INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. ups fetatn r,()dit—ra htare that drifts—areas (2) dis- ore, the further extracting for is of solely body outlined purpose stopes—areas ore (1) the into panel, cretized each pan- Within 88 into els. divided subsequently are which zones, 11 mine the time. of that fringes extend con- the may although at remain, exploration life mineral mine tinued of Approx- people. years are 400 two ore nearly imately employs of and six tonnes week operates a mine 6,300 days The daily. as shipped surface the many and to As extracted transported mine. been have the mil- three ore from over of writing, tonnes this of lion time zinc largest the Europe’s at of producers; one become has mine Lisheen and zinc high-grade defined. similarly was hor- content, of separate million-ton lead two bodies 22.5 of ore a comprised izontal drilled, mid-1990s, was been the which had By deposit, holes (lead). 550 (zinc) galena after sphalerite percent ore- percent an three 15 of and meters the almost 6.5 in containing nearly body drilled revealed 1990, hole, of seventh pro-spring The drilling commenced. a correspondingly, gram profitable; be might D 204–221 (print) pp. 0092-2102 2014, ISSN March–April 2, No. 44, Vol. h w r oisa ihe r attoe into partitioned are Lisheen at bodies ore two The the then, Since extracted. was ore first the 1999, In ihe rbd,lctdi ot eta Ireland, the central south that in demonstrated located orebody, surveys Lisheen 1980s, the uring htad au otemnn prto y()sitn ea rdcinfrad 2 euigwsemining smoother waste enabling reducing (4) History (2) and schedule forward, production, a ore production Keywords produce in metal drops to shifting mill-halting heuristic (1) expensive a by management. avoiding with workforce operation (3) model mining delays, programming the backfilling extraction to and integer to between is and value our sequencing operation extraction and adds solve mining monthly production, maximum We the that on metal of operations. sub- constraints goal monthly backfilling to and The minimum subject extraction and Ireland. and mine, of in the maximum mine of schedule quantities, underground life a backfilling the complex (i.e., over a production schedule for metal production voids) maximize a the of determine filling to sequent optimization mathematical use We hspprwsrefereed. was paper This : negon iepouto ceuig nee rgamn applications. programming integer scheduling; production mine underground : xrcinadBcfilShdln na in Scheduling Backfill and Extraction — SN12-5X(online) 1526-551X ISSN iiino cnmc n uies ooaoSho fMns odn ooao80401 Colorado Golden, Mines, of School Colorado Business, and Economics of Division ope negon Mine Underground Complex óa ’ulvn lxnr Newman Alexandra O’Sullivan, Dónal dnlsgalcm [email protected]} {[email protected], 204 ieapistremnn ehd oetatore: extract drift-and-fill. to Lisheen and the methods stoping, meters, mining long-hole 30 room-and-pillar, three to applies 1 thick- from mine that and thickness blocks slope and in strength body range rock ore host to varying the addition With as ness. in the such body), (i.e., factors ore rock other the host encompasses the that of rock strength engi- geotechnical the mine, consider the of neers area given a in employ underground. of blocks disposed ore are only adjacent and of are extraction facilitate blocks to waste extracted whereas to concentrate, refinement and or mineral extraction content for Ore candidates mineral block. are each blocks combined for calculated a is grade 5:1, zinc-equivalent zinc- of a ratio with block. deposit to-lead that the polymetallic a of on is grade based Lisheen or waste Because content or mineral ore of either percentage as which block grade, a cut-off classifies profit-maximizing a of mination extraction). for candidates (i.e., contained blocks deposit Lisheen mining At the 1,193 block. writing, a as this pillar of or time drift, the stope, any presenta- to of refer the ease we for tion, For infrastructure. that (or) blocks mine and ore the pillars—large stope support (3) a and ore, to of access extraction develop to mined odtrietebs xrcintcnqeto technique extraction best the determine To deter- the is production planning in factor critical A http://dx.doi.org/10.1287/inte.2013.0730 04INFORMS 2014 © INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. eo h r ob xaae.Teoei hndildadbatdand 1997). blasted (Hamrin and crusher into drilled the it load to then and transport is scoop for vehicles ore trucks load-haul-dump developed The where is sublevel excavated. the drift to be sublevel falls to a ore process, the stoping below long-hole the In 2: Figure effi- Finally, economically 2). Figure strong and (see is method large-scale stoping rock long-hole the host cient to the the which suited and in thick are mine particularly is the pre- is of body is Areas ore ore 1). mining the Figure room-and-pillar (see and ferred angled, strong is steeply rock not host the Where proceeds from extraction pillar the as furthest 1997). in (Hamrin the cave exit to with the rock starts toward host the that allowing sequence exit, ore mine a pil- the the remain, in encompasses pillars removed that only rock When are extracted. the lars is support ore to remaining place the in while pil- body, left some are method, ore self-supporting of a lars mining, room-and-pillar In 1: Figure INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan Draw point Benching ofthickerparts Vertical benching Blasted ore Pillar Stope drilling and Large-hole blasting ceuigi ope negon Mine Underground Complex a in Scheduling Pillar Loading crosscut Undercut Transport drift Drill access tosoe oia eknso uigunplanned during or weekends oper- holiday mill over continual ensure ations pile to surge production above-ground into ore small feeds buffers a that Lisheen, ore At the mill. of the quantity and quality Many con- the precisely trol stops. more to within process ore the stockpile blended the companies enters be mining otherwise, must that range; period specific ore given a the a of during average grade) mill the head and dif- (i.e., quantity is the quality requirement because satisfy close This to as possible). ficult at as mill capacity the full running filling to continually recommends (i.e., trans- Lisheen mill is at the concentrate. plan ore metal into operational refined the be The to to ground, mill the conveyance above pieces to before ported the Once sizes break surface. manageable to the used into panels machine the ore from a of routes, ore crusher, haulage the the transport of to to network used are extensive which an has mine and remainder. percent, the 20 constitutes mining another room-and-pillar for drift- extraction, accounts the mining of and-fill percent Long-hole 70 tailored. dominates are stoping how- operations Lisheen; the reality, at in operations drift- ever, the 1–3 strength, Figures of 3). rock representative Figure are host (see practiced poor is mining has and-fill mine the where eetbsdmxuet rvd tutrlspotbfr utn an a cutting using before filled 1997). (Hamrin then support is ore is the structural drift, through void a drift provide adjoining remaining as to The known mixture body. ore, ore cement-based of corridor the a from mining, removed drift-and-fill In 3: Figure ih1 er fpouto led opee,the completed, already production of years 12 With Exhaust airway Transport drift Ramp Hydraulic Drilling sandfill 205 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. to fboksae n h eeto fextraction of cre- selection the the for and basis shapes cut-off the block of form of choice pockets ation their these by and material grade high-grade of pock- incon- ets highlight an Engineers of with metal. of body interaction distribution ore sistent The an produced between strength. has plates lines rock these fault different veins along of narrow located plates of ore number high-grade a of satisfac- follows complicated is further mining mill is the because assignment reaching block, difficult ore each This of tory. of blend the grade that and extrac- so size the of and rate backfilling requirements, the including the method, activities mining between consider block’s dependencies each must plan- with associated the Lisheen tion plan, at production a ner coordinated produce To and driver profitability. timely significant operation’s mining a the is of previously described process areas. the extrac- backfilled require time that the blocks from which adjacent support after the on set, begin to may allowed tion cement are paste days Once the 24 fill. additional for to an month complete, may a is size, to filling day its a on from depending the anywhere into void, require down A hoses above filled. the plant being via area a pumped in then mixed is paste, ground, void and Backfill underground first panels surface. the the wooden must from to run with it that it hoses void, sealing installing a by prepared backfilling to to be to mining areas allow Prior some to