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p..- ,.I..ilI--... -4.,I-.,.I .-. ,:I.-p.I- .- II
1.-III.,I-.,-,, .,.Iq..I.-,-I.I.-...,....-i I...-,.
I II-I.:. I-.I-I- I.r,I.
, Ii-...I,-:.,%-,-.: :,,,..,-1-.I.L ---",, .,.. ...I.:..I,.II ..-- II.-I,7 .. IIII ,..II-I-III--:-: ,,,-,,, I-.I--.I.I.II..:.I.--. ..-.,.,;-.,.1--1I.-.7: -.:,-I:-:-I,--..-,.,.t,. , I,-,..,I-, .. A, ,.I.I.I--..III--.I-II-. ..-. ,z%-II.1,I--III.,.,, 1II.-I-II-.I.. ,, -.-,
,,--- .I--I -I I.-,.I-I -I.II 1 I--...,.-..I , I- ..II-- .. 1.I1,I:-,
: ,..I-I , ,-I.III.II.I-I...I--I-.I...--.I-I-.,...
,..III.---- i-.,,I.
Deterministic Network Optimization A Bibllography by Bruce L. Golden and Thomas L. Magnanti OR 054-76 June 976
Supported in part by U. S. Oepartment of Transportation (Contract DOT-TSC-1058), Transportation Advanced Research Program (TARP).
-2- Oeterministic Network Optilizatlont A Bibliography Introouct ion
In recent years, Network Optimization has grown to be a popular and fruitful area of operations research. T. C. Hu considers this area a new branch of combinatorial mathematics and applied graph theory GEN18I. The remarkable emergence of this subject is brought to light by eKamining the one-page bibliography in ai S.TlC Usesg by O. Ore (1963) where the author states, "The number of books on graph theory s very
small." In this report, we present a categorized bibliography on Deterministic Network Optimization which Includes a number of books and nearly 7uj entries. As the reader might note, most of our citations have appeared since Ore's book was published.
We do not intend to be encyclopedic in this compllation; rather, we have included references which are, for
the most part, accessib le and substant ia. We emphas ize algorithms for network optimization and underlying theory.
Mathematica GEN24] and Kivestu and Simpson [GENi91 provide comprehensive bibliographies which emphasize applications.
There are several noteworthy general reference books which should be mentioned. Ford and Fulkersons monograph GEN81 Is the original reference on the theory of flows n networks. In addition to containing results on static maximal flow and minimal cost flow problems, this source ntroduces network analysis as a
fresh viewpoint for studying purely combinatoral problems. More recently, Frank and Frisch [GENO] have written a very comprehensive treatment of the theory of networks, entailing both deterministic and probabilistic networks. Garfinkel and
Nemhauser [GEN131 cover integer programming, theory and applications. The relaticnship between nteger programming and graphs Is emphasized throughout the book. Christofides' GEN41 new book on graph theory, written by an operations researcher, stresses algorithms for classical operations research network problems. It Includes a chapter on matching theory and an
in-depth discussion of the Chinese postman Prob lem. The
excellent survey of deterministic networks by Bradley (GEN2] is also recommended highly.
Network models are important not only because of their direct applicabilty. In many cases, network optimization problems form subproblems for more cosplex and general real-world situations. Successful applications of network models Include
transport of goods, assignment problems, analysis and synthesis of transportation and communication networks, routing of
vehicles, traffic e quilibrium, equipment replacement, project
planning, production and inventory cont ro l, optimal capaci ty scheduling, and a host of others (see Fulkerson GEN12l).
We have divided our bib Iography on deterministic network optimization Into several categories n order to make It more readable and valuable to network researceers. These
Deterministic Network Optimization A Bibliography Intro duct ion
categories arel NETWORK ANALYSIS NET WORK SYNTHESIS UNIFYING TOPICS A. General References
B. Shortest Path Problems and Variants
C. Network Reliability
0. Single and Multi-Commodity Flows
E. Traffic Equilibrium
F. The Chinese Postman Problem and Matching
G. Travel ing Sa lesman Probl ems and Extensl ons (Vehicle Routing)
H. Minimal Spanning Trees and Variants I. Location of Facilities on a Network J. Design of an Optimal Network
K. Implementation Issues L. Complexity Theory
H. Hatrolds and Graph Theory
It should be noted that these categories are not
mutually exclusive. On the other hand, we do feel they represent
most research areas In Deterministic Network Optimization.
In compiling a bibllography of this nature, we have of course, benefited from many previous compilations. The books
mentioned above have served as general sources. In addition, papers by Assad [MULT1], Francis and Goldstein tLOCZ41] Glover and Kingnan [IMP191, Pierce SP361, and Wong IDES591 have been useful sources for special topics. The authors welcome
suggestions for improving this bibliography and hope that It will serve as a useful reference n this rmportant research field.
Finally, we would like to thank Ross Shachter who designed a computerized system for composing and updating this bibliograph y.
-3--4- Deterministic Network Optmizationt A Bibliography
General References
GENI. E. BECKENEACH (ed.), An.all aoM a.glorlal Matheai5,
John Wiley and Sons, New York (1964).
GEN2. G. BRADLEY, "Survey of Deterministic Networks,"
Alif
Iransactia1z,2 Z(3) 222-234 (1975).
GEN3. R. BUSACKER and T. SAATY, nite fCQJaa .ag Ntaorhs McGran- Hill, New York (1965).
GEN4. N. CHRISTOFIOES, G [J:b
beayI
AD
A. L!aorjthi9CLAg.g.aCh Academic Press, New York (975).
GEN5. G. DANTZIG, LI ear
Egca.
ralg and EXtgaslnonsPrinceton Unl versity Press, P r nceton, New Jersey (1963).
GEN6. S. ELHAGHRABY,
S
oaa ] blaGkdG.J
,nD
OQau.LIln1AQAlCQ Springer-Verlag, New York (1970).
GEN7. S. EVEN, AloCthmic Co ajinai.C2ci, Macml Illan, New York (1973).
GEN8. L. FORD and D. FULKERSON,
E[IgJv
in tacrj, Princeton University Press, Princetont N.J.GEN9. H. FRANK and I. FRISCH, "Network Analysis," ScLenttjC Ala.irma , (July 1970).
GENIO. H. FRANK and I. FRISCH, CQniBnlcati.j Transmssion and ICansortAaUGn NJIw DLt b Addison-Wesley, Reading, Mass.
(1971).
GENIIo I. FRISCH (ed.), Proceedings of the Symposium on Large-Scale Networks," fJg br, i2(1), 1975.
