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A linear programming and sampling approach to the cutting-order problemHamilton, Evan D. 15 November 2000 (has links)
In the context of forest products, a cutting order is a list of dimension parts along
with demanded quantities. The cutting-order problem is to minimize the total cost of
filling the cutting order from a given lumber grade (or grades). Lumber of a given grade
is supplied to the production line in a random sequence, and each board is cut in a way
that maximizes the total value of dimension parts produced, based on a value (or price)
specified for each dimension part. Hence, the problem boils down to specifying suitable
dimension-part prices for each board to be cut.
The method we propose is adapted from Gilmore and Gomory's linear programming
approach to the cutting stock problem. The main differences are the use of a random
sample to construct the linear program and the use of prices rather than cutting patterns
to specify a solution. The primary result of this thesis is that the expected cost of
filling an order under the proposed method is approximately equal to the minimum possible
expected cost, in the sense that the ratio (expected cost divided by the minimum
expected cost) approaches one as the size of the order (e.g., in board feet) and the size of
the random sample grow large.
A secondary result is a lower bound on the minimum possible expected cost. The
actual minimum is usually impractical to calculate, but the lower bound can be used in
computer simulations to provide an absolute standard against which to compare costs. It
applies only to independent sequences, whereas the convergence property above applies
to a large class of dependent sequences, called alpha-mixing sequences.
Experimental results (in the form of computer simulations) suggest that the proposed
method is capable of attaining nearly minimal expected costs in moderately large
orders. The main drawbacks are that the method is computationally expensive and of
questionable value in smaller orders. / Graduation date: 2001
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Determining optimal primary sawing and ripping machine settings in the wood manufacturing chainLindner, Berndt Gerald 04 1900 (has links)
Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: For wood manufacturers around the world, the single biggest cost factor is
known to be its raw material. Thus maximum utilisation, specifically volume
recovery of this raw material, is of key importance for the industry. The wood
products industry consists of several interrelated manufacturing steps for converting
trees into logs and logs into finished lumber. At most primary and
secondary wood processors the different manufacturing steps are optimised in
isolation or based on operator experience. This can lead to suboptimal decisions
and a substantial waste of raw material. The objective of this study
was to determine the optimal machine settings for two interrelated operations,
namely the sawing and ripping operations which have traditionally been optimised
individually.
A model, having two decision variables, was developed which aims to satisfy
market demand at a minimal cost. The first decision was how to saw the log
supply into different thicknesses by choosing specific sawing patterns. The second
was to decide on a rip saw’s settings, namely part priority values, which
determines how the products from the primary sawing operation are ripped
into products of a certain thickness and width.
The techniques used to determine the machine settings included static simulation
with the SIMSAW software to represent the sawing operation and mixed
integer programming to model the ripping operation. A metaheuristic, namely
the Population Based Incremental Learning algorithm, was the link between
the two operations and determined the optimal settings for the combined process.
The model’s objective function was formulated to minimise the cost of production.
This cost included the raw material waste cost and the over or under
production cost. The over production cost was estimated to include the stock
keeping costs. The under production cost was estimated as the buy-in cost of
purchasing the under supplied products from another wood supplier.
The model performed well against current decision software available in South
Africa, namely the Sawmill Production Planning System package, which combines
simulation (SIMSAW) and mixed integer programming techniques to
maximise profit. The model added further value in modelling and determining
the ripping priority settings in addition to the primary sawing patterns. / AFRIKAANSE OPSOMMING: Die grootste enkele koste vir houtprodukvervaardigers wêreldwyd is dié van
hulle roumateriaal. Die maksimale gebruik van rou materiaal, of volume herwinning,
is dus van primêre belang vir hierdie industrie. Die vervaardigingsproses
in die houtprodukte-industrie bestaan uit ‘n verskeidenheid interafhanklike
stappe om bome na stompe te verwerk en stompe na eindprodukte. By meeste
primêre -en sekondêre houtvervaardigers word die verskillende vervaardigingsstappe
in isolasie ge-optimeer. Hierdie praktyk lei tot sub-optimale besluite
en ‘n vermorsing van roumateriale. Die doelwit van hierdie studie was om die
optimale masjienverstellings vir twee interafhanklike prosesse, die primêre -en
kloofsaag prosesse, te bepaal. Tradisioneel word hierdie twee prosesse individueel
optimeer.
‘n Model met twee besluitnemingsveranderlikes is ontwikkel wat poog om die
markaanvraag te bevredig teen ‘n minimum koste. Die eerste besluit was watter
saagpatroon gekies moet word om die stompe in die regte dikte produkte
te saag. Die tweede besluit was wat die kloofsaagstellings, ook bekend as prioriteitswaardes,
moet wees sodat die regte wydte produkte gesaag word.
Die tegnieke wat gebruik is sluit statiese simulasie met SIMSAW sagteware in
om die primêre saagproses te modelleer en gemengde heelgetalprogammering
(“mixed integer programming”) om die kloofsaagproses te modelleer. ‘n Metaheuristiek
genaamd die “Population Based Incremental Learning” algoritme,was die skakel tussen die twee operasies om die optimale masjienstellings vir
die proses te bepaal.
Die model se doelfunksie was geformuleer om die koste van produksie te minimeer.
Hierdie koste sluit die roumateriaal afvalkoste en die kostes van oor -en
onderproduksie in. Die oorproduksiekoste was ‘n skatting van die voorraadkostes.
Die onderproduksiekoste was ‘n skatting van die koste om voorraad
van ‘n ander verskaffer aan te koop.
Die model het goed opgeweeg teen die beskikbare besluitnemingssagteware in
Suid Afrika, die “Sawmill Production Planning System”, wat ‘n kombinasie van
SIMSAW en ‘n gemengde heelgetalprogrammeringstegniek is. Die model het
verder waarde toegevoeg deur die kloofsaag se prioriteitswaardes te modelleer
saam met die primêre saagpatrone.
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