continue. in and integrity required structural is maintain backfilling tailings, of fill- technique a for extraction, paste by cement backfilling. left as voids a known the create of Remaining some to exhausted. ing used is are mining tailings drained once be will covered that pond and from Most tailings a discarded. waste into are deposited the tailings) are and (i.e., process shipped, milling and the trucks on the loaded within is surface the head limits. reaching average acceptable and ore mill’s quantity the the at of that extraction grade so for time schedule one they any that carefully blocks must the planners select mine capability, limited with stockpiling Therefore, operations. blending not to is suited stockpile this However, shutdowns. production 206 h ult fteshdl o h production the for schedule the of quality The disposal the for location a providing from Aside is concentrate the mill, the at refinement After ’ulvnadNewman: and O’Sullivan rmig(P odtrieana-pia schedule near-optimal a determine to (IP) behind. gramming leave to which blocks about which and decisions take to critical man- blocks horizon, make the must also on requirements agement closure milling mine satisfy With reserves to diminishes. ore available the mining of is grade in that as variety the and important depletion approach especially effects These become activity decision. extraction mining each future with on associated effects intertemporal the of make straightforward. would which activities level, sequencing zone the is at rules even mining impossible, general developing that mining specific requirements such has Lisheen at Conse- a panel months. in each quently, requires extracted others be excavating can while blocks vary day, some can result, blocks a the As of greatly. equal shape of and blocks size in into the a subdivided dimensions, mining, is beside open-pit body ore located unlike the which addition, block In ore block. high-grade some- waste we a and find blocks, times adjacent can between block a greatly of grade vary the Hence, 4). Figure (see mining methods targeted a waste, as defined per- now 12 area is of suitable. grade the approach is cut-off of different method a at a most ore rock, With as classified waste cent. material much shows D too the Box min- percent, excavate used. drift-and-fill nine now Because of C). would (Box grade ing diminishes cut-off ore rea- a as into classified At method divided material process). mining be single drift-and-fill can a which the with B), (e.g., extracted results (Box and percent ore blocks seven as homogeneous classified of sonably area grade large cut-off nonuniform a a a with in Selecting body ore metal. of ore section of determining a shows distribution in A factor Box significant size. and a shape is block selection grade Cut-off 4: Figure nti ae,w hwhww s nee pro- integer use we how show we paper, this In because difficult particularly is creation Schedule 9% u-f rd:7 %12% 9% 7% Cut-off grade: 7% 9% 12% ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces CD AB 7% 12% INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. ae 20)apyaMPmdlt ceuepro- schedule palladium and to platinum model underground and MIP an Carlyle at a horizon. duction apply of 17-period value (2001) a produces present for Eaves he net mine model, the copper the maximizes a of that size schedule the a reduce restric- to variable tions Introducing a presents scheduling. (1995) mine production underground Trout to mine. approach MIP coal generalized more German sched- multiperiod a she a for time, produce ule a to at simulation model on schedule. relies MIP single-period multiperiod one a Solving generating this when with illus- approach associated and complexity apply- scheduling exponential the mine of trates underground advantages to linear MIP the piecewise ing relation- as highlights costs operational She the model functions. model to also to but Zambia. ships, only in not mine integer con- employs variables, copper (1996) six Winkler by a for approach similar for A schedule shifts a work produce secutive to (MIP) simulation mak- programming and decision mixed-integer an a combines discrete He as modeling at ing. IP for production recognizes method schedule (1990) viable required to Chanda level. logic decisions operational the method binary enforce the the to reduction, problems incorporate cost mining cannot or strategic blending certain involving suits pro- programmingapproach mine linear underground their poten- Although in planning. the duction optimization demonstrated for first role (1973) tial al. et Williams Review Literature the of possible. of level as ability long acceptable the as operationally for critical and an production a mine, sustain the along to of pillars mine out haulage pertain path goals of retreat those extraction as the especially mine, to remain- the of the life for ing goals to profit-maximization extracted be the should blocks satisfy dic- which to in sequence our able a are with tate we operations However, mining extent procedures. impact the scheduling can limits we legacy years. paper, which few our to past in the describe only we in As project became the we However, with ago. involved decade a pro- than have scheduling more would automated cedure an mine from the greatly remaining Arguably, benefited its operation. for of mine years underground Lisheen the for INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan ceuigi ope negon Mine Underground Complex a in Scheduling rudmnn ehd n h soitdrules applicable. under- associated where three backfill, uses the and that and extraction mine governing methods a (3) mining and ground areas, content) of metal their set regarding and spa- temporally, and (i.e., tially, complex nonhomogeneous (but and a metal ill-defined (2) extremely involving parameters), economic objective explicit discounted no a application (1) our to are relevant aspects scheduling Specific difficult. production general is mine underground one for writing model Therefore, different policies. of each implementation operational such, underground the As standard necessitates variants. six method many have The rehan- methods costs. requiring mining nuisance, its may a and others as dling output; policy of a such quality regard associated its blend- base exploit and to ing stockpile containing long-term may from mines mine deviations Some minimize contracts. a value, to be present for may net metal objective maximize pre- the to containing be whereas mine may a metal for cious objective mines; between appropriate differ an to tend manner. resource objectives specific example, a constraints, For in operates (e.g., mine sequencing each similarities restrictions), periods, have models blocks, scheduling pro- duction mine underground produc- all operation. almost for although mining model However, underground an IP in an scheduling implement tion and solve, late, heuristic. decomposition operational a 48-month detailed using a satisfy horizon for to solutions resolu- produce term They greater near requirements. provides the same model in the That tion for mine. production schedule ore to short-term iron (2011) and MIP Newman long- a the and both forms solve Martinez model for This to horizon. basis heuristic 60-month a aggregation for model an minimiz- use of quantities, objective they production contracted an from With deviations iron Sweden. ing underground in an mine at ore production opti- long-term (2007) mize Kuchta profit-maximizing and a a Newman to schedule. in model results 100-week their study case Applying solu- mining model. coal exact MIP their an for produce tion to expansion technique mine decomposition of number a for scenarios. model their solv- by ing revenue ore discounted maximize They mine. iia otewr ect rvosy eformu- we previously, cite we work the to Similar Benders’ a developed (2005) West-Hansen and Sarin 207 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. ssfcett epteml unn scoeto close as running mill the possible. keep as capacity to production ore sufficient planned Gantt that is a such 5), on Figure activities (see chart approximately backfilling and of extraction arrangement 2,000 manual semi-annually, the difficult performed requires man- This task, to schedules. time-consuming and software production planning generate ually mine 2012) (MineMax exhaustion the reached. economic realizes is before mine that the blocks from value of is most combination then the challenge extract time The to This exhaustion. close. economic will called mine is blocks metal the jus- ore ground, although the to below and, able extraction when remain be its of longer come costs no the will will as tify produces time However, mine profitable. a the that is mines, continue operation other will the at production as ore long mine, as Lisheen the Mine At Lisheen at Scheduling Production detail. more optimizing in to schedule respect production with its mine the describe now We 208 rdcinshdlr tLsenueiGantt use