GEN12. D. FULKERSON, "Flow Networks and Combinatorial Operations Research, AULrjan fat &matLac.l nUtblX,
Z23
(2), 115-138 (1966).GEN13. R. GARFINKEL and Go NEHAUSER,
Lntea
r PC n,
Wlley, New York (1972).GEN14. F. HARARY, Gra.b IJ rcY, Addison-Wesley, Reading, Mass.
( 1969).
GEN15. 8. HARRIS (ed.), irah hC r Q. g l A oolicatloQn
Academic Press, New York (1970).
GEN16. T. C. HU, JItJgJr Proagramm n ang tInrLcrk FL s,
-5- Deterministic Network Optimization: A Bibliograhy
General References
GEN17. T. C. HU, "Recent Advances n Network Flows, SM RBSIt IJf, 354-359 (1968).
GENJ8. T C HU, "Some Problems in Discrete Optimizatlon,"
dath ErQg., 1 02-112 (1971).
GEN19. P. KIVESTU and R. SIMPSONI "Applications of Network Optimization 8A Bbl iography," MIT Technical Report (forthcoming)
GENZO Do KNUTH, It Ai g/ o utar eroaraslalq Y .,
Addison-Wesley, Reading, Mass. (968).
GEN21. Do KNUTH, b JL.At of g.J EauS era!anralng Mg.L 3, Addison-Wesley, Reading, Mass (1973).
GEN22- E. LAWLER, Combinatorla Qgtltz&atongl Networh Jg
fJtl s Holt, Rinehart, and Winston (forthcomilng).
GEN23. C. LIU9 Introauctlion tQ ~gaGlatrial laheatlcs McGraw-H11, New York (1968).
GEN24. MATHEMATICA "Bibliography of Network Theory Publications," In preparation.
GEN25. O. ORE, fiEC
m
IlgaLhejr
Uoi. , Random House, The L. W.Singer Company, New York (1963).
GEN26. A. NIJENHUIS and H. WILF GgInL±l.Oa ALaorthma,
Academic Press, New York(1975)o
GEN27. R. POTTS and R. OLIVER, E.LGI In IransDortation HJktw]rhI Academic Press, New York (1972).
GEN28. Re READ (ed.), ragh CTbeoy Ig GoIli.qla Academic Press, New York (1972).
GEN29. T. L. SAATY, 0Lmz2atLo in ID lalAr ad Rsia3 d
Ej~Cjcs eoblQa~sq* McGraw-H111, New York (1970).
GEN30o H. SALKIN, Inte9er ecggaeulg, Addison-Wesl ey Reading, Mass. (1975).
G EN31. A. SCOTT, gohloat:.La ECac QG & at.L AnLYiLis
aDgl. Plnniag Methuen, London (1971).
GEN32. M. ELLS EaIjmo °Sf 1 llGnat ociAL Cooulta g Pergamon Press, New York (971).
GEN33. M. ZELKOWITZ and A. AGRAWALA, "KWIC Index for ComAuter
Deterministic Network Optlmization: A Blblography
Shortest Path Problems and Variants
SPi. Me BAZARAA end R. LANGLEY, "A Dual Shortest Path Algorithm, ' L AaLd
l
figAh~ 2i(3)* 496-501( 1974).
SP2. R. BELLMAN, "On a Routing Problem,'" Bar, Anis
ath.
t£, 87-90 (1958).
SP3. J. BROWN, "Shortest Alternating Path Algorithms,"
NU QCat kS ,(4)* 311-334 (1974).
SP4. L. BUTAS, "A Directlonall y Oriented Shortest Path
Algorithm," Ira soortatLo n seaC 2, 253-268 (1968). SP5. V. CERF. . COWAN, R. MULLIN and R. STANTON, "LjaLg
fgund a Ib Araga Sbar eat~ In BASIlAr firtinbh"
LtirbCksg .t(4), 335-342 (974).
SP6. K. COOKE and E. HALSEY, "The Shortest Route through a Network with Time-Dependent Internodal Transit Times,"
Mathb. A na A&g A et . t1 493-498 (1966).
SP7. G. DANTZIG, "On the Shortest Route Through a Network,"
ft" L., · t 187-190 (1960).
SP8. E. OIJKSTRA, "A Note on Two Probl ems n Connection with Graphst" blumL. atbematlk, t1 269-271 (1959).
SP9. S. DREYF US, "An Appraisa I of Some Shortest-Path Algorithms·," Ons
B.-.
1.Z(3). 395-412 (1969).SP10. R. FLOYD, "Algorithm 971 Shortest Path," fjQG& g jog 1(6) 345 (1962).
SPIl. B FOX, "Finding a Minimal Cost to Time Ratio Circuit," Q2nna BiaS. 12I, 546 (1969).
SP2. H. FRANK, "Shortest Paths In Probabilistic Graphst
QOans- B&, 1S(4). 583-599 (1969).
SP13. J. GILSINN and C. WITZGALL "A Performance Comparlson of Labeling Algorithms for Calculating Shortest Path Trees," National Bureau of Standards Technical Note 772
(1973 ).
SP4.o F. GLOVER, 0. KLINGMAN, and A. NAPIER, "A Note on Finding All Shortest Paths," Lcans. Sl-., (i),* 3-13
( 1974).
SP15. 8. GOLDEN, "Shortest Path Algorithmst A Comparlson, Working Paper OR 044-75, Opers. Res. Center, M.I.T.
-Deterministic Network Optimization A Bbliography Shortest Path Problems and Variants
(October 1975), forthcoming in QarL.t Res,
SPj6. A. GOLDMAN and G. NEMHAUSER, "A T-ansport Improvement Problem Transformable to a Best-Path Problem,"
Irml.l,
rL L , 295-307 (1967).SPJt. S. HAKIMI, "Shortest Paths In Grapis-A Review,"
IJ;Ef
:tt.. SaM * icuit IThery 368-369 (1972).
SP18. J. HALPERN and I. PRIESS, "Shortest Path with Time
Constraints on Movement and Parking," thawomr.s I(3), 241-253 (1974.
SP19. P. HART, N. NILSSON, and B. RAPHAEL, "A Formal Basis for the Heuristic Oetermination of Minimum Cost Paths," IEEE tran g S ste Sa n;c l fSr tPcs
·S=. (2), 100-107 (1968).
SP20. L. HITCHNER, "A Comparative Investigation of the
Computational Efficiency of Shortest Path Algorithms. Tech Report ORC 68-17, Opers. Res. Center, Univ. of Calitf. at Berkeley (July 1968).
SP21. A. HOFFHAN and H. ARKOWITZ, "A Note on Shortest Path, Assignment, and Transportation Problems," taYt. Bjri. Lag., Q., ., 375-380 (1963).
