Optimization methods for solving transportation problems on networks

doctoral dissertation

Katja Prnaver (Author), Blaž Zmazek (Mentor), David Pisinger (Co-mentor)

Abstract

In this thesis we study problems from real situations, which can be applied to network graphs and solved using mathematical graph theory. We start with the problem of oriented network design. The problem originates from networks, where the flow over the arcs is important and many times limited with the capacity of the networks. There are several techniques and results on the problem of assigning the flow through the network channels. In our problem, we try to find the optimal network structure, which could be used in the design phase of the network. With metaheuristics, we search for optimal network structures for a given number of nodes. We define triangle neighborhood and compare the results of the algorithm with the conjecture by Choplin et al. [8]. Further, we study the problem of order picking and order batching in block structured warehouses. For order picking problem, we present the extension of a dynamic programming algorithm by Ratliff and Rosenthal [42], which enables the development of an algorithm for an unlimited number of blocks. In order to achieve this, a new presentation of states and transitions of dynamic programming algorithm is given. We prove that the resulting path is optimal for the given structure. We compare the optimal path lengths to the results found in literature and also investigate the impact of warehouse layout parameters onto the routing. Closely related to the problem of order picking, we investigate the order batching problem. We discuss the variation of the order batching problem with time windows and present the algorithmic approach to solving the problem. The previously presented optimal path algorithm is applied in the algorithm to ensure even better quality of results. We introduce the evaluation function of a batch and compare the results of the algorithm with the test data from the literature as well as with data from the real warehouse. We conclude by summarizing the results and stating some possible extensions and further work.

Keywords

omrežja;iskanje najkrajše poti;problem trgovskega potnika;algoritmi;metahevristike;komisioniranje;

Data

Language:	English
Year of publishing:	2011
Source:	[Maribor
Typology:	2.08 - Doctoral Dissertation
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	K. Prnaver]
UDC:	519.17:519.85(043.3)
COBISS:	256276736
Views:	4536
Downloads:	217
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Other data

Secondary language:	Slovenian
Secondary title:	Optimizacijske metode za reševanje transportnih problemov na omrežjih
Secondary abstract:	V doktorskem delu smo preučili problem iz vsakdanjih situacij, ki jih je mogoče prevesti na problem na omrežnih grafih in jih rešili z uporabo matematične teorije grafov. Začnemo s problemom usmerjenih omrežij. Problem izvira iz omrežja, kjer je pretok skozi loke pomemben in velikokrat omejen s kapaciteto omrežij. Obstaja več tehnik ter rezultatov za problem določanja pretoka skozi omrežja. Pri našem problemu poskušamo najti optimalno omrežno strukturo, ki bi se lahko uporabljala v fazi načrtovanja omrežja. Z metahevrističnim pristopom iščemo optimalne strukture omrežja za določeno število vozlišč. Definiramo trikotniško soseščino in primerjamo rezultate algoritma z domnevo, ki so jo postavili Choplin in drugi. Nadalje preučujemo problem iskanja optimalne poti v bločno strukturiranem skladišču. Za problem predstavimo nadgradnjo algoritma dinamičnega programiranja, ki sta ga uvedla Ratliff in Rosenthal, in ki omogoča razvoj algoritma za neomejeno število blokov. Predstavljen je nov način zapisa stanja in prehodov med fazami dinamičnega programiranja. Dokažemo, da je rezultantna pot optimalna. Primerjamo naše rezultate za dolžino optimalne poti z rezultati iz literature in preučimo vpliv parametrov na najkrajše poti pri različnih postavitvah skladišč. Preučimo še tesno povezan problem komisioniranja, in sicer različico z časovnimi okni. Predstavimo algoritmični pristop k reševanju problema. Uporabimo predhodno predstavljen algoritem za iskanje optimalne poti,in s tem zagotovimo še večjo kakovost rezultatov. Uvedemo ocenitveno funkcijo za množico naročil in primerjamo rezultate algoritma s podatki iz literature, kot tudi s podatki iz dejanskega skladišča. Delo zaključimo s povzetkom rezultatov in navedemo nekatere možne razširitve in nadgradnje.
Secondary keywords:	Teorija grafov;Disertacije;Optimizacija;
URN:	URN:SI:UM:
Type (COBISS):	Dissertation
Thesis comment:	Univ. Maribor, Fak. za naravoslovje in matematiko
Pages:	131 str.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;combinatorial analysis;graph theory;kombinatorika;mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;operational research (or): mathematical theories and methods;operacijsko raziskovanje;mathematical programming;
ID:	20434