Lisheen at schedulers Production oiotlbr.Teti ie ewe h asrpeettepeeec eainhp ewe h activities. timeline. the as the between activities on relationships activities backfilling precedence these and the arrange extraction represent planners shows bars targets, chart the production Gantt meet between To a lines thin using The scheduling bars. manual horizontal of example This 5: Figure ’ulvnadNewman: and O’Sullivan h aeo iigfrta ra sarsl,for result, a fixed As same area. the assume that change also for we or activity, mining mining, mining each of of order rate an new the for block a ore extraction the establish redefine of to shape, method planner the the require are may in area area change mining A each for fixed. drift-and-fill) stoping, hole that render might price mine. spot to the with uneconomical in associated metal drop mine’s the a is in when risk late life metal much of on quantities too metal large scheduling sells market, Lisheen behind spot because rationale the that, The possible. is as objective mine this remain- the the planners of in front life mine up ing metal much they the as information, produce Although to financial seek consider mine. explicitly the not do of life the schedules. closure generating mine with when associated costs, costs operational and prices, consider mineral explicitly not do Planners mining the about assumptions operation: following the adopts .Temnn ehd ie,ro-n-ilr long- room-and-pillar, (i.e., methods mining The 3. over production metal maximize to is goal The 2. ignored. are operation the planner of the aspects Financial task, 1. the of scope the narrow To ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. aaiyo h akl ln htpoue h paste the the and produces mill that plant the backfill by the waste of as capacity on produced depends tailings availability Paste the surpassed. be not must the of operational grade within limits. maintained head are and mill the quantity feeding produc- ore the metal that on ensure minimum constraints tion and blending maximum These levels. monthly between tained and mill, the feeds waste. that necessary ore of the produc- extraction Mine and month. includes time that tion one in days at working active of of be number number can the that on areas based working month each capac- for production constraint a ity has mine The exceeded. be following cannot extrac- the each given for activity, date backfilling constraints: start and a tion determine must ner the labor. by or limited equipment not of is availability Lisheen at Production schedule. work or size to fleet length). tantamount (e.g., shift be decision strategic would mod- a rates scheduling changing the most changing in and assumption This els, activity. cal- standard an quickly a complete can to is required planner time the the volume, culate dis- void excavation tonnage, or block tance, the on Based fixed. are 4). Figure (see plan engineering new development a the of require also would mine’s change the the increase value, could grade cut-off indicate different might a mine that conditions the maximize economic to Although grade value. the cut-off mine, a the is selects of content planner design mineral engineering of the During percentage fixed. the on based waste or crusher. blocks the with ore panels the connect to reach routes to haulage passageways) access (i.e., new developing drifts consider not does planner manual The its generate to used has schedules. Lisheen that rates INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan otl ii ncmn at o backfilling for paste cement on limit monthly A • main- be must mill the from output Metal • production mine for targets tonnage Monthly • plan- mine the mind, in assumptions these With the implement to place in are resources Sufficient 7. activities backfilling and extraction for rates The 6. as or ore as block a defines that grade cut-off The 5. fixed. are infrastructure and design mine The 4. ceuigi ope negon Mine Underground Complex a in Scheduling iae o xrcin n fe oti valuable contain often and can- extraction, also haulage are for pillars along didates these crusher Moreover, called blocks pillars. ore the large haulage by to supported are panels which routes, criti- the carry mine’s from trucks the mine, ore of the to part Throughout ever, infrastructure. form if cal that when, blocks is ore planner extract the facing decision value. ficult its destroy and ore of area week’s an access next to prevent unintentionally the may satisfy quota conse- to production decisions have tac- scheduling example, can For tical that activities. mining today mindful future for be made quences must decisions planner extraction the con- Finally, these satisfy straints. that have schedules alter- often producing of planners difficulty Consequently, number staggering scenarios. a native enumerate the require to this would planner problem of blending nature and combinational sequencing the requirements. produc- problems, blending ore large the the grade For to and in adhering limits forward simultaneously production while metal plan, trial-and-error bring tion a to adopts planner approach the busi- objectives, Lisheen the ness satisfy To challenging. is constraints structural in result would instability. or voids blocks of of entire backfilling extraction the Partial partial extracted. that be assumption will the block design under engineering blocks The defines completion. until tinuously Otherwise, the panel. that ensure feasible. a remains to of schedule explicitly for combination defined are the chosen defined precedences of methods called be consequence Often mining a may activity. as relationships other implicitly void these any a of and precedences, between exist backfilling activity that or rules that sequencing block any a satisfy must of extraction The does tailings production. of paste availability limit the not Lisheen, need extraction at by filled created be voids to the of because fraction However, a period. only previous which a pro- in mill, the ore by of the constrained duction be reaching may ore backfilling that of the means of grade function and a is quantity tailings of production The cement. sLsenapoce lsr,apriual dif- particularly a closure, approaches Lisheen As these under production ore of scheduling Manual con- proceed must activity an started, Once • observed. be must constraints Sequencing • 209 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. 3 4 rP ol euti h etuto ftehuaept nthat in path haulage the of panel. destruction pillar the the of to in Removal access result last. eliminating P5 would area, and P5 first these or taken for P4, be precedence P3, P1 extraction west that the collapses require Hence, path would removed. haulage pillars is The that exit. pillar mine any the arrows of The of P1–P5. direction as shown the route. are haulage route indicate haulage a the to support adjacent that panel pillars mining The a shows example This 6: Figure events. arise unexpected may of that because changes IP any an address objective thus generate and qual- quickly solution, highest solution can the planner the of the measure Moreover, in ity. a show results then that and value, one schedules, multiple the enumerate select to planner the allows permuta- solution the schedule’s impossible. of the is quality plan- the of the measuring Finally, therefore, all tions; zone). examine that cannot update for an ner rates necessitate mining and the area of slow that would in panel mining to a down poorer- in respect that quality ground with realization than-expected (e.g., operation values the parameter other evaluate scenario to of possibility analysis any com- precludes to Lisheen, weeks at manual several plete from require of can far process which are time-intensive scheduling, that the solutions Also, in optimal. result can scheduling a of 6). of Figure extraction (see cost the pillar with opportunity haulage associated the ore the consider sterilizing must Hence, be reserves. to planner longer sterilized pillar no the termed can the are extraction these require their reached; is for that place pillar blocks in haulage remain ore a the once removed, However, ore. high-grade 210 ycnrs,amteaia piiainapproach optimization mathematical a contrast, By manual task, the of nature challenging the Given P1 P2 PANEL P3 P4 N P5 ’ulvnadNewman: and O’Sullivan 02 eel ht lhuhmitiigafeasible a maintaining although computer- (Maptek that, Vulcan a reveals Maptek’s using in 2012) relationships model Inspec- block iGantt schedule. generated the iGantt of existing tion the would precedences inte- return encoded our simply these solving with pro- and program freedom, set that ger of precedence degrees from few iGantt output vides the an However, scheduling—are software. dur- manual iGantt con- ing in the precedence precedences—encoded These emphasizes complex straints. (1998) with associated Smith difficulty scheduling, programs integer mine solving for of challenge a unclearly. describing defined In and