SP22. W. HOFFMAN and R. PAVLEY, "A ethod for the Solution of the Nth Best Path Problem, "'JAC, , 506-514 (1959). SP23. W. HSIEH and A. KERSHENBAUM, "Constrained Routing In
Large Sparse Networks, "Eocg LnL gf Internationa f
CQ&utr SvaOSils, August 20- 22 Taipei, Taiwan (1975) ..
SP24. T. C. HU, A ecomposition Algorlthm for Shortest Paths
in a Network," GQD,& igi.L, .1, 91-102 (1968).
SP25. T. C. HU and . TORRES, "Shortcut n the Oecomposit on
Algorithm for Shortest Paths In 3 Network," JIM djoCrZnL qI sea r a. evelolon an 13, 387-390 (1969).,
SP26. H. JOKSCH, "The Shortest Route Problem With Constraints," JL
.,
j Wh AJl.& .an A&J.L A , 191(1966).
SPZ7. O. JOHNSON, "A Note on OJlkstra's Shortest Path
Algorithm," JAClJ 2iG(3), 385-388 (1973).
SP28. D. JOHNSON, "Algorithms For Shortest Paths," Ph.O. Thesis, Cornell University (1973) .
-8- Deterministic Network Optlmization A Bibliography Shortest Path Problems and ariants
SP29. E. JOHNSON, "On Shortest Paths and Sorting,"
ECesegnas I 1Z AU C QB2.fI lnc Boston, (August 1972), 510-517.
SP30. R. KIRBY and R. POTTS, "The Minimum Route Problem for
Networks with Turn Penalties and Prohibit ons,"
TrarnsorAation Bsarch, 3, 397-408 (1969).
SP31. V. KLEE, "A String Algorittm for Shortest Paths In Directed Networks, "DnsA. &L.
L.
428-432 (1964).SP32. G. MILLS, "A Decomposltlon Algorithm for the Shortest-Route Probl em," Ons.
B.
. 1(2), 279-291(1966).
SP33. Go MILLS, "A Heuristic Approach to Some Shortest Route Prob I ems," ng.ia a QOeratloL B Garch jaLt
gurnaaL, (Harch 1968).
SP34. G. NENHAUSER, "A Generalized Permanent Label Setting Algorithm for the Shortest Path Between Specified Nodes," JlL g JathbL Anaj ad &Aal 38, 328-334
(1972).
SP35. U. PAPE, "Implementation and Efficiency of Moore-Algorithms for the Shortest Route Problem," l.
r.G.,
r
,
212-222 (1974).SP36. A. PIERCE, Bibliography on Algorithms for Shortest Path, Shortest Spanning Tree, and Related Circuit
Routing Problems (1956- 194)," Itworbrs, (2), 129-150 ( 1975).
SP37. I. POHL, "Heuristic Search Viewed as Patl Finding n a Graph," ACtfilJCL It.ll.ilgenc 1, 193 (1970).
SP38. R. POTTS and R. OLIVER, Fl1QI in Icansporatal/a
tiLgdorks, Academic Press, New York (1972).
SP39. n. SAKAROVITCH, "The K Shortest Chains in a Graoh,"
1anS a., , 1-11 (1968)
SP40. J. SAKSENA and S. KUMAR, "The Roting Problem with "k"
Specified Nodes, "Q.ns,. &., 14, 909-913 (1966).
SP41. J. F. SHAPIRO, "Shortest Route Hethods For Finite State Space Oeterministic Dynamic Programming Problems," JI
L& gon QQM li. , If1, 1232-1250 (968).
SP42. O. SHIER, "Algorithms for Finding the K Shortest Paths in a Network," paper presented at ORSA/TIMS Spring Meeting, Philadelphia (1976).
-9- Deterministic Network Optimizationt A Bibliography
Shortest Pat9, Problems and Variants
SP43. O. SHIER, "Computational Experience with an Algorithm
for Finding the K Shortest Paths n a Network," aJu.nal G/ BRa gari b. i f h9 Z, 139-165 (974).
SP44. P. SPIRA, "A New Algorithm for Finding All Shortest Paths n a Graph of Positive Arcs i'n Average Time
O((nlogn)++2)," IAM LL gcutIng, Z(i) 28-32 (1973). SP45. P. SPIRA and A. PAN, "On Finding and Updating Spanning
Trees and Shortest Paths," .LAUt AL ".RBoltgl2t (3),
375-380 (1975).
SP46. A. WEINTRAUB, "The Shortest and K-Shortest Routes as Assignment Problems," QJGJs 3(1), 61-74 (1973).
SP47. T. ILLIAMS, "An Improved Shortest Path Algorithm for
Networks in which the Maxlmum Outward Degree s Less than n/2," Presented at the 1975 ORSA/TIMS Meeting, Las Vegas, Nevada.
SP48. J. YEN, "An Algorithm for Finding Shortest Routes from
All Source Nodes to a Given Destination n General Networks," aC.terl Jdurnal f &lad MathematIrs1& 2,i 526-530 (1970)
SP49. J. YEN, "On Hu's Oecompositlon Algorithm for Shortest Paths in a Network, "lns. ]9 g. (4), 983-985 (1971).
SP50O. J. YEN, Finding the Lengths of All Shortest Paths in N-Node Nonnegative Distance Complete Networks Using
1/2N+3 Additions and Nee3 Comparlsions" JACM 12(3),
-10- Deterministic Network Optimization A Blbliography
Network Reliability
REL1. M BALL and R. VAN SLYKE9 "Backtracking Algorithms for Network Rel lab I lity Anal ysis" &[A £iJ.etlnqtf39 (1),
B-73 (975).
REL2. R. BARLOW and F. PROSCHAN, ItJbnswati JJ.l bIhQrx .jl Bal.lahii.tI Wiley (1965).
REL3. M. BELLMHOREt "Optimal Al locaton of Resources In a Communicatlons Network," Ph.O. Thesis, John Hopkins University, Baltimore, Maryland (1965).
REL4. M. BELLMORE and P. JENSEN, "An Impl cit Enumeration Scheme for Proper Cut Generation," Tachnometrics, 1Z(4) (1970).
REL5. 0. BROWN, "A Computerized Algorithm for Determining the Reliability of Redundant Configurations," IEF .r.ans.
gD
Rellaibllt· -2n(3) 121±-24 (J971).REL6. H. FRANK and W. CHOW, "Topological Optimization of Computer Networks," ro.g ce.ed inl s
L
ji 1385-1397 (1972).REL7. H. FRANK and I. FRISCH, "Analysis and Design of Survivabl e Networks," ,EE. lca.itS1InS CoI. LLQ Tc.· Co·gL(5) 502-503 (1970).
REL8. V. FU and S. YAU, "A Note on the Rellabl Ity of Communication Networks," . SL j /(3) 469-474
( 1962).
