Thesis (PhD (Logistics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Packing problems are common in industry and there is a large body of literature on the subject.
Two packing problems are considered in this dissertation: the strip packing problem and the
bin packing problem. The aim in both problems is to pack a speci ed set of small items, the
dimensions of which are all known prior to packing (hence giving rise to an o ine problem),
into larger objects, called bins. The strip packing problem requires packing these items into a
single bin, one dimension of which is unbounded (the bin is therefore referred to as a strip). In
two dimensions the width of the strip is typically speci ed and the aim is to pack all the items
into the strip, without overlapping, so that the resulting packing height is a minimum. The bin
packing problem, on the other hand, is the problem of packing the items into a speci ed set of
bins (all of whose dimensions are bounded) so that the wasted space remaining in the bins (which
contain items) is a minimum. The bins may all have the same dimensions (in which case the
problem is known as the single bin size bin packing problem), or may have di erent dimensions,
in which case the problem is called the multiple bin size bin packing problem (MBSBPP). In
two dimensions the wasted space is the sum total of areas of the bins (containing items) not
covered by items.
Many solution methodologies have been developed for above-mentioned problems, but the scope
of the solution methodologies considered in this dissertation is restricted to heuristics. Packing
heuristics follow a xed set of rules to pack items in such a manner as to nd good, feasible
(but not necessarily optimal) solutions to the strip and bin packing problems within as short
a time span as possible. Three types of heuristics are considered in this dissertation: (i) those
that pack items into levels (the heights of which are determined by the heights of the tallest
items in these levels) in such a manner that all items are packed along the bottom of the level,
(ii) those that pack items into levels in such a manner that items may be packed anywhere
between the horizontal boundaries that de ne the levels, and (iii) those heuristics that do not
restrict the packing of items to levels. These three classes of heuristics are known as level
algorithms, pseudolevel algorithms and plane algorithms, respectively.
A computational approach is adopted in this dissertation in order to evaluate the performances
of 218 new heuristics for the strip packing problem in relation to 34 known heuristics from
the literature with respect to a set of 1 170 benchmark problem instances. It is found that
the new level-packing heuristics do not yield signi cantly better solutions than the known
heuristics, but several of the newly proposed pseudolevel heuristics do yield signi cantly better
results than the best of the known pseudolevel heuristics in terms of both packing densities
achieved and computation times expended. During the evaluation of the plane algorithms two
classes of heuristics were identi ed for packing problems, namely sorting-dependent and sortingindependent
algorithms. Two new sorting techniques are proposed for the sorting-independent
algorithms and one of them yields the best-performing heuristic overall. A new heuristic approach for the MBSBPP is also proposed, which may be combined with
level and pseudolevel algorithms for the strip packing problem in order to nd solutions to the
problem very rapidly. The best-performing plane-packing heuristic is modi ed to pack items
into the largest bins rst, followed by an attempted repacking of the items in those bins into
smaller bins with the aim of further minimising wasted space. It is found that the resulting
plane-packing algorithm yields the best results in terms of time and packing density, but that
the solution di erences between pseudolevel algorithms are not as marked for the MBSBPP as
for the strip packing problem. / AFRIKAANSE OPSOMMING: Inpakkingsprobleme kom algemeen in die industrie voor en daar is 'n aansienlike volume literatuur
oor hierdie onderwerp. Twee inpakkingsprobleme word in hierdie proefskrif oorweeg,
naamlik die strook-inpakkingsprobleem en die houer-inpakkingsprobleem. In beide probleme is
die doel om 'n gespesi seerde versameling klein voorwerpe, waarvan die dimensies almal voordat
inpakking plaasvind, bekend is (en die probleem dus 'n sogenaamde a
yn-probleem is), in
een of meer groter houers te pak. In die strook-inpakkingsprobleem word hierdie voorwerpe
in een houer, waarvan een dimensie onbegrens is, ingepak (hierdie houer word dus 'n strook
genoem). In twee dimensies word die wydte van die strook gewoonlik gespesi seer en is die doel
om al die voorwerpe sonder oorvleueling op s o 'n manier in die strook te pak dat die totale
inpakkingshoogte geminineer word. In die houer-inpakkingsprobleem, daarenteen, is die doel
om die voorwerpe op s o 'n manier in 'n gespesi seerde aantal houers (waarvan al die dimensies
begrens is) te pak dat die vermorste of oorblywende ruimte in die houers (wat wel voorwerpe
bevat) 'n minimum is. Die houers mag almal dieselfde dimensies h^e (in welke geval die probleem
as die enkelgrootte houer-inpakkingsprobleem bekend staan), of mag verskillende dimensies h^e
(in welke geval die probleem as die veelvuldige-grootte houer-inpakkingsprobleem bekend staan,
afgekort as VGHIP). In twee dimensies word die vermorste ruimte geneem as die somtotaal van
daardie deelareas van die houers (wat wel voorwerpe bevat) waar daar geen voorwerpe geplaas
word nie.