activities complicated, between idiosyncratic, relationships sequencing are the The govern practice. that problem in rules solve the to of difficult it complexity makes the terms, mathematical and Martinez 2007, 2011). Newman Kuchta and extraction metal (Newman base operation a monetary short- in explicit occasionally the an happens of in factor lack mine) Indeed, time. the possible of est constraints (subject sales operational in metal to greatest forward the content realize metal to schedule highest the the pro- pull to with we is blocks which solution intent, the our the obfuscate change would and con- not duce, a would by formulation objective factor the the stant (see Multiplying 1 appendix). the to in normalize we which price, (Klotz run- programs 2013). the Newman mathematical first improve and the of also in performance can extracted time discounting ore would of Such a 2 tonne produces week. week factor the or this with 1 of solution addition week The in equivalent. either be extracted tonne ore one Specifically, with of solution schedule. a factor, the discount in this without forward produc- brought metal is which in tion solution a encourage to solely scheduling. manual to relation incorporate in pre- also mentioned viously We assumptions life. and constraints its same over the mine pos- the metal from discounted sible of the amount recov- near- maximum of cast the objective a We ering the mine. determine with Lisheen mathematically, we the problem for approach, schedule IP optimal an Adopting Approach Integer-Programming lhuhrltvl tagtowr odsrb in describe to straightforward relatively Although metal constant a assume we value, measure To objective the to factor discount small a apply We ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. o ahpnl eietf h rtclhuaepillar haulage critical the identify we extracted. depen- been panel, has each the pillar For in haulage the a mining once further create panel dent the any instead of prevents and mining existing that finished, the rule the until has reverse wait panel to must we dependent ever, pillar end, a if that this when, logic, To choose to them. freedom allow extract critical to the want a model we is Hence, our schedule. pillars mine extrac- the haulage the of high-grade aspect of these timing of the tion mentioned, previously finished. have to As activities panel extraction dependent all was requiring until pillar wait often the which mining scheduled, in existing order previously the the reflects cases, unneces- simply most are rule In panels pillars restrictive. dependent haulage in sarily activities infrastructural other of to extraction cer- the relat- mining rules merelying of precedence the order Specifically, rules blocks. the ore in tain some choice subjective rules, a reflect many requires schedule INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan h ilr htspotteehuaerue fe oss fvlal r lcs oee,oc eoe,we removed, once However, mining pillar. blocks. extracted a extraction. ore the through for valuable of candidates of east routes are consist area haulage the often that show to routes blocks access haulage containing lines lose these panels dashed support major the that by routes, pillars bordered The are haulage routes critical haulage of These example zone. this In 7: Figure ceuigi ope negon Mine Underground Complex a in Scheduling ed oavldcntan rwehri smrl a merely is it whether or constraint it if valid determine a to to activities leads of rela- pair a precedence between spend each tionship to examining have explicit would effort Without we considerable implement. rules, mining not solu- objective IP could and an we produce that likely or- tion would execution rules these defining their without no Including for model our which defined. in activities for are phaned activities rules from sequencing arises constraints ing panels 7). mining Figure and (see pillars rela- haulage the between characterize tionships that mine haulage critical the delineate throughout we routes way, ore this remaining In panel. sterilize that would haulage in extracted, the criti- that along if blocks one that, constraint all route that for a but for pillar, define just haulage cal not then relationship, We activ- this panel. further enforces that any in prevent ity would extraction whose nte ifiut ncntutn h sequenc- the constructing in difficulty Another 211 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. lc,sc sasoe h mletbok a emndi a rless. or larger day a a extract. in of to mined extraction be months can facilitate require blocks largest to smallest a The The used to stope. cut a correspond cross as blocks such a block, smaller or size, drift block access of small histogram this In 8: Figure day. a than has less in Lisheen mined be illustrates, can 8 that however, areas Figure small extract; many in to histogram blocks month the large a as homogeneous, than has more require that that mine a for well variables combination. start-time defining and by activity fidelity each finer for for we because account cost, must computational a at But, inter- comes activities. benefit schedule time this can the we solving together smaller were closer the the we val, Thus, if fidelity. month monthly practice a in at for extract scheduled to day be a would require interval would example, that time For block full begin. a could the activity dependent require a interval to before the activi- appear than which less complete take in to would practice, schedules in that, in ties results discrete of intervals a use However, time at hour. start or to day, activity month, an specific assign begin. could defines can we activity model scheduling, an In which the the during of for times discrete fidelity, deter- fidelity the or The makes interval, difficult. which time greatly, problem standard of vary a size can The mining block blocks. ore ore the an of heterogeneity the from prece- new defining by needed. and where rules dents subjective remov- the and identifying ing by set precedence we the Lisheen, redefine with Working choice. planning subjective 212

Number of blocks work may fidelity monthly at produced solution A arises also approach IP our with complication A 150 200 250 300 350 100 50 0

1,000 2,000 3,000 4,000 5,000 Size ofblock(tonnes) 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000 More ’ulvnadNewman: and O’Sullivan nwe ri ek2 o eune novn more involving sequences For 2. week either in mined or be 1 to week starting in B Cor- block week. represent formula- third that the the tion from of variables start remove the extract we least respondingly, to at has begin until cannot A B we block then block requires extract, A (2) to block weeks B, (3) and two block 1, period to in be extraction access started must the obtain A if block to example, (1) mined hold, For conditions date. three extracted start following be early cannot specific blocks rates a mining before certain and that extracted, determine sequence be to prescribed must blocks blocks the considers which start, in variant to (Martinez Our scheduled mine already 2011). caving Newman place- sublevel machine a and for in procedure dates activities existing start ment an early of panel establishing variant for for a Consequently, use panel we restrictive. for activities, too approach is same the activities using rules panels, precedence between relax we we pillar because which However, haulage from retreats. for basis restrictions start-date manual a early The provides develop solution. iGantt feasible, in any schedule an variables, in even zero eliminate or of value to optimal, a assume serve of necessarily only would quality which but the compromise solution, not the do activity; restrictions by each these number for this restrictions start-date reduce implementing We 2,214 variables. contains binary 232,470 problem activities) resulting backfilling life and projected The (extraction the mine). horizon to the two-year corresponds a of that for horizon fidelity a weekly (i.e., at solution a block precludes precedences, mining aggregation. the com- the of the to in addition plexity variation in high blocks, adjacent the within where grades Lisheen, at Such case homogeneous requirements. the blending is is grade out, that ignore points to grade (1998) enough contain Smith rarely As blending made. deposits which be at can an resolution decisions such areas the However, mining size. reduces similar smaller approach of the clumps larger aggregate fidelity into such to address is to problems approach used areas. dependent frequently of A times extraction unnecessar- the extraction, extending for areas ily month small a these allotted fidelity be because monthly would delays, with schedule in model results a applying Therefore, opouea mlmnal ceue erequire we schedule, implementable an produce To ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces × 0 (weeks) 105 = INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. nytesbe fhg-rd ciiis eslethe solve we