REL9. 0. FULKERSON and L SHAPLEY "MHnimal K-Arc Connected Graphs," 1aIwoks, 1(1). 91-98 (971).
RELlO. S. HAKIMHI "An Algorithm for Construction of the Least
Vulnerable Communication Network," IEEU rars.a
rircult
1jagc1. CTL-. 229-230 (1969).REL11. S. L. HAKII and A. AIN, "On the Design of Reliable Networks," I.njt.grks 3(3) 241-260 (1973).
REL12. E. HANSLER, A Fast Recursive Al gorithm to Calculate
the Re labi lty of a Communication Network,"
IUg
ICI/ans an Q mfuDlIcatlons, C.2a( 3) , 637-640 (1972). REL13. E. HANSLER, G. CAULIFFE, and R. WILKOV9 "Exact
Calculation of Computer Network el lability," Ne~tocksi 4(2), 95-112 (1974).
-11- Deterministic Network Optimization8 A Bbllography Network Reliability
Triconnected Components," SL&N L. ogmgut., Z(3) (Sept. 1973)
REL15. J. HOPCROFT and R. TARJAN, "Efficient Algorithms for Graph Hanipulation," gaJ gi. &Q,, (16) (June 1973) . RELI6. T. C. HU, "ost Reliable Routes in a Network," SIA
RBAXLx (2), 261 (1966).
REL7. P. JENSEN and H. BELLMORE, "An Algorithm to Determine
the Reliability of a Complex System," EE TransactSlns 920 a liab lt R-i(4) (969).
REL18. P. JENSEN, "A Graph Decomposition Technique for the
Design of Redundant Electronic Networks," Ph.D. Dissertation, Johns Hopkins Univarsity, Bait., Maryland
(1967).
RELI9. A. KERSHENBAUM and R. VAN SLYKE, "Recursive Analysis of Network Rellabl ty," Nletwanck [(j1)9 81-94 (1973).
REL20. Y. KIM, K. CASE, and P. GHARE, "A Method for Computing Complex System Reliability," IEEE IrCa~S Qn
e llaltiA. R21(4), 215-219 (1972).
REL21. J. LEGGETT "Synthesis of Reliable Communication Networks, Ph.D. dissertation, University of Pennsylvania (1968).
REL22. W. MAYEDA, Gran Ieor. John Wiley and Sons, New York ( 1972).
REL23. P. IRCHANOANI, "Analysis of Stochastic Networks in Emergency Service Systems, Innovative Resource Planning in Urban Public Safety Systemst Tech. Report
TR-15-75, Opers. Res. Center, M.[.T, (March 19751.
REL24. K. MHISRA, "An Algorithm for the Reliability Evaluation of Redundant Networkst" T.lfE tc an . R elabllt,
-1_21(4)* 146-151 (1970).
REL25. K. MISRA and T. RAO, "Reliability Analysis of Redundant Networks Using Flow Graphs," L.LE Itans Qn
BRleJjakjL1x, g(1), 19-24 (1970).
REL26. E. MOORE and C. SHANNON, "Reliable Circuits Using Less Reliable Relays," & I Fran.aal I nsttuteta 2f, 191-208 (Part I) and 281-297 (Part II)(1956).
REL27 F. . OSKOWITZ, "The Analysis of Redundancy Networks,"
A&ILE .I.caU E m. a al roES. s J, ., 627-632
-12- Oeterministlc Network Optimlzation A Bibliography Network Reliability
REL28. J. MHURCHLAIDO, "Calculating the Probablilty that a Graph is Dlisconnected," Report JD-82, Planning and Transport Research and Computation Co., London (Feb.
1973).
REL29. J. HURCHLANO, "Fundamental Relations for Repairable Iterms" Report JOM-177 Planning and Transport Research and Computation Co., London (Feb. 1973).
REL30· J. MURCHLAND and 0. SHIER, "Calculating the Probability that an Undirected Graph Is Disconnected," Report JDM-186, Planning and Transport Research and
Computation Co., London (1973)·
REL31. S. PARIKH and I. FRISCH, "Finding the Most Reliable Routes In Communication System," IEEE l ansaaau
xstas,
CS-1i± 402-407 (1963).REL32. A. ROSENTHAL, "Computing Relab lity of Complex Systems," Ph.O° Thesis, U.· of Cal., Berkeley (1974). REL33. S. SESHU and H. REED, Linear (rAi.bZ mnQa E Ictri al
tiagacrkse Addilson-Wesley (1971).
REL34. J. SUURBALLE, "Disjoint Paths n a Network," Ulworkspt .(2)* 125-146 (1974).
REL35. R. TARJAN, "Depth First Search and Linear Graph Algorlthms," SiL & fAa
ai.-,
(2) (June 1972).REL36. R. VAN SLYKE and H. FRANK, "Rellab llty of Computer-Communication Network, " Proc tb QCon.
d
SlulatiAn AFIPS Press, Providence, 71-82, (1971).
REL37. R. VAN SLYKE and H. FRANK, "Nletwork Rel labil ity
Analysiss Part Ir" Nerk9t 1(3), 279-290 (1971).
REL38. R. VAN SLYKE, H. FRANK, and A. KERSHENBAUM, "Network
Rel iability Analysist Part 2. " ltaorks(to be published).
REL39. R. WILKOV, "Analysis and Design of Reliable Computer
Net works 9" JEF Ians g QMaiLcL a s,1 M-20 ( 3) . 660-678 (1972).
REL4O. O. WING, "Algorithms to Find the Most Reliable Path In
a Network," .LB ITrans. . cLt T.rIheo ..A ,. 78-79
-i3- Deterministic Network Optimization A Bibliography Single and Multi-Commodity Flows
MULTI. A. ASSAD, "ulticommodity Network Flows - A Survey," Operations Research Center M. I.T., Working Paper OR
u 45-75.
MULT2. E. BALAS and P. L. IVANESCU, 'On the Generalized Transportation Problem," an. SaCJl 11t 88-202 (1964).
MULT3o E. M. L. BEALE, "An Algorithm for Solving the Transportation Problem When the Shipping Cost over Each Route is Convex," Nay B 1. LQaL Q.9 fa 43-46 (1959). MULT4. M. BELLMORE, G. BENNINGTON, and S. LUBORE, "A
Multivehicle Tanker Scheduling Problem," Irans ., J9 36-47 (1971)
MULT5. M. BELLMORE and H. RATLIFF, "'Optima I Defense of Multi-Commodity Networks," e I"Lel an. j1(4)
174-185(1971).
MULT6. G. E. BENNINGTON, "An Ef ficlent Minimum Cost Flow
Algorithmn" atl .a L, 1J(9), 1021-1051 (1973).
