Using aggregation to optimize long-term production planning at an underground mine

Motivated by an underground mining operation at Kiruna, Sweden, we formulate a mixed integer program to schedule iron ore production over multiple time periods. Our optimization model determines an operationally feasible ore extraction sequence that minimizes deviations from planned production quantities. The number of binary decision variables in our model is large enough that directly solving the full, detailed problem for a three year time horizon requires hours, or even days. We therefore design a heuristic based on solving a smaller, more tractable, model in which we aggregate time periods, and then solving the original model using information gained from the aggregated model. We compute a bound on the worst case performance of this heuristic and demonstrate empirically that this procedure produces good quality solutions while substantially reducing computation time for problem instances from the Kiruna mine.

[1]  R. P. Mohanty,et al.  A Hierarchical Production Planning Approach for a Steel Manufacturing System , 1992 .

[2]  Alexandra M. Newman,et al.  Long- and Short-Term Production Scheduling at Lkab's Kiruna Mine , 2007 .

[3]  Torgny Almgren,et al.  An approach to long range production and development planning with application to the Kiruna Mine, Sweden , 1994 .

[4]  Ravi Kannan,et al.  Polynomial-Time Aggregation of Integer Programming Problems , 1983, JACM.

[5]  I. Grossmann,et al.  A decomposition approach for the scheduling of a steel plant production , 2001 .

[6]  Ronald L. Rardin,et al.  Optimization in operations research , 1997 .

[7]  M. Smith,et al.  Using MIP for strategic life-of-mine planning of the lead/zinc stream at Mount Isa Mines , 2003 .

[8]  Subhash C. Sarin,et al.  The long-term mine production scheduling problem , 2005 .

[9]  Ignacio E. Grossmann,et al.  Preliminary screening procedure for the MINLP synthesis of process systems—I. aggregation and decomposition techniques , 1994 .

[10]  Amy v. Puelz.  A Stochastic Convergence Model for Portfolio Selection , 1998 .

[11]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[12]  David R. Twigg.  Operations and production management on the Internet , 1997 .

[13]  Laurence A. Wolsey,et al.  Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs , 2001, Manag. Sci..

[14]  Dimitris Bertsimas,et al.  The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach , 2000, Transp. Sci..

[15]  R. R. P. Jackson,et al.  Production Planning and Control , 1965 .

[16]  Laurence A. Wolsey,et al.  Aggregation and Mixed Integer Rounding to Solve MIPs , 2001, Oper. Res..

[17]  Wilbert E. Wilhelm,et al.  A PROCEDURE FOR OPTIMIZING TACTICAL RESPONSE IN OIL SPILL CLEAN UP OPERATIONS , 1997 .

[18]  R. P. Mohanty,et al.  Multilocation plant sizing and timing problem: a study of spatial—temporal decomposition procedure , 1996 .

[19]  James R. Evans,et al.  Aggregation and Disaggregation Techniques and Methodology in Optimization , 1991, Oper. Res..

[20]  Fred W. Glover,et al.  A New Knapsack Solution Approach by Integer Equivalent Aggregation and Consistency Determination , 1997, INFORMS J. Comput..

[21]  John L. Burbidge,et al.  Production planning and control: A personal philosophy , 1985 .

[22]  Erkan Topal,et al.  Implementing a Production Schedule at LKAB's Kiruna Mine , 2004, Interfaces.

[23]  Martin L. Smith.  Optimizing short-term production schedules in surface mining: Integrating mine modeling software with AMPL/CPLEX , 1998 .

[24]  G. B. Mathews.  On the Partition of Numbers , 1896 .

[25]  W. Matthew Carlyle,et al.  Underground Planning at Stillwater Mining Company , 2001 .

[26]  W. Matthew Carlyle,et al.  Underground Planning at Stillwater Mining Company , 2001, Interfaces.

[27]  Fred W. Glover,et al.  Aggregating diophantine equations , 1972, Z. Oper. Research.

[28]  A. S. Cullick,et al.  Optimal Planning and Scheduling of Offshore Oil Field Infrastructure Investment and Operations , 1998 .

[29]  R. Kipp Martin,et al.  Large scale linear and integer optimization - a unified approach , 1998 .