activities, high-grade of subset the two however, Considering only activities. only activities; low-grade consider and activities pillar we high-grade here, sets: panel for approach for sets the illustrate sets five to three to or three two and use practice, In might into content. we metal activities lower extraction approach, progressively the of this prob- sets separating With smaller by stages. of begin in we series solve solu- we a decomposing a which by into find lems, activities problem to the original insight all the includes this model. that of the tion advantage in take activities fewer We including by problem time of problem amount 9). reasonable reduced Figure a (see the in schedule on a heuristic produce to a but employ size, of problem also approach the exact we reduce the to use variables we eliminating do intractable. only remains not Therefore, problem a the over with constraints, however, million variables; 56,276 to reduces problem approach cannot the This chain extracted). precedence be a to of begin end possibly the before at time block a a (i.e., which predetermined result exact a an at the in produces and blocks which determine rate, all mined, cases, be to these must in sequence sequence block; the the given date a in of start date block the start first the to the add blocks predecessor simply of all we block, of predecessor durations single a than INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan ecnslesalrisacso h (reduced) the of instances smaller solve can We Solve 2 Solve 1 lda h qiaetwe hnsligti rbe,btnwlwgaepnlbok n ilr r also are pillars and blocks panel low-grade sched- now remain but to problem, required now this are solving solution 1 The when Solve point. within week this included. scheduled equivalent at were schedule the that the blocks at constitute considered that uled extracted are shows activities are 1 2 pillar Solve blocks Solve fidelity. and these from weekly panel which resulting at high-grade at twice only times problem which The the during scheduling. solve horizon for we 12-week method, a solution for heuristic solution the the of shows example this In 9: Figure ceuigi ope negon Mine Underground Complex a in Scheduling HH HH HH panel block Low-grade panel block High-grade L L 48124 H HH H haulage pillar Low-grade L ecnsletemdlfrteetr oio na in horizon haulage entire introduce we the as for however, minutes; model of the matter pillars, be solve haulage would the can exclude that we we If blocks result. a panel total as pil- dependent the sterilized against haulage the weighed a of be adding must value schedule of the the value during to the point lar any (2) at and extraction horizon, for consequently scheduled if can be few, and have requirements, they precedence (1) any, because problem of pillars the Haulage number model. complicate the the in by included pillars largely problem’s haulage determined the because is Lisheen, complexity for solution optimal cur- the in solve. present rent are successors the whose in absent solve predecessors current the the extract to for between required placeholders time precedence insert must enforce we solves, to successive that solu- high-grade Note fixed a the activities. obtain around scheduled activi- now are low-grade which the we of ties, subset that some first is includes the that result tion from net dates The to start solve. activities weekly high-grade corresponding the those in the basis. fixing activities run, weekly low-grade model of a next set on the plan- activities include the then high-grade We in the sched- weeks for production all a ule yields for solution The fidelity horizon. time ning weekly a at (P model hsapoc ln ilntpoueanear- a produce not will alone approach This L 8 H ,gvni h pedx o hs activities those for appendix, the in given ), H H haulage pillar High-grade L L 12 Weeks Weeks 213 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. et eg,tenme frqie al bolting iGantt cable using required schedule our of require- implementing number resource Thus, bits). future the forecast (e.g., to ments or backfill usage, historical paste summarize to short- schedules, produce work term to example, reporting for extensively, iGantt’s capability uses to management planner Lisheen infeasi- bilities. other the or problems enabling sequencing identify schedule, model quickly the block of three-dimensional addition, a animation In present interdependencies. can iGantt scheduled their of timeline and a a i.e., day. as activities 5), graphically Figure each (see schedule chart use Gantt the planners displays software the The that features reporting is that way a planners. in Lisheen’s schedule to our familiar present schedul- to iGantt software Lisheen’s ing with solution we to Therefore, our Lisheen implement. integrate for to difficult impractical is and weeks. schedule validate sched- start the of format, corresponding list this their In a and merely activities is the 2011), uled from file (IBM output solver the in CPLEX appears it as schedule, Our Implementation stages. more introduc- thus, and, gradual with pillars more of horizon, a tion the requiring of number length horizons The the longer heuristic. on the depends in stages activities stage of pillar-to-panel each of at use include ratio number to we the the and horizon, determine activities given of to a approach For trial-and-error next heuristic. a the the during of schedule the stage entering from too them prevent- far and ing blocks scheduled panel solu- are dependent that the sterilizing early, pillars blocks, some panel contains fewer tion with in too or, case includes intractable, tractable it becomes the problem If the stage. pillars, solve many next remaining the accommodate during pillars to schedule, the opportunity the solu- in less that mining If leaving panel then heuristic. much pillars, too the few contains tion of too includes stage solve each activ- initial right in backfilling the and and included extraction activities find ities other pillar to of of number is number the to stages the key between in The balance problem intractable. the becomes quickly solving problem increases the complexity until problem’s the pillars, 214 Gntpoie fetv ceuevsaiainand visualization schedule effective provides iGantt ’ulvnadNewman: and O’Sullivan rivldsqecn osrit.Tecmlxt of missing complexity of The because constraints. infeasi- sequencing standpoint be invalid practical may or a schedule from our point, ble this fea- for At schedule sibility. our iGantt examines the planner Using the schedule. visualizer, iGantt an into solution our operation. mining prevail under underground necessarily realistic an in that more conditions be unanticipated may the and a within horizon, producible provides given metal schedule the the our of week), estimate five requires a conservative that requiring activity as (e.g., an record time days we in model, gaps constraints. our leave in milling may schedule (or) likely our and Although would production activity) ore preceding at violate the begin to of forward end-date iGantt the in man- activities (i.e., window moving allowable ually Shifting the impractical. of is outside milliseconds sched- activities of a level and shift the window, at to allowable ule an discretion within use software. dates iGantt can our the sched- planners with manual use mine that could However, mine or the allows at level iGantt ulers the that activity at the scheduling fidelity on not of are based iGantt; we them into Admittedly, set rates. import iGantt to let dates we instead, end do We activity iGantt. specify in date not converted inte- that the the use of in and beginning scheduled horizon, the begin- is from the milliseconds it to on which program in ger based week starts the activity of the ning an convert iGantt’s We which whereas milliseconds. at week, in time start given a is fidelity of these time terms dates; that in start script activity given IP customized are the a adopt to auto- using iGantt these by forces override dates We start date. from mated differs start that schedule’s activity IP each the incor- software for date the is start of a creates functionality chooses default iGantt the that because rect schedule but as resulting straightforward, iGantt the is into file our comma-separated-value information to a this according a begins Importing add activity solution. week we each the file, which with populate during this we To which and column, activity). start-date activities extraction of an rows associated tonnage with with (e.g., attributes data, activity of the columns of file import the in continuity operations. providing managerial daily of mines’ benefit added the has eiwadvldto r osbeoc eformat we once possible are validation and Review an creating by iGantt to schedule our transfer We ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. al :Tetbesosacmaio fteI n aulygenerated manually and IP horizon. the 104-week of a comparison for a solutions shows table The 1: Table 115 947 mined Waste paste 320 1621 Backfill 2 3211154 production Ore output Metal metal of quantity significant a bring pro- does metal total it increase duction, not preclude may program might Although integer extraction. price the metal’s spot the of future viability low economic mine’s men- a the have in because late we life metal with of As quantities comfortable remain- possible. large not the scheduling as is in management mine Lisheen front the tioned, up of metal life desire much ing management’s as satisfies produce This to schedule. metal forward the bring can in we that so production future properly solution. can IP the a we of consider before quality must the measures assess we other However, of result. poor number indica- is a output of in metal tive taken total in When for shortfall program approach. this assigned isolation, manual integer metal the the less than mine, percent recovery the 0.17 of shows life solution produc- the metal over maximizing of tion With objective 1). the extracted Table to (see on respect usage (based paste output backfill production metal and ore example, material), mill), for we the of, generated basis (from horizon, manually the 104-week the on with a schedule solution for our model compare IP our Solving Results schedule. workable correc- a and obtain review we of until process tion the or continue illogical pro- and integer gram any our in correct constraints sequencing we overlooked Lisheen, With schedule. from iGantt animated guidance the highlight in we minor mistakes however, these priori; spot a to omissions difficult or it conflicts makes rules sequencing the INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan (tonnes) (cu.m) used (tonnes) (tonnes) otsgicnl,teitgrpormdiscounts program integer the significantly, Most ceueI ceueI an()Comment (%) gain IP schedule IP schedule 4 2 1414298 1444446 Manual 9 1141424 1790 8101273 1104 ceuigi ope negon Mine Underground Complex a in Scheduling 5I improvement IP −14045 8I improvement IP −1018 improvement IP −1023 improvement IP No −017 in o h ilt prt eo iiu ore minimum a below operate to mill ineffi- are highly the in is reasons, for it of drops cient because number particular, temporary a In for large problematic. which, for production responsible ore be also activity delay. backfill schedule less for a potential scheduling the in Thus, reduces resulting value. schedule, extrac- of the forcing loss of again two outside require complete, activities can to tion or longer harden or backfill- to months fail Consequently, sometimes hardening. can ing prevent- delaying paste, or backfill Lisheen, the ing at with set, backfilled interact to often a month oxides one although requires addition, generally have void In otherwise precluded. would that been reduc- activities valu- include this extraction to setting, planner able prof- the and enables more backfilling pouring, in to up, tion time set wait labor reducing backfill releasing by for and By activities mine. extraction remaining itable the the percent of over 14.45 consumption life paste a in to reduction fewer corresponding significantly activities, schedules effi- backfill also more it generates. schedules extraction; program schedule cient integer manual the the less Therefore, with than percent activity, 1.18 mining and mining production waste ore in less reduction percent 1.23 greater by accompanied even is yield an metal decreased 10). the Figure because (see year first the in production percent metal 10.51 increasing by schedule, the in forward pro- integer the schedule. production production, the metal in forward annual metal of brings example gram this In 10: Figure Metal (tonnes) hncnurnl ceue,bcfilatvte can activities backfill scheduled, concurrently When costs reduce also would schedule IP the Following 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 500,000 – Integer programschedule Manual schedule er1Ya Total Year2 Year 1 215 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. aaeett raeamr taywr o than flow does. work plan steady manual more the mine a enables the create solution to for IP management tonnes the Thus, of 14,796 schedule. with production manual compared in tonnes production an change 10,132 with ore method, month-to-month manual schedules average the than also consistently it more but bring production, would that off decision Lisheen. lay against a worse, action workforce, or union the duties of other to part miners production reassign forced lower to be drops would because management mill-halting workers, Also, fewer no requires production. suffers ore pro- it for result, in bound a lower a as 11). sets Figure duction; model (see IP year the second contrast, the By of two start for the level at this below shutdown, months falls mill schedule in manual results the ore and of in approxi- tonnes drop below 80,000 the production mately rectify Lisheen, can For cannot alone production. rescheduling planner if the sure in However, be activities schedule. production manual shift the in to trial- production approach a boost use and-error planners To Lisheen restarts. periods, shut- low-production mill costly in and result downs levels production low threshold, 216 o nyde h Pshdl vi isin dips avoid schedule IP the does only Not ooeaecniuly ycnrs,temna ceuesfesfo o rdcinsatn nwe 8 which 48, week problems. in labor starting and production shutdown low mill from mill temporary suffers the a allowing schedule than in tonnes, manual result production 80,000 the would month-to-month above contrast, consistent remains By schedule more continually. IP has operate the solution to in IP Production the schedule. generated example, manually production the ore this In 11: Figure Tonnes ore 100,000 120,000 140,000 160,000 20,000 40,000 60,000 80,000 0 204060801000 Min. production IP schedule Manual schedule Weeks ’ulvnadNewman: and O’Sullivan ieslf,adt aemr nomdmn closure mine the informed more lengthening make or to and shortening life, by mine’s change sched- the might thus how ule alternatives, understand to production management enabling feasible it not components, generate does financial can model these reha- our incorporate and explicitly Although closure expenses. mine bilitation significant eco- and including prices reaches metal costs, Lisheen future on which depends opera- at exhaustion its nomic time justify The to costs. metal tional can enough at mine produce the schedule longer and the manual no occurs in the exhaustion point from economic the which estimate is It best process. a scheduling is life operational alternative scenarios: we of production, dates. set of closure Because important end design. the one approaching examine engineering is unforeseen in mine for gen- the changes account the or to expediting use- schedules events for new is or of method analysis eration IP scenario for the weeks ful Consequently, several the require complete. than can shorter to significantly which fewer is approach, in This manual schedules hours. produces 20 than program integer The Analysis Scenario h lsr aeta ensteedo h mine’s the of end the defines that date closure The ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. 2 n/a metal comparing by 3201621 scenarios mine-life IP shows production. table The 2: Table 2881165 horizon Long case base Life-of-mine hr horizon Short Scenario or similar scenario. a base-case produce the than might metal of horizon quantity solution greater shorter a schedule slack, a base-case output for the or production if sufficient that, has possibility the the metal exam- ining in of Con- interested and is again. management weeks levels Lisheen production sequently, maximum 20 approach ore never first schedule, output the IP after 104-week that 2). observation Table (see production metal on scenar- case these base of our results to the ios horizon compare extended We an weeks. (2) 122 of and horizon, 92-week option a early-closure program an with integer (1) our scenarios: mine-life solve two we for case, base a providing with 12). scenarios Figure (see run horizons we different insight, provide To decisions. INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan h al-lsr cnroi oiae ythe by motivated is scenario early-closure The life mine 104-week a for results previous our With ong nec ekdrn h rtya sacneuneo h o ere ffedmi h precedence the model. in our in freedom pillars of these degrees on low constraints across the more precedence differs flexible of production more metal consequence life. the weekly a extraction, mine reflecting for is current scenarios, candidates production year become the the pillars first in for haulage Similarity the when solution Lisheen. Later, for during rules. IP option week viable the a each against be would in horizons months tonnage time three another varying by life for mine solutions the Increasing IP compare We 12: Figure Tonnes metal 10,000 15,000 20,000 25,000 5,000 2wes14wes12weeks 122 weeks 104 weeks 92 1 3421614 3111511 2791532 9 n/a 2801095 – ceuigi ope