MULTi. 6 BOZOKI, "Minimum Cost Hulticommodity Network Flows,"
Ph. D Thesis, Purdue Univ. (June 1969).
NULT. So P. BRAOLEY9 "Solution Techniques for the Traff tic Assignment Problem," Tech. Report ORC 65-35, Opers. Res. Center, Univ. of Calif. Berkeley (1965).
MULT9. D. G. CANTOR and M. GERLA, "3ptImal Routing ln a Packet-Sw itched Computer Network, " IfEE TCan 9
CQUL±M*..l .t-I ±0g 10062-1068 (J974).
MULT10. A. CHARNES and W. W. COOPER, "The Stepping Stone Method of Explaining Linear Programming Calculations In
Transportation Problems," Man, SjLo 1 49-69 (1954).
MULT1. A. CHARNES and W. W. COOPER, "Multicopy Traffic Network Models," In Thor . TrafI.LL ELt (R. Herman, Ed. )
Elseviewn Amsterdam, 84-96 (19611.
MULTZ2. S. CHEN and R. SAIGAL, A Primal Algorithm for Solving a Capacitated Network Flow Problem with Additional
Linear Constraints," Tech, Report, Bell Laboratorles,
Holmdel, N. J. (1975).
MULTI3. J. E. CREMEANSe R. SMITH and G. TYNDALL, 'Optimal
Multicommodity Flows with Resource Allocation," tNil *es LQg Q *r 1, 269-280 (970).
-14- Deterministic Network Optimization: A Bibliography
Single and Mu ti-Commodity Flows
MULTt4. G. B. OANTZIG, "Application of the Simplex ethod to a Transportation Problem," AGt.Iy ily A!nalzs.gs i g Liaa . ana Al. JLSatiLgn Cowles Commission Monograph
139 Wiley, 359-373 (1951).
MULT15. G. B. OANTZIG and O. R. FULKERSON, "On the Max-F I ow MHn-Cut Theorem of Networks," In Lear Ineouuallites
angi RglatJa
Systsi nnat ,38
215-21(1956)
MULT16. G. B. ANTZIG and A. J. HOFFMAN, "ilworth's Theorem on Partially Ordered Sets," in LILa C Iaua ils Ana
Baiatea
SsX.ta
9 A, 9.t Math. S tud , PrincetonUniv. Press., Princeton, N. J. 207-214 (1956).
HULT17. J. 8. DENNIS9, A High-Speed Computer Technique for the
Transportation Problems" JA,9 A, 32-151 (1958).
MULTi8. P. OWYER, "The Direct Solution of the Transportation Problem with Reduced Matrices," ,a.L 1j.,, 1.(1), 77-98
( 1966).
MULTj9. P. S. DWYER, "The Solution of the Hitchcock Transportation Problem with a Method of Reduced Matrices," Univ. of MiHch. (1955).
MULT20. J. EDMONOS and R. H. KARP, "Theoretical Improvements In
Algorithmic Ef ficency for Network Flow Problems," Lrf: 9. 248-264 (1972).
MULT21. P. ELIAS, A. FEINSTEIN, and C. E. SHANNON, "A Note on the Maximal Flow through a Network," IE IJCan.. nICBr&A Ih.eorC I1_2. 117-119 (1956).
MULT22 H. . FLOOD, "On the Hitchcock iJstribution Problem,"
ea;u iLa.. t I ., 369-386 (1953).
MULT23. L. R. FORD and 0 R FULKERSON, "Maximal Flow through a
Network," Can, L MLath. 1.i9 399-404 (1956).
MULT24. L. R. FORD and O. R. FULKERSON, "Solving the Transportation Problem," aAM ig, ,9 24-32 (1956).
nULT25. L. R. FORD and D. R. FULKERSO N "A Pri 1a l-Dual
Algorithm for the Capacitated Hitchcock Problem," aL
Res L& .Q- *. 47-54 (1957).
MULT26. L. R. FORD and 0. R. FULKERSON, "A Simple Algorithm for
Finding Maximal Network Flows and An Application to the
Hitchcock Probl em," Ca
n.
J Ihtb3 9! , 210-218 (1957).-15- Deterministic Network Optimization A Bibliography Single and Multi-Commodity Flows
Dynamic Flows from Static Flows," Qns. B .9o 419-433
(1958).
MULT28. L. R. FORD and 0. R. FULKERSON, "A Suggested Computation for Maximal Multi-Commodity Network Flows,"
1M
U..
"i. i. 97-101 (1958).MULT29. L. R. FORD and 0. R. FULKERSON, "Network Flow and Systems of Representatives," Ql..L A fatfLt. . 1j, 78-85
(1958) .
MULT30. L. R. FORD and O. R. FULKERSON, F l os i N. QotarJIi Princeton Univ. Press, Princeton, N. J. (1962).
MtULT31. H. FRANK and W. CHOU, 'Routing in Computer Networks," Jors, (2), 99-112 (1971).
MULT32. H. FRANK and I. T. FRISCH, Qgu3jlatio.o.ns Transmlsslon
Aug TCTansgotaati NatjrCk, Addison-Wesley, Reading, Mass. (1971) .
MULT33o I. T. FRISCH, "Optimum Routes in Communication Systems with Channel Capacities and Channel Re liabilities,"
IUEE cUanls " S ystieaf, .5±l· 241-244 (1963). MULT34. T. FUJISAWA9 "A Computatona I Method for the
Transportation Problem in a Network," ". OQrc t.. aQGJ ,JaaL- , 157-173 (195°).
MULT35. T. FUJISAWA, "Maximum Flows In a Lossy Network," in
Po e ed AlQin Connu erL lft n IrcuI t A.D
xatl hJUas:tY Urbana I I., 385-383 (1963).
MULT36. O. R. FULKERSON, "Note on Ollworth's Decomposition Theorem for Partially Ordered Sets," In Proc aBIQe
lAtlb SQC, Z, 701-7C2 (1956).
MULT37. 0. R. FULKERSON, "A Network Flow Feasibility Theorem and Combinatorial Applications," C an, A.tL Ha , 11,
4 4C-4 51, (1959) ·.
MULT38. 0. R. FULKERSON, "An Out-of-K I ter Method for Minimum-Cost F low Problems," J& UAis 9 18-27 (1961).
MULT39. 0. GALE, "A Theorem on Flows In Networks," Ea. J.
flthl-. Z, 1073-1082 (1957).
MULT40. O. GALE, "Transient Flows In Networks," Lch. attg L,
f, 59-63 (1959).
MULT41. A. N. GLEYZAL, "An Algorithm for Solving the Transportation Problem," Res. Paoer 2583, Uji J.A, 54,
-16- Deterministic Network Optimilzatlont A Blbliography Single and Multi-Commodity Flows
213-216 (1955).