Verskeie oplossingsmetodologie e is al vir die bogenoemde twee inpakkingsprobleme ontwikkel,
maar die bestek van die metodologie e wat in hierdie proefskrif oorweeg word, word beperk tot
heuristieke. 'n Inpakkingsheuristiek volg 'n vaste stel re els waarvolgens voorwerpe in houers
gepak word om so spoedig moontlik goeie, toelaatbare (maar nie noodwendig optimale) oplossings
tot die strook-inpakkingsprobleem en die houer-inpakkingsprobleem te vind. Drie tipes
inpakkingsheuristieke word in hierdie proefskrif oorweeg, naamlik (i) heuristieke wat voorwerpe
langs die onderste randte van horisontale vlakke in die houers pak (die hoogtes van hierdie vlakke
word bepaal deur die hoogtes van die hoogste item in elke vlak), (ii) heuristieke wat voorwerpe
op enige plek binne horisontale stroke in die houers pak, en (iii) heuristieke waar inpakking
nie volgens horisontale vlakke of stroke beperk word nie. Hierdie drie klasse heuristieke staan
onderskeidelik as vlakalgoritmes, pseudo-vlakalgoritmes en platvlakalgoritmes bekend.
'n Berekeningsbenadering word in hierdie proefskrif gevolg deur die werkverrigting van die
218 nuwe heuristieke vir die strook-inpakkingsprobleem met die werkverrigting van 34 bekende
heuristieke uit die literatuur te vergelyk, deur al die heuristieke op 1 170 toetsprobleme toe
te pas. Daar word bevind dat die nuwe vlakalgoritmes nie 'n noemenswaardige verbetering in
oplossingskwaliteit in vergeleke met soortgelyke bestaande algoritmes in die literatuur lewer nie,
maar dat verskeie nuwe pseudo-vlakalgoritmes wel noemenswaardige verbeteringe in terme van
beide inpakkingsdigthede en oplossingstye in vergeleke met die beste bestaande algoritmes in die
literatuur lewer. Assessering van die platvlakalgoritmes het gelei tot die identi kasie van twee
deelklasse van algoritmes, naamlik sorteringsafhanklike- en sorteringsonafhanklike algoritmes.
Twee nuwe sorteringstegnieke word ook vir die deelklas van sorteringsonafhanklike algoritmes
voorgestel, en een van hulle lewer die algeheel beste inpakkingsheursitiek.
'n Nuwe heuristiese benadering word ook vir die VGHIP ontwikkel. Hierdie benadering kan
met vlak- of pseudo-vlakalgoritmes vir die strook-inpakkingsprobleem gekombineer word om
baie vinnig oplossings vir die VGHIP te vind. Die beste platvlakheuristiek vir die strookinpakkingsprobleem
word ook aangepas om voorwerpe eers in die grootste houers te pak, en
daarna in kleiner houers te herpak met die doel om vermorste ruimte verder te minimeer.
Daar word bevind dat die resulterende platvlakalgoritme die beste resultate in terme van
beide inpakkingsdigtheid en oplossingstyd lewer, maar dat oplossingsverskille tussen die pseudovlakalgoritmes
nie so opmerklik vir die VGHIP is as wat die geval met die strookinpakkingsprobleem
was nie.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/3992 |
| Date | 03 1900 |
| Creators | Ortmann, Frank |
| Contributors | Van Vuuren, J. H., University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Logistics. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 252 p. : ill. |
| Rights | University of Stellenbosch |
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