negon Mine Underground Complex a in Scheduling 0204060 Short horizon LOM basecase Long horizon n/a Weeks lsr,terslsso htmngmn should management that mine show delay results would the schedule closure, mill, the the stop implementing to enough and low not horizon. pro- these are Although its drops metal metal. production of in low gain end this of accompany the periods duction by additional case two more base However, tonnes the 21,993 104, than includes week metal at schedule production case extended base the the the than to less corresponding tonnes amount 9,109 metal scheduled is Although production case. interesting more a be the to attention scenario. our horizon turn extended we option, using early-closure gains limited the significant no Lisheen’s increase base-case With flexibility. illustrating not the production thus does in metal, horizon period scheduled the same Shortening the solution. in amount over forward the total than scheduled lower the metal tonnes schedule, 8,070 of is this produced metal quantity with However, small schedule. infeasibilities, the a activities these moves backfill precludes and horizon the over 92-week omit optimized the schedule sched- The would infeasible closure. before the calendar it an required for produce a because would solution of ule weeks base-case end 92 the the first taking weeks to Simply 92 corresponds year. to horizon it the because shortened we Specifically, h 2-eketne ielf cnropoe to proves scenario mine-life extended 122-week The 010120 100 80 217 INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. a rdcinshdln.Freape h integer the example, man- For during scheduling. made production decisions ual subjective and myopic previously a 13). through Figure route (see area haulage backfilled even differ- new or a access, a new selecting blasting developing (e.g., method), mining design ent engineering these chang- the involve capturing ing can for methods These methods blocks. high-value alternative planners explore prompted has to forward insight This blocks of schedule. these the rearranging bring into would manual production iGantt of in economic amount activities an no and from would schedule, that excluded blocks be IP valuable always the the particular, highlight In schedules alone. gains changes metal significant scheduling precedence for from and allow Lisheen design not at mine do planners current relationships the the that hand, see in can results IP the With Insights study. our model to our tangential for be interface would analy- commercial scenario a limited developing ses, includes scope academic because our However, the scheduling. production to scenario on interface perform analysis IP user could graphical users our nontechnical this to optimizer, add iGantt to we in If interface made model. software changes a transfer changes. writing instantly corresponding by this the eliminate time could make requirepreparation we application, to would commercial a week we For a study, to this up of meth- completion activities. between mining Upon relationships shapes, precedence block and redefine ods, and, cut- cases, reexamine the to some in engineers change in require number a would a example, grade For take off update. can to task, days involved of process; more quick a and between activities, easy relationships precedence alter- an changing approach, is however, our values Using parameter iGantt. ing import into and solution model, the our prepare time changes, additional require data we make day, to a than less in instance spot metal future. low dips the potentially with in and prices associated a production risks metal from production, early-closure in metal gains the total the (2) higher and with (1) life between mine longer tradeoff a consider 218 o h lnes h Psltosas highlight also solutions IP the planners, the For scenario new a solve can model our Although ’ulvnadNewman: and O’Sullivan ihe otk meit cin npriua,teIP the particular, In action. immediate take to Lisheen shortfall the for solution production. a in prevent- determining be mind, from not him planner’s could ing the in pillars remained those early that rules, taken bias precedence cognitive and the routes but since haulage had new configuration pre- mine included a The on design. reliance mine subjective vious not produc- of had the because prevent decrease planner manual to tion The pillars the these deficit. in using this late considered pil- cover extracted to be haulage IP to schedule of The were retreat schedule. which manual a lars, the forward in brought year start schedule the second at a the occurred Additionally, of production grade. ore in head decrease the large mill. balance the times, to feeding such ore at required is, for ore grade low-grade feasibility, head maintain a To high too in pan- ing result- different simultaneously, scheduled in occasionally blocks was high-grade els very from of to production number that uneconomical a ore overlooked was had low-grade Planners determined very mine. had of Lisheen area that an scheduled program this, into pillars Realizing these pillars. incorporate to four schedule. arrows) the these (dashed bypass to that a preference added show Lisheen would in results route extracted IP haulage same the be the However, always along finished. pillars activ- has higher-grade the all profitable zone Under once more shown). western possible (not be the west only in the would ity to pillars connect- zone these arrows) ore mining (solid plan, large route original a haulage with main pil- crusher The existing the design. an ing mine of as current part the pillars given form haulage mined lars high-grade be never four would identifies that schedule blocks IP The 13: Figure nihsgie rmteI eut aeprompted have results IP the from gained Insights ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. t1 Indices follows. as are model the of elements primary The Formulation Model Appendix. lives. operational their of end the near they especially as operations, other for to underground adapted package be room-and-pillar can here the software outline the However, we that general challenging. approach made too a far, mining of such underground so idiosyncrasies of the have, creation market, operations the underground on are packages life. operational mine’s engineering the underground increase the to of design deci- much revise management’s to in sion instrumental capability, been analysis has scenario which a program with integer mine the work- the provides addition, smoother In enabling management. (4) force and production, drops mill-halting ore expensive in avoiding backfill- (3) and delays, mining ing waste reducing in (2) mining forward schedule, production the the metal to shifting value (1) by add operation schedules presentation IP for our iGantt the purposes, in and are produced schedules manually IP-produced the goals method both managerial scheduling Although manual with was. previous consistent mine’s the more than is produc- that ore a contains tion Over schedule mine. our underground horizon, 104-week complex production a near-optimal for produces schedules approach IP Our Conclusions design mine between IP optimization. process schedule new iterative and an a con- be will generate to Lisheen with tinue and work our model way, this the In IP incorporate schedule. the will into we When complete, changes the mine. are the changing designs of of areas these process many in the IP design in the engineering areas with is These accordance Lisheen in schedule. schedule. mined mining being currently the are into depen- blocks pull that to dent earlier panels production of into brought number be must a highlighted have schedules INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan iigo akligactivity, backfilling or Mining a: t ˆ lhuhmlil pnptotmzto software optimization open-pit multiple Although Period, : t = T 1 0 0 0 1 . ceuigi ope negon Mine Underground Complex a in Scheduling a = n. 1 0 0 0 1 g1 A Sets Parameters betv Function Objective Variable Decision ¯ T P P P A e1 v p ¯ P max (P) ˆ ˜ ¯ ˆ e falperiods. all of Set T: M t g at at B t a a a a a g m p r e a a b ¯ e falbcfiln activities. backfilling all of activities. Set extraction : all of Set : e fatvte htms rcd activity precede must that activity activities which of in Set periods : of set Restricted : e fatvte htms o rcd activity precede not must that activities of Set activity precede : must which of each activities, of Set : t t ˜ ˆ y aiu n iiu loal ong fore of tonnage allowable minimum and Maximum : aiu n iiu loal ea produced metal allowable minimum and Maximum : at ple nperiod in applied Paste activity : backfilling for required periods of Number activity extraction : for required periods of Number : icutrt sdt eraetevleo h metal the of value the decrease to used (cubic rate month Discount each : in backfilling for paste Available : from produced ore the of grade percentage Average period : in obtained ore of Volume : ujc to subject at fi occurs. it if xaae namnh epciey(tonnes). respectively month, a in excavated (months). (months). (tonnes). respectively month, a in mill the by ligactivity filling rdcdi uueperiods. future in produced meters). activity extraction activity extraction started = ( otherwise0 0 activity if 1 y a∈A t  e g X X ∈ at a∈A ≤ T ≤ ˆ X a B ≤ a∈A a y t a∈A M X X ∈ X at u∈ T ttime at ∀ t ˆ X M ∈ a ≤ M T a a T ˆ p a. ˆ t a 0 t X a ∈ 0 at 1 X trsdrn period during starts ∈ ∈ u≤t 2 T t X ˆ T ˆ t ∈T ˜ X ˆ a y P a v ¯ at ∀ g −t g a at t t ˜ a a 1 a ≤ a ie htw tre back- started we that given , a m v t ˆ v 0 cbcmeters). (cubic y a ∈ −t at p at at ¯ ∈ t ˆ a ttime at b A t ˆ y 0 y ≤ y A at M at ∀ a e M 0 4 ¯ ≤ ∪ t u ˜ 1 ∈ ∪ g A + ¯ ∀ T1 A B t r5 t ˆ 1 t ˆ B ∀ ∈ ie htwe that given , (tonnes). − t 1 t t ˆ ˆ T1  ∈ ∈ t 1 , T1 a a. T ˆ a start. can a 1 a. 219 (4) (5) (2) (3) (1) a, a a INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. ities activity not an does activities. use between rules its of precedence that enforce sequencing use that ensure the the constraints are and (5)–(7) track Constraints period availability. 