MULT42. F. GLOVER and 0. KLINGMAN, "On the Equivalence of Some Generalized Network Problems to Pure Network Problems,"
alJ Etag·. . .(3), 369-370 (1973) ·
MULT43. F. GLOVER, D. KLINGMAN, and G. R. ROSS, "Finding Equivalent Transportation Problems," hayi B.s. L
21(2)* 247-2539 (974).
MULT44. B. GOLDEN A Minimum Cost Multicommodity Network Flow Problem Concerning Imports and Exports," NeSwgCmjZ9
i(4)
331-356(975)-MULT45. M. O GRIGORIADIS and W. W., WHITE, "A Partitioning Algorithm for the Multicommodity Network Flow Problem,"
tiabl, etag-, (2), 157-177 (Oct. 1972).
MULT46. M. D. GRIGORIAOIS and W. W. WHITE, "Computational Experience with a Multicommodity Flow Algorithm," In
QotialzatIC / I&r 6Mhas ftarp AI 1 caon, (R. Cottle and Krarup, Eds.) English Univ. Press, 205-226
(1972)
IULT47. R. C. GRINOLO, "A Multicommodity Hax-FIow Algorithm," QQa1, B 16· 1i234-1238 (1968).
MULT48. S. L. HAKIMI, "Simultaneous Flows through Communication Networks," J TLans. ir L. cL. 1J- Q j-_ 9, 169-175
(1962).
MULT49. J. HARTMAN and L. LASOON, "A Generalized Upper-Bounding Algorithm for Multicommodity Flow Networks," 3LktlhS
1, 33-354 (1972).
MULT50 I. HELLER, "Constraint atrices of Transportation-type Problems," , asa.U Ls..L ., i, 73-78 (1957).
MULT51. F. L. HITCHCOCK, "The Distribution of a Product from Several Sources to Numerous Localities," h Nattl. EhtS-, 2, 224-230 (1941) ·
MULT52 T. C. HU, "'Multicommodity Network Flows," ons USs.,
l1t 344- 360 (1963).
MULT53. T. C. HU, "'On the Feasibility of Simultaneous Flows in a Network," Q.5 Bjft., "j, 359-360 (1964).
MULT54. T. C. HU, Minimum Convex Cost Flow n Networks," Nay,
BaS La. 2&Lt * , 1-9 (1966).
-17- Deterministic Network Optimizationt A Bibliography Single and Multi-Commodity Flows
Problems," "L QjlCA& Res Soc. Jaanq 3 27-87 (1960). MULT56. W. S. JEWELL, "Optimal Flow through Networks," Tech.
Report No. 8, Opers. Res. Center, M.I.T. (June 1958).
MULT57. N. S. JEWELL, "Optimal Flow through Networks with Gains,' Qnns. L B.o /- 476-499 (1962).
MULT58. W. S. JEWELL, "Multicommodity Network Solutions," Tech. Report ORC66-23, Opers. Res. eitero Univ. of Calif. Berkeley, (1966).
MULT59. W. S. JEWELL, "A Pri mal-Oal Mu Iticommodity
Flow-Algorithm," Tech. Report ORC 66-24, Oers. Res. Center, Univ. of Callf., Berkeley (1966).
MULT60. E. JOHNSON, "Networks and Basic Solutions," Qnn s.· fb ,
,· 619-624 (1966).
MULT61. L. KANTOROVITCHI, "On the Trans location of Masses," GIaJ &ea" (I0Qokladl J;i r S i·, Lt, 199-201, (1942).
MULT62. L. KANTOROVITCH and M. K. GAVURIN, "The Application of Mathematical Methods In Probl ers of Freight Flow
Analysis," I QlQlectlon G/ EIiLuA fgSLncerned ]ilt3 Increasing 1S Etfectiveia L2 TCanLsYor' Publ of
the Akademii Nauk SSSR 1i10-138
(1949)-HULT63. J. KENNINGTON, "Mul ticommodity Network Flowst A State-of-the-Art Survey of Llnear Models and Solution Techniques, " Tech. Reports IEOR 75014 and IEOR 75015, Dept. of Ind. Eng. ano Opers. Res., SMU (Dec. 1975).
HULT64. M. KLEIN, "A Primal Method for Minimum Cost Flows with Application to the Assignment and TransportaProblems,"
H~. , 1A(3)- .L 205-220 (1967).
MULT65. D. J. KLEITMAN, 'An Algorithm for Certain Multi-commodity Flow Problems," Networ 9 J, 75-90
( 1971).
MULT66. R. W. KLESSIG, "An Algorithm for Nonlinear Multicommodity Flow Problems," UtwQror _l4)343-356
(1974).
MULT67. O. KLINGHAN and G. T. ROSS, Finding Equivalent NeTwork Formulations for Constrained Network Problems," MaL
SJL (to appear).
MULT68. O. KLINGHAN and R. RUSSELL, "Solving Constrained Transportation Problems," QDns. 2B"j 23(1), 91-106
-18- Deterministic Network Optlmilzation A Bibliography
Single and Multi-Commodlty Flows
MULT69. T. C. KOOPMANS and S. REI TER, "A Mode I of Transportation, in AG&i. ity Anal.Y.i a.t eCgloduc tQD a
Alocgation, Cowles Commission Monograph 139 Wil ey,
222-259 (1951).
MULT70. H. W. KUHN, "The Hungarian Method for the Assignment Problem," a1a B.L Log, *g.o2 83-97 (1955).
MULT71. H. . KUHN9 "Variants of the Hungarian Method for the Assignment Problems," t.QA&L is. LQ9 9., 3, 253-258
(1956).
MULT72o S. AIER, "A Multi-Item Network Flow Model with Capacity Constraints," Tech. Report 69-149 Dept. of Opers. Res., Stanford Univ. (Oec 1969).
MULT73. S. MAIER, 'A Compact Inverse Scheme Applied to a Multicommodity Network with Resource Constraints," In
QpUalzait
1b
JE
ar
source
All
acatlJsn
Eng l sh
Univ. Press, 179- 203 (1972).
tULT74. W. MAYEOA and M. E. VAN VALKENBURG, "Properties of Lossy Communication Nets," EJ; Trans. CIrcu&L t ]t.
CTLtzp 344-388 (1965).
MULT75. J. MINTY, "Monotone Networks," Prg& y.Q Sc.
Londng
ZA
A 2.L, 194-212 (1960)MULT76. T. S. MOTZKIN, '"The Assignment Prob Iem," In ero.S
.h^ . gSoeslum In Ag.LL :Ltj .M , McGraw-HI I , 109-125 (1956).
MULT77. J. F. MUARRAS, "Optimization of the Flow Through Networks with Galns," ah... t Egs 4(2), 135-145 (1972) MULT78. J. MUNKRES, "Algorithms for the Assignment and
Transportation Problem," L.
