OUTLINE. A model for the Container Stowage and Routing Problem. Container Stowage and Routing Problem. Container Stowage and Routing Problem

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1 OUTLIN mode for the ontaner Stowage and Routng Probem INS ombra na Moura, 3 Pauo Trunfante Martns ntóno ndrade-amos 3 Vctor Lobo The ontaner Stowage and Routng Probem (SRP; Mxed Integer Programmng Mode for the SRP; Test robems and resuts; oncusons and Future wor. Portuguese Nava cadem 3 eartment of conomcs, Management and Industra ngneerng, Unverst of vero ontaner Stowage and Routng Probem ontaner Stowage and Routng Probem Proosed robem ogstc mode for a feet of contanershs wth routes defned dnamca deendng on cargo arrva at orts and dever deadnes What route for each sh? haenges addressed: ontanersh characterstcs and oeraton costs ontanershs routes What contaners to carr? ontaners carred n each ourne ontaner characterstcs and deadnes How to stow the contaners? 7 das das Harbour fee erthng 9 das 8 das Factes Pot uraton T 5 das 8 das 0 das 3 4 SRP - ata SRP - ata set of orts defned b: Geograhca coordnates Fxed tarffs Vstng costs Su and demand (set of contaners set of vesses characterzed b: mensons Stabt characterstcs Veoct Oeraton costs Fue consumton Sots ostonng set of contaners n each ort: Standard contaners Weght Orgen and destnaton ort eadne ost and tme of a movement 5 tered from Wson and Roach (999 6

2 SRP ecsons SRP ontaner Loadng ecsons ecsons to be made Route cost? ontanersh utzaton cost? t each ort Stowage an.3 Movement cost? What contaners shoud be carred b each vesse? What sots shoud be occued? Severa movements are erformed -> the stowage an s norma rearranged Stowage an. Stowage an. Stowage an. Stowage an. Stowage an.3 Obectve Unoaded contaners -> destnaton s reached ontaner shftng -> the access to other contaners that must be unoaded s boced Re-handes -> contaners re-ostonng to mrove the overa stowage (stabt and access Load new contaners to dever 7 8 SRP Routng ecsons MIP Mode for the SRP Ports data Whch orts shoud be vsted b contanershs Vstng sequence f 4 d 3 G( P, P{,..., } {(, :, P, } 7 das das d Length of arc (, n mes 9 das 8 das 5 das 8 das 0 das u Vstng cost n uros b tme unt (hours of ort b vesse that deends of: Port utzaton Port taxes 9 0 MIP Mode for the SRP Vesses data MIP Mode for the SRP ontaners data { } V,..., Set of vesses L Vesse s characterstcs,, T,,, GT, Q, s _ fue ve tc c s Vesse s trave veoct (assumed constant ost trave oeraton (er unt dstance, n uros that deends of, the cost of the fue/mes ost of the vesse utzaton Tme at whch vesse arrves at ort contaners have standard dmensons n TU s { α,..., α } { } α,..., α n Set of contaners n each ort, to dever n severa destnatons Set of contaners to ort t Servce tme of vesse n ort q α d α ontaner s weght ever deadne of a contaner

3 MIP Mode for the SRP Loadng data ecson varabes m α T ost of a movement (oad or unoad of a contaner α n a vesse n ort Matrx of sots aced n vesse x, f vesse vsts ort mmedate after servng ort 0 otherwse For the sae of smct each sot corresonds to a set of contaners - to be shed from ort to ort. The transortaton matrx s caed feasbe f n each ort the tota caact requred to stow the contaners destned for subsequent orts s no more than the caact of the sh z x, f vesse s used 0 otherwse tered from Wson and Roach ( ecson varabes Obectve functon α (x, δ α, f contaners of ort are transorted b vesse 0 otherwse Mn W v ( dtc x xu route cost v W c ( cost of vesse utzaton γ α ( x,, f oad oeratons of contaners α were erformed n vesse and sot (x, 0 otherwse W v 3 ( γ α x z x z m (,, β α (,, α cost of contaner movements β α ( x,, f unoad oeratons of contaners α were erformed n vesse and sot (x, 0 otherwse W, W and W 3 must be tuned for each acaton 5 6 onstrants reated to routes, onstrants reated to contaners ostonng and oadng x x s d α α qαδ α α Q P α x x 0 α δ α α α s t d ve s M ( x, P x δ α P α 7 das das 9 das 8 das 7 5 das 8 das 0 das 8

4 onstrants reated to contaners ostonng and oadng MIP Mode for the SRP decson varabes Shfts oeratons: α α x γ α ( x, α P T β α x z x x z x (,, β α (,, P T α α α α x δ α β α ( x, α P T Shfted contaner γ α γ ( x, ( x, z α 0 α T When a shft s erformed the contaner s oaded n a dfferent sot; x β α(x, γ α(x, 9 0 Test Probems Test Probems Ports ontaners/demands #{ α,..., α} 700 Probem : α 00 ; α 00; α 00; α 00; α 00 Probem : 8 q α #{ α,..., α} 400 α 400 ; α 00; α 400; α 00; α 00 X Inta ort: 8 d α 0 Oeraton cost and ort fees HVY Inta ort: ontanershs Port tarfs (sh reated costs ontaners reated costs Voage costs Shs Length eam raught Seed (nots N.º TU Gross tonnage Fue (t/h ot charges SQRT(GT ; berthng 03 ; sace 0,668 * GT 0,0357 * GT * (das- ; tugs and towng ; ort tarff / TU - 9,733 ; contaner embaraton 35 ; contaner dsembaraton 35 ; contaner shft 35 ; fue /t; crew reated 00 / da; X HVY Resuts GLPK - GNU Lnear Programmng sover The mode was tested on a ore uo Mean runnng tme to acheve an otma souton 7 mn Probem Traveed Sh Route Tota tme mes h X h HVY Probem Obectve functon oncusons omex features refect dstrbuton short sea shng robems reat; Mathematca rogrammng mode: Forma descrton of the robem; He to understand the underng rncas and the robem comext. Usng a smfed scenaro t was concuded that t s ossbe to: Turn the martme transort more fexbe wth cost reductons; Manage a feet consderng the cargo deadnes and reducng tme duraton when necessar; Sh X HVY Route Traveed Tme mes nterva h 63 6 h Obectve functon nass of rea scenaros wth rea data (coaboraton requred. 3 4

5 Future Wor Insert n the mode other constrants: Stabt It s cruca n contanersh s oadng; LIFO In order to reduce: ontaner shftng; ontaner re-handes; Imrove the Genetc agorthm mementaton for route seecton and cargo dstrbuton that has aread been done. 5