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ILOG (2011) IBM (1997) H (2003) Hamrin BW Kernighan DM, Gay R, Fourer simu- and programming integer of application An (1990) Stillwater E at Chanda planning Underground (2001) BC Eaves WM, Carlyle References Colorado resources. the his for at of Mines Group Kaiser of Computing Tim School Dr. Performance thank commit- his High we for and the Finally, Consultants time AMC advice. of and their this Hall comments Brian for with thank Fox also us We Noeleen ment. thank providing and we particular, Bailey for In Tom research. Mine the supporting Lisheen and project the thank We core quad Acknowledgments X5570 Xeon RAM. Intel of dual GB 48 two 2011) and (IBM with processors 12.3 machine version solver, 2003) a CPLEX al. on the with et it (Fourer solve 20090327 and version language, gramming extracted. activity con- an pillar Sequencing that solution. (6) haulage ensure better, constraints yet (7) follow feasible, straints to a the many for of relaxing allows all according (5), Although characterized constraints C. initially to block were this before precedences that mine mined constraint blocks’ we mine the be if impose we must only mined that we block generality, be Then, of to A. loss need block only without both Assume, not C. do block B predeces- and a all A in whether blocks mining block of a of of regardless order sors maintained, the that be sequenc- of ensures panel set (6), second The without constraints, first. C B ing block block and mine A cannot block we mining Therefore, C. block access emnA uhaM(07 sn grgto ootmz long- optimize to aggregation Using (2007) M 2012, Kuchta A, 1, Newman December Accessed iGantt. MineMax (2012) opti- MineMax for approach solution A (2011) AM http://www Newman 2012, MA, 1, Martinez December Accessed Vulcan. (2012) Maptek Klotz emdloritgrpormuigteAP pro- AMPL the using program integer our model We tions CA). Grove, Programming Pacific Mathematical for Language body. ore stratiform Tech. a Sci. for planning production to lation Company. Mining empouto lniga nudrrudmine. underground an at Res. Oper. planning production term -Br http:/ LKAB’s at scheduling mine. production Kiruna short-term and long- mizing .maptek.com/products/vulcan. Sci. programs. ment linear integer mixed cult index.html. -01.ibm.com/softwar ,Nwa M(03 rcia udlnsfrsligdiffi- solving for guidelines Practical (2013) AM Newman E, ochure.pdf. AlsCpo Stockholm). Copco, (Atlas /www.minemax.com/downloads/Minemax-iGantt 18(12):18–32. 11(2):165–172. 176(2):1205–1218. a a ud oUdrrudMnn ehd n Applica- and Methods Mining Underground to Guide u.J pr Res. Oper. J. Eur. 0 0 ∈ ∈ P ˜ P a ˆ Interfaces a e/commerce/optimization/cplex-optimizer/ nwihteatvt eed,is depends, activity the which on , aebe xrce.I hsexample, this In extracted. been have ceuigi ope negon Mine Underground Complex a in Scheduling nefcs4() p 0–2,©21 INFORMS 2014 © 204–221, pp. 44(2), Interfaces 31(4):50–60. 211(1):184–197. uvy pr e.Manage- Res. Oper. Surveys a antocroc a once occur cannot Topo Learning, (Thompson ML Modeling A AMPL: Mining u.J. Eur. INFORMS holds copyright to this article and distributed this copy as a courtesy to the author(s). Additional information, including rights and permission policies, is available at https://pubsonline.informs.org/. oigbnfis i a oqikyeaiealternative examine dates quickly closure mine to different fol- way e.g., the scenarios, a with end-of-mine-life metal (i) us maximizing benefits: provides of tool lowing objective However, optimization primary the schedule. the extraction, manual to the addition in in support encoded generally decisions schedules opera- optimized the mining The the of Lisheen. years at two tion last the for planning duction after ground the whilst in LOM, left the resources closure. schedule varying over mineral mining at extracted the a mine metal minimizing the generates the maximizes in optimizer the that remaining of The end ore operate, grades. the still to Zinc At is profitable (LOM). there longer life-of-mine LOM, the no defines is a this it to and which decreases eventually beyond areas profile point working production increas- available becomes The of Maximizing usu- mine number declines. complete. the the and as of to challenging life operation ingly weeks the more over mining extraction or our metal three of takes part ally intensive labor Ireland, Tipperary, Co. Thurles, Moyne, writes: Killoran, Mine, Letter Verification com- in costs fix period optimize to MILP Using (1996) B underground Winkler of Planning (1973) PM Wells L, Smith JK, using Williams scheduling production mine Underground (1995) L Trout in schedules production production short-term mine Optimizing long-term (1998) M The Smith (2005) J West-Hansen S, Sarin INFORMS 2014 © 204–221, pp. 44(2), Interfaces Newman: and O’Sullivan W r urnl sn h piie oass norpro- our in assist to optimizer the using currently are “We and difficult a is production ore scheduling “Manually Lisheen Engineer Services Technical Chief Bailey, Tom pl yps pl iea nut (APCOM), Indust. 441–446. PA Mineral , Appl. problems. Sympos. scheduling Appl. and sequencing mine plex 251–254. Africa, South Johannesburg, (APCOM), Indust. eral mining. copper 395–400. Australia, Brisbane, (APCOM), Indust Mineral put. programming. integer mixed with software modeling 12(4):149–155. mine Integrating AMPL/CPLEX. mining: surface problem. scheduling 0hItra.Ap.Smo.Ap.Cmu.Min- Comput. Appl. Sympos. Appl. Internat. 10th nent .SraeMnn elmto Environ. Reclamation Mining Surface J. Internat. I Trans. IIE ceuigi ope negon Mine Underground Complex a in Scheduling 5hItra.Smo.Ap.Com- Appl. Sympos. Internat. 25th 37(2):109–121. nvriyPark, University 6hInternat. 26th oisadtcnlg.H sa cnmccnutn with consultant economic Company. eco- an and in is Galt course He undergraduate technology. specialized modeling. an and taught market nomics he he power Mines, school Colorado and at consulting the While graduate power at Before electric economics in Mines. energy and of mineral School completed in has PhD he and a University, Brown from engineering iiayoeain.Sei evn sascaeeio of editor associate INFORMS. as of serving and Research is industries, Operations She mining is and operations. it energy as military the particularly logistics, modeling, to optimization applied in lie Naval research interests primary the Newman’s at Professor pro- Department School. Research assistant Postgraduate Operations research the of in appointment fessor of the School held Colorado she the Mines, joining of to University Prior industrial Berkeley. the in from California, the PhD research from operations a and research and engineering Berkeley, operations California, in of MS Uni- University an the of from Chicago, School mathematics of applied Colorado in versity the BS a at holds Business She Mines. and Economics of sion the that before areas mining for identify them to closes.” free mine and to mining areas additional grade need high forward our pull in included being now ore Schedule. extra c.120kt LOM of in revised resulted ZnEq has percent This 13 areas. acceler- at these to in plans extraction new the initiated have ate infor- we how this hand, matter With to vicinity. now no neighboring mation mined the in be mine not we will quickly potentially that areas ing for scheduled scheduled manually ore high-grade of extraction. labor simultaneous much identification consistent too the more e.g., week generate infeasibilities, (iii) one to and from us tonnage enabling shifts; production next, the the in to change less (ii) lxnr Newman Alexandra O’Sullivan Dónal W ilcniu oepo h piie ohto both optimizer the employ to continue will “We identify- in useful particularly been has optimizer “The and andaB neooisadaB in BA a and economics in BA a earned sa soit rfso nteDivi- the in professor associate an is n sa ciemember active an is and Interfaces, 221