SA!,
i
32-38 (1957) .MULT79. K. ONAGA, "Optimum Flows in General Communicat ion Networkst" A EnbJ.L idlasts 283s 308-317 (1967).
HULT80O A. ORDEN, "The Transhipment Problem," em" a. 1J., 3
276-285 (1956).
MULT81. J. H. PLA, "An Out-of-Kilter Algorithm for Solving
Minimum Cost Potential Problems," Jit EC.r.Q P.g 275-290 (971j)
MULT82. M. R. RAO and S. ZIONTS, "Allocation of Transportat on Units to Alternative Trips," Qga RjU.,
Zk.
52-63(1968)
' 4 ' ' ,\
-19- Deterministic Network Optimizatlon A Bbliography Single and Multi-Commodity Flows
NULT83. J. T. ROBACKER, "On Network Theory," Res. Memorandum RM-14989 The RAND Corp. (May 1955).
MULT84. 8. ROTHFARB, Comblnatoric Methods for Multlicommodity Flows," Ph.D. Thesis, Univ. of Catlf., Berkeley (1968). HULT85. B. ROTHFARB and I. T. FRISCH, "On the Three-Commodity
F low Problem," SM a gQ AaaL& at.-, i , 46-58
(1969).
MULT86. 8. ROTHFARB, N. P. SHEIN, and I. T. FRISCH, "Ccmmon Terminal Hulticommodity Flow," 2Qrasa R,.t h, 202-205
(1968)
MULT87. 8. ROTHSCHILD and A. WHINSTON9, Feasiblllty of Two Commodity Flows," onsr. ft.a., lp 112112129 (1966).
HULT88. B. ROTHSCHILD and A. WHINSTON, "On two Commodity Network Flowst QgD. fjL-, ,4, 377-387 (1966).
MULT89. R. SAIGAL, "Multlcommodity Flows in ODirected Networks," Tech. Report ORC 69-14, Opers. Res. Center, Univ. of
Callf .9 Berkeley (Sept. 969).
HULT90. N. SAKAROVITCH9 "The Multicommodity Max Flow Problem', Tech. Report ORC 66-25, Opers. es. Center, Univ. of Calif., Berkeley (1966).
MULT91. H. SAKAROVITCH, "The Multicomeodity Flow Probleat," Ph.O. Thesls, Opers. Res. Center, Univ. of Callf., Berkeley (1966).
MULT92. J. F. SHAPIRO, "A Note on the Primal-Dual and Out-of-K Il ter Algorithms for Network Optimrai zat ion
Problems," .ititlZS (to appear).
MULT93. L. S. SHAPLEY, "On Network F lw Functions," Res. Memorandum RM-2338, The RAN'D Corp., (March 1959).
MULT94. C. SWOVELAND, "Oecomposit ion Al gorithms for the
Multicommodity Distrlbution Problei," Working PaPer No. 184, Western Sci. Man. Instit., UCLA (June 1975)
MULT95. W. SZWARC9 "Instant Transportation Solutions," at.L
iti. Lga Quart., 2· (3), 427-440 (1975).
MULT96. W. SZWARC, "The Transportation Paradox," tlv. as. L, uaLIbt., ±&, 185-202 (1971).
MULT97. W. SZWARC9 "The Transportation Problem with Stochastic Demand, an, Sclp "l 33-50 (1964).
-20- Deterministic Network Optimization A Bibliography
Single and Multi-Commodlty Flows
MULT98. D. T. TANG, "Comments on Feasibility Conditions of
Simultaneous Flow In a Network," 2Q2.iA. "sg-. 1/ ,
143-146 (1965).
MULT99. O. T. To TANG, "Communication Networks wlth Simultaneous
F low Requirements," I Tal c . ICh.c , .t1-
.,
176-182 (1962). MULT100. MULTO11. MULT102. MULT103. MULTJ04
0. T. TANG, "Blpath Networks and Multicommodity Flows,"
I E E Ia,, 1ru.uI I:," C J.1 468-474 (1964).
N. TOMIZAWA, On Some Techniques Useful for Solution of Transportation Problems," ItQioIC.a 19' 173-194 (1972)o J. A. TOMLIN, 'Minimum Cost ulticommodity Network F low" Qs. U.qL, ,LA, 45-51 (1966).
J. A. TOMLINt"A Mathematical Programming Model for the Combined Oi s tr ibut ion-Ass i gnment of Traffic,"
.ca.s
·.1, , 120-140 (1971).
A. . TUCKER, "Analogues of Kirchhoff's Laws," ~eraa Has!lngton UnL . JLItJ Er I, (1950).
MULT105. MULT10 6. MULT107. MULTiC 8. MULT109. MULTiO. MULT111.
J. VON NEUMANN, A Certain Zero-Sum Two-Person Game Equivalent to the Optimal Assignment Problem," In
Q CcibutJ=Q .Q tba h eory qgf Gagl, Ann. Math Study 28, 5-12 (1953).
D. F. VOTAW Jr., and A. ORDEN, "The Personnel Assignment Problem," Prolect SCOOP, Manual 10, 155-163
(1952).
H. . WAGNER, "On a Class of Capacitated Transportation Problems," la, Sl., Ji 304-318 (1959).
A. C. WILLIAMS, "A Treatment of Transportation Problems by Oecomposition," Le. SIA , 1, 35-48 (1962).
N. nHITE, "Oynamic Transship ment Networks: An
Algorithm and its Application to the DiOlstribution of Empty Containers," Networbs, 2(3), 211-236 (1972).
R. . WOLLHER, "HMuticommodity Network F lows with Resource Constraintst The General zed Multiccmmodlty Flow Problem," tocrk, 1(3), 245-263 (1972).
8. YAGED, "Minimum Cost Routing for Static Network Models," LaearkI4S, 1(2), 139-172 (971).
N. ZADEH, "More Pathological Examples for Network Flow
-21- Deterministlc Network Optimization A Bbliography
Single and Multi-Commodity Flows
Problems," Hath
.Er.
g. 5(2). 217-224 (1973).MULT113. N ZADEH, A Bad Network Problem for the Smplex Method and Other Minimum Cost Flow Algorithms," ath, erg2., 5(3), 255-266 (1973).
lULT114. W. I. ZANGWILL9 "A
Multi-Echelon Model o
Production System- A
11(9). 506-527 (1969).
Backl oggl ng Model and a f a Oynamic Economic Lot Size Network Approach," M I j., 9
-22- Oeterminist lc Network Optimization A Bibliography
Traffic Equilibrium
EQUIL1. M. J. BECKMANN, "On the Theory of Traffic Flow in
Networks," If.L= Quartur..· , 109-117 (1967).
EQUIL2. M. ECKMANN, C. 8. cGUIRE and C. B. WINSTEN, .A
tLdA
in Economics f I ansportation Yale Univ. Press. New Haven (1956).EQUIL 3. K. BHATT, "Search in Transportation Planning A Critical Bibliographye" Research Report R 68-46, M.I.T. Oepartment of Civil Engineering (1968).
EQUIL4. R. BROOKS, "Allocatlon of Natur al Gas in Times of Shortage," Ph.D. Thesis, Opers. es. Center, MIT, (Aug.
1975).
EQUIL5. A. CHARNES and W. COOPER,"Mul ticopy Traffic Network Models," n Th.ory 21 1rafj.Q .w (R. Herman, Editor), Elsevier, Amsterdam, 84-96 (196). G. OANS and 0. GAZIS, "Opt ival Control of Oversaturated Store-and-Forward Transportation Networks," ICDn.s.
Cla L)(1), 1-19 (1976).
EQUIL6. S. C. OAFERMOS, "An Extenoaed Traffic Assignment Model
with Applications to Two-Way Traffic,'" Irans.L S21., , 366- 389 (1971).
EQUIL7. S. C. DAFERMOS, "The Traffic Assignment Problem for Multi-Class User Transportation Networks," Tran. S,
(1), 73-87 (1972).
EQUIL8. S. C. DAFERMOS and F.T. SPARROW The Traffic Assignment Problem for a General Network," L Re&. Sal ~jtE.. D
73B, 91-118(1969).
EQUIL9. J. FERLANO, H. FLORIAN, and C. ACHIM, "On Incremental Methods for Traffic Assignment,"
Iran&.
Rs. 9( (4), 237-239 (1975).EQUIL1G.
EQUILi1.
EQUIL 2.
M. FLORIAN and S. NGUYEN, A Method for Computing Network Equilibrium with El astic Demands," Trans.
.GI.,
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H. FLORIAN and S. NGUYEN, "Recent Experience with Equilibrium Methods for the Study of a Conjested Urban Area," presented at the Int. Symp. on Traff ic Equilibrium Methods, Montreal (Nov. 1974).
M. FLORIAN, S. NGUYEN and J. FERLAND, "On the Combined
-23- Deterministic Network Optlmizatlont A Bibliography Traffic Equilibrium 43-53 (1975). EQUIL13o EQUIL14. EQUILI5. EQUIL16.
L. FRATTA, H. GERLA and L. KLEINROCK, "The
Deviation Methodt An Approach to Store-and-F Communicatlon Network Designg" NgL~Jorhj1 (2),
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N. GARTNER9 "Area Traffic Control and Network
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A. GIBERT, "A Method for the Traffic Assignment Problem," Transport Network Theory Unit Report LBS -TNT 959 London Business School, London (1968).
A. GIBERT, "A Method for the Traffic Assignment Problem when Demand s Elastic," Transport Network Theory Unit Report LBS-TNT 85, London Business School London
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H. H. HALL, E. O. HEADY, A. S SPOSITO, "Spacial Equilibrium I
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H. A HALL and E. L. PETERSON, Analyzed via Geometric Programmi No. 130, Center for Math. Studies Scl.tNorthwestern Univ. (1975). N. O. JORGENSON, Assignment Prob Calif, Berkeley TOECKER, and n U.S. Agricult "Traff lc Equi qg," Discussion in Econ. and V. A. ure A 1Z(2), libria Paper M an
"Some Aspects of the Urban Traf fic lem, I.T.T.E. Graduate Report, Univ. of (1963 ) .
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D. KULASH, "A Transportation Equilibrium Model," Institute Paper 708-45, Washington, D.C. (Sept.
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L. J. LEBLANC, L. J. MORLOK, and W,. PIERSKALLA, An Accurate and Efficient Approach to Equilibrium Traffic Assignment on a ConJested Networks," Tran. Res. Record 491J Interactive Graphics and Transportation Systems
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L. J. LEBLANC and E. MORLOK, "An Analys Comparison of Behavioral Assumptions In
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Icaas ,IL., LZ(2), 168-176 and L. Opt ma I (1 973 Is and Traf f Ic Traf fic TROTTER, "A Column Traf fic Asslgnment," EQUILI7.
EQUIL18.
-24- Deterministic Network Optimization A Bibliography Traffic Equilibrium EQUIL24. EQUIL25. EQUIL26. EQUIL27. EQUIL28. EQUIL29-EQUIL3O. EQUIL31. EQUIL32. EQUIL33. EQUIL34. EQUIL35. EQUIL36.
B. MARTIN and M. MA HEIM, 'A Researcth Program for Comparison of Traffic Assignment Techniques," iLhJt/
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O. K. MERCHANT and G. . NiEMAUSER, "A Model and an Algorithm for the Oynamic Traffic Assignment Problem,'" ft Ir Ll& Sya, 9.13
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lCal c FaullibrLUm fBib9.S t Montreal (Nov. 1974).J. O. MURCHLANO, "Road Network Traffic Distribution in
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S. NGUYEN, A Unified Approach to Equilibrium Methods for Traf ic Assignments," presented at the Int. Syrp. on Traffic Equilibrium Methods," Montreal (Nov. 1974). S. NGUYEN, "An Algorithm for the Traffic Assignment Problem," ILr&r GiL, (3), 203-216 (Aug. 1974).
E. L. PETERSON, "'A Primal -Dua I Traffic Assl gnment
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C. PINNELL and G. SATTERLY, 'Analytical Mettods in
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E. R. RUITER, "Equi librium and Transportation Networks," presented at the Int. Symp. on Traffic
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P. A SAMUELSON, "Spatial Price Equilibrium and Linear
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T. TAKAYAMA and G. G. JUDGE, "Alternative SPacial Equilibrium Models," ItL Gf ReaLgQDiL
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T. TAKAYAMA and G. G JUDGE, "Spaclal Equllibrluw and Quadratic Programming," . °.
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T. TAKAYAMA and A. O. WOODLAND, Equivalence of Price and Quantity Formulations of Spacial EquIl Ibriuml
Purified Duality n Quadratic and Concave Programming,
-25- Deterministic Network Otimizationt A Blbiograhy
Traffic Equilibrium
EQUIL37.
EQUIL38.
EQUIL39.
H. IGAN , "Benefit Assessment for Network Traffic
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M. WIGAN and T BANFORO, "A Perturbative Model for
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O. WILKIE an R STEFANEK, Precise Oetermination of Equillbrium in Travel Forecasting Problems Using Numerical Techniques," tnLttav _aie carc FSacord
AL
1971.EQUIL4O. A. WILSON,
O str ibut ion
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