. Fouché, Equipment selection with heterogeneous fleets for multiple period schedules,, Journal of the Operational Research Society, 62 (2010), 1498.  doi: 10.1057/jors.2010.107.  Google Scholar

[6]

C. N. Burt and L. Caccetta, Match factor for heterogeneous truck and loader fleets,, International Journal of Mining, 21 (2007), 262.  doi: 10.1080/17480930701388606.  Google Scholar

[7]

N. Çelebi, An equipment selection and cost analysis system for openpit coal mines,, International Journal of Surface Mining, 12 (1998), 181.   Google Scholar

[8]

T. Cebesoy, Surface mining equipment cost analysis with a developed linear break even model,, International Journal of Surface Mining, 11 (1997), 53.  doi: 10.1080/09208119708944060.  Google Scholar

[9]

M. Chen, A heuristic for solving manufacturing process and equipment selection problems,, International Journal of Production Research, 37 (1999), 359.  doi: 10.1080/002075499191814.  Google Scholar

[10]

K. Dagdelen, E. Topal and M. Kuchta, Linear programming model applied to scheduling of iron ore production at the Kiruna mine, Sweden,, in Mine planning and equipment selection 2000 : Proceedings of the Ninth International Symposium on Mine Planning and Equipment Selection /Athens/Greece/6-9 November 2000 (eds. G. Panagiotou and T. Michalakopoulos), (2000), 6.   Google Scholar

[11]

K. Dagdelen and M. W. Asad, Optimum cement quarry scheduling algorithm,, in Application of computers and operations research in the mineral industry (ed. S. Bandopadhyay), (2002), 697.   Google Scholar

[12]

D. Edwards, H. Malekzadeh and S. Yisa, A linear programming decision tool for selecting the optimum excavator,, Structural Survey, 19 (2001), 113.  doi: 10.1108/EUM0000000005628.  Google Scholar

[13]

S. Erçelebi and C. Kirmanli, Review of surface mining equipment selection techniques,, in Mine planning and equipment selection 2000: Proceedings of the Ninth International Symposium on Mine Planning and Equipment Selection /Athens/Greece/6-9 November 2000 (eds. G. Panagiotou and T. Michalakopoulos), (2000), 6.   Google Scholar

[14]

M. Hassan, G. Hogg and D. Smith, A construction algorithm for the selection and assignment of materials handling equipment,, International Journal of Production Research, 23 (1985), 381.  doi: 10.1080/00207548508904715.  Google Scholar

[15]

A. Jayawardane and F. Harris, Further development of integer programming in earthwork optimization,, Journal of Construction Engineering and Management, 116 (1990), 18.   Google Scholar

[16]

T. B. Johnson, K. Dagdelen and S. Ramazan, Open pit mine scheduling based on fundamental tree algorithm,, in Application of computers and operations research in the mineral industry (ed. S. Bandopadhyay), (2002), 147.   Google Scholar

[17]

M. Kumral and P. Dowd, A simulated annealing approach to mine production scheduling,, Journal of the Operational Research Society, 56 (2005), 922.  doi: 10.1057/palgrave.jors.2601902.  Google Scholar

[18]

A. Michiotis, D. Xerocostas and N. Galitis, A new integrated system for selecting mining equipment,, Computers industrial engineering, 34 (1998), 391.  doi: 10.1016/S0360-8352(97)00164-2.  Google Scholar

[19]

S. H. L. Mirhosseyni and P. Web, A hybrid fuzzy knowledge-based expert system and genetic algorithm for efficient selection and assignment of material handling equipment,, Expert Systems with Applications, 36 (2009), 11875.  doi: 10.1016/j.eswa.2009.04.014.  Google Scholar

[20]

B. Morgan, Optimizing truck-loader matching,, in Mine Planning and Equipment Selection 1994 : Proceedings of the third International Symposium on Mine Planning and Equipment Selection, (1994), 18.   Google Scholar

[21]

S. Rajagopalan, Capacity expansion and equipment replacement: A unified approach,, Operations Research, 46 (1998), 846.  doi: 10.1287/opre.46.6.846.  Google Scholar

[22]

D. Raman, S. Nagalingam, B. Gurd and G. Lin, Quantity of material handling equipment - a queuing theory based approach,, Robotics and Computer-Integrated Manufacturing, 25 (2009), 348.   Google Scholar

[23]

S. Ramazan and R. Dimitrakopoulos, Production scheduling optimisation in a nickel laterite deposit: MIP and LP applications and infeasibility in the presence of orebody variability,, in Twelfth International Symposium on Mine Planning & Equipment Selection MPES 2003 (eds. M. D. Kuruppu and P. A. Lilly), (2003), 3.   Google Scholar

[24]

S. D. Smith, G. S. Wood and M. Gould, A new earthworks estimating methodology,, Construction Management and Economics, 18 (2000), 219.  doi: 10.1080/014461900370843.  Google Scholar

[25]

E. Topal and S. Ramazan, A new MIP model for mine equipment scheduling by minimizing maintenance cost,, European Journal of Operational Research, 207 (2010), 1065.  doi: 10.1016/j.ejor.2010.05.037.  Google Scholar

[26]

D. Webster and R. Reed, A material handling system selection model,, AIIE Transactions, 3 (1971), 13.  doi: 10.1080/05695557108974781.  Google Scholar

[1]

Ardeshir Ahmadi, Hamed Davari-Ardakani. A multistage stochastic programming framework for cardinality constrained portfolio optimization. Numerical Algebra, Control & Optimization, 2017, 7 (3) : 359-377. doi: 10.3934/naco.2017023
[2]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (47)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences