Optimization: A Bibliography 8. L. Golden T. L. Magnanti Massachusetts Institute of Technology Cambridge, Massachusetts

INTRODUCTION

I n recent years, Network Optimization has grown t o be a popular and f r u i t f u l f i e l d i n operations research. T .C . Hu con- s iders t h i s subject a new branch of combinatorial mathematics and applied graph theory IGEN241. The remarkable emergence of the subject i s brought t o l i g h t by examining the one-page b ib l i - ography i n Grmphs and Their Uses by 0. Ore (1963) where the author s t a t e s , "The number of books on graph theory is very small." I n t h i s paper, we present a categorized bibliography on Determin- i s t i c Network Optimization which includes a number of books and nearly 1000 en t r ies . As the reader might note, most of our c i ta - t ions have appeared since O r e ' s book w a s published.

We do not intend t o be encyclopedic i n t h i s compilation; ra ther , we have included references which are, f o r the most pa r t , accessible and substantial. We emphasize algorithms f o r network optimization and underlying theory. Mathematica [GEN31] and Kivestu and Simpson [GEN251 provide comprehensive bibliographies which emphasize applications.

There a re several noteworthy general reference books which should be mentioned. Ford and Fulkerson's monograph [GEN13] is the or ig ina l reference on the theory of flows i n networks. I n addition t o containing resu l t s on s t a t i c maximal flow and minimal cost flow problems, t h i s source introduces network analysis a s a f resh viewpoint f o r studying purely combinatorial problems. More recently, Frank and Frisch IGEN151 have writ ten a very comprehen- sive treatment of the theory of networks, en ta i l ing both deter- ministic and probabi l i s t ic networks. Garfinkel and Nemhauser [GEN181 cover integer programming, theory and applications. The relat ionship between integer programming and graphs is emphasized throughout the book. Christofides' [GEN81 new book on graph

Networks, 7: 149-183 @ 1977 by John Wiley & Sons, Inc. 149

150 GOLDEN AND MAGNANTI

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 Problem. The excellent survey of deterministic networks by Bradley [GENB] is also recommended highly.

Network models are important not only because of their direct applicability. In many cases, network optimization prob- lems form subproblems for more complex and general real-world situations. transport of goods, assignment problems, analysis and synthesis of transportation and communication networks, routing of vehicles, traffic equilibrium, equipment replacement, project planning, production and inventory control, optimal capacity scheduling, and a host of others (see Fulkerson [GEN171).

We have divided this bibliography into several categories in order to make it more readable and valuable to network re- searchers. These categories are:

Successful applications of network models include

A. B. C.

E.

G.

NETWORK D.

ANALYSIS F.

H. NETwoFuc I. SYNTHESIS J.

K. UNIFYING L. TOPICS M.

General References (GEN) Shortest Path Problems and Variants (SP) Network Reliability (aL) Single and Multi-Commodity Flows (FLOW) Traffic Equilibrium (EQUIL) Matching and the Chinese Postman Problem (MTCH) Traveling Salesman Problems and Extensions (Vehicle Routing) (TSP)

Minimal Spanning Trees and Variants (MST) Location of Facilities on a Network (LOCI Design of an Optimal Network (DES)

Implementation Issues (IMP) Complexity Theory (COMP) Matroids and Graph Theory (MATR)

These categories are not mutually exclusive. On the other hand, we do feel they represent most research areas in Deter- ministic Network Optimization.

course, benefited from many previous compilations. The books mentioned above have served as general sources. In addition, papers by Assad IFLOW31, Francis and Goldstein [LOCZSI, Glover and Klingman [IMPZO], Pierce ISP581, and Wong IDES671 have been useful sources for special topics. We owe thanks to a number

In compiling a bibliography of this nature, we have, of

DETERMINISTIC NETWORK OPTIMIZATION 151

of our colleagues who have contributed citations to an earlier version of th is report. M. Ball, F. Boesch, M. Florian, R. Grinold, D. Klingman, and w. Pulleyblank for their suggestions.

Finally, we would l i k e to express special thanks to Ross Shachter who designed a computerized system for composing and updating th i s bibliography.

W e are particularly grateful to

Supported i n p a r t by U. S. Department of Tramportation (Con- tract DO!T-TSC-2058), Trampor ta t ion Advanced Research Program (TARPI.

Bruce L. COZden is naj at the University of M q t a n d , Cotlege Park, MzryZand.

Comolex i t v Theorv

COHPI.

COHP2.

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COHP4.

CO'4P5.

COHPb.

COHP7.

COMPF.

COMP9.

COMPIO.

COHPlI.

COMP14.

COHPl5.

COMPI6.

COHPl7.

COHPl8.

COHP19.

COHPZO.

A. AMO. J. HOPCROFT. and J. UCLMANI U S W O O dDd A o p l Y S k i !al C-C -1-r Addlson-Ueslev, Reaalng, (19741.

A . aoRooIN. "Cornouta t iond l c o m o ~ e x l t y - l h e o r v and p r a c t i c e . " I n CYCCMtf l a Lbclorx nt C n u n n , (A . Aho, ed.1. P r e n t l c e - M a l l , Englewood C l l t l s , N. J.1 35-89 (19731.

W. CMEN. "1000103 lca l F o r n u l a t l o n s ana Oraer o i C o m o l e x l t v o t A c t l v e N e t w o r k s t A Un1f le .J Survey." z (3 ) . 237-265 11972).

N. CHRISIOFIOES, - N o r s t - c a s e A n a l v s I s o f a yew H e u r l s t l c ( o r t h e T r m e l I n g Salesman Problem." P r e s e n t e o a t t h e Svnooslum on Hen O i r e c t l o n s an3 Recent R e s u l t s I n A l g o r l t h m s and COmDleXltV. P l t t s b u r a h , PA ( A D r l l 19761.

S . COOK, " l h e C a m o l e x i t v o i t h e Theorem-Prov lng Procedures." Ecnr. nf IJu Lhkl m n r L u a Q(1 m r u ;11 u#nuu+ 151-158 (19711.

G. CORhUEJJLC and G. hEMHAUSER. - 1 l g h t Rounds l o r C h r i s t o i l d e s ' T r a v e l I n g Salesman H e u r l s t l c . " CORE O l r c u s s l o n oaoer 7627 I A u a u s t 1976).

G. OANTiIG. Y. ?LATTYERI and H. R P O . " A l l S h o r t e s i Routes f r o m a F l x e d O P i g l n I n a Graoh." Theory o i 5raohs. I n t e r n a i l o n a ~ svmooslun. Rome, JUIV 1966. Proceedings OUDllShCd b v Gordon and Breach. N e w Vork. 85-50 119671.

E. O I h I C . " A l g o r i t h m ( o r S o l J t l o n o i a Prob lem o i Maxlmum F l o m I n a N e t u o r k w i t h pOuer t s t l m a t l o r . " a x r h h l . , &A1 1277-1250 (1970).

J. EOHONJS a r 3 9. UARP, " T h e o r e t l c a l Imorovements I n A l g o r l t h m I c E i f l c l e n c v f o r Network F l o u Proolems." Jm, 19. 246-264 119721 .

5 . EVEN:. AUnrlm& C e n p l w p r L r 5 , . H a c m l l l a n . New Vork. (19731 .

S . EVEN. A. I l A I an0 A. SHAHIR. "On t h e C o m o l e x l t v o t T r m e t a b l e a d H u l t l c o m m o l l t v F low P r o o l w s . " S m Js CPmulhn. 5, 691-7011 119761.

P. F L O V O . " N o n d e t e r m l n l s t l c A I w r l t h m s . " J A D , UI, 636-6114 11967).

M . FREOHAL. "On t h e O e c l s l o n l r e e C o m o l e x i t v o t tbe S h o r t e s t P a t h Problem." S h ~ ~ i l ~ lnnvaL SYQRA PP Esurartunos !al C n w c s w , 98-99 119751.

M . FREOHAh. "NeU Bounas o r t h e C o m o l a x l t v o f t h e S h o r t e s t P a t h Problem." LIM J. C a u U g . 5 i i i . n 3 - e 3 11976).

G. fREOtSICKSONr M. HECWT. and C. K I M . " L o o r o x l m a t l o n A l ~ o r l t h a s i o r Soma R o u t l n g Problems," f o r t h c o m i r ) I n SUM J., m n u U .

H. GABON. " A r E f f l c l e n t I a o l e m e n t a t l o n o t EdlOnds' A l ~ o r l t h m f o r Maxlmun H a t c h l n q s on G-aohs." dAM. Z J t 2 l I 2 2 1 - 2 3 4 119761.

M. C A R E Y and 0. JOHNSOh. "The C o m o l e x l t v o f Near -Oot lma l Graoh Co lor lng . " JMfi. I t 0 Aooearl .

H . C A R E Y . >. JOHhSOh. and L. STOCKMEYFQ. "Some S l m o l I i l e ~ N O - C ~ m ~ l e t e PPoble'1sr" SA&U UM SU!M.Slua PO I h n U C n a n u U o r 47-63 11974).

R . L. GCPMPH. "3ounos on H d l t r o r o c e s s i n g T l m l n g Anomalles." Js pi -As linlb.. llr 416-42q 119691.

J. MOPCROFI and R . KARP. "An N1.*15/2) A I g o r l t h m ( o r Maxlmum Lcatcblngs I n 3 1 o a r t l t c t raons . " SX& Jr t n g ~ . . 2 , 225-231 11713) .

COMPPI. J. HOPCQOFT an3 R . TARJAN. " E i f i c l e n t A l g o r l t h m s f o r Graoh H a r l o u l a t l o n r " !&ma B a n . . l B ( b l . 372-378. 119731.

COMP22. F . M U A N i . " O r S t e l n o r Mlnl'13l Tree U l t h R e c t l l l n e a r Olstance." XM A d p p h m. I t 0 a o o e a r l .

COMPZJ. 0. I O A R R I I in0 S. SAHhI. "P-Comolete Prob lems a d A o o r o x l n a t e So lu t ions . " l e c h n l c a l R O D O V i 7b-5. U n i v e r s i t y ,of Minnesota l19711l.

CO~p24. 0 . JOHNSON. "Near ODtlnal bln P a c k l n g A l q o r l t h n s . " D o c t o r a l Thesls. Oeot. o i Mathematlcs, H . I . T . (1973).

COHP25. 0. JOHNSOhe " f a s t A l g o r r t h m s f o r 41n P a c k l n o r " ,la w t m u a t a r 272-314 (19141.

COMP26. 0. JOHNSOh. " A o o r o x l m a t i o n A l g o r l t h m s f o r C o m b i n a t o r l a l Problems." h n u L lusmr. 9. 256-271 111741

COMP27. 0 . JOHNSON. A. JEMERSI J. ULLMAYI '4. C A R E Y . and R. GRAMAH. " n o r s t - C a s e P e r f o r m a w e 4ounds ( o r S r n o l e 3ne-Olmens lona l PaCk lnJ A lgor l thms. " J pl m u m r 3. 234-325 119741.

COMPZ8. R. KARP. " ~ e o u c r b l l i t v Amonl C o r a i n a t o r l a l Prooleas." I ; p L p u x 91 L W n c Emm- le . H I I I e r 3na J. l n a t c h e r . eas.1. Plenum Press . hew V O r k , 85-104 11972).

COMP29. E. KARP. "Yn tnr C o m o u t a t i o n a l i o a o l e x i t v o i C o m b l n a t o r l a l Problems.' wm. 2. 45-64 119751.

COHP30. V . <LEE a n j G. M I N I V 1 "How Good L S t n e SImolex A l7or l thm." Math. N o t e No. 643. Roe lng S c l e n t l l l c RCSearCh L a b a r a t o r l e s 119701.

152

COMP31. I(. KRAUSE, " A n a l v s l s o f Computer S c h e d u l l r g n l t h Memorv Constraint+*" O o c t o r a l Thesls. Computer S c i e n c e Oeoartment, P v o u e U n l v e r s l t v 119731.

E . LAWLEQ. " A l ~ o r l t h n s e Grams. a n d ComDlexltv." Mu-. Z I l J . 89-92 (19751.

s. LIN. "Heuristic Programnlnq as a r A i d t o h e t w o r k Oeslgn." mu. 5111. 3 3 - 4 4 (19751 .

IJ. MATULA. G . MARBLE. and J. ISSLCSON. "Graoh C o l o r l n g A I J o r l t h r s r " In R. Scad 4od.J. 5- l t e ~ ~ v am W u U u . Acaoemlc Press , Nen Vork. 109-122 1197ZI.

G . L. NEMr4USER and L . A. WOLSSY. ''Best A l g o r l t h m s F o r ~ l o ~ r o x l n s t l n g t h e Maxlmum o f a Submodular S e t Funct lon." COPE O l s c u s s l o n Paoer 7636 IOEc. 1976).

c. H. PAPAJIWIIRIOU. "The E u c l l d e a n I S P Is NP-Complete," TR NO. 191. Ooot . o f EIec. Enq.. P r l n c e i o n U., P r l n c e t o n . h.J. 119751.

C. ti. PAPAIIMITRIOUI "On t n e C o n o l e x i t v 01 Edge Traverslng." &,ill, a t 3 l . 544-554 119761.

C . H. P4PAJIMIICIOU and U. STEIGLIIZ. "On t h e C o n o l e x i t v 01 L o c a l SearcP ( o r t h o T r a v e l l n q Salesman Problem." TR No. 1 9 9 . ~ I e o t . o f EIec. Enq., P r l n c e t o n U., P r l n c e t o n . N.J. (19751 .

0. ROSENK2ANli. R. STEARf4S. and P . LEWIS. "Aoprox lmate A l g o r l t h m s ? o r t h e l r a v e l l n g S a l o s ~ c r s o n

119741. ProDlem." %srrrllnsm at lhi m n b W IEE SvionrLur pn Saltchlno acd b u h a a h Ibnu* 33-42

COHP32.

COHP33.

COMP34.

COMP35.

COMPJB.

COMP37.

COUP3 8.

COHP39.

COMPZO. S . SAWI. "Some R e l a t e 0 PPOblemS l r o m Network F lons . Game Theorv. and I n t e g e r Proqrammlnq." CnnUcsnsz Besac& EL€ U l b 4 ~ d a l Sxmusly. PI) S U M d u 1 W -1130-138 f i P 7 2 l .

C O n P * l . S . ~ A H N I . "Aporox lmato A l 3 0 r l t h m s l o r t h e 0 - 1 I ( ra0sack Problem," ,lm , 22. 115-124 119751.

COHP42. S . S A H N I . "Some P e l a t e o ProDlems f r o m Network F lons . Game Theorv. So lu t lons . ' ~ u s A . A o a s !2l l h r lxb AMYpl L E E SxBSQSiua Qn inllrhlna nRil 28-32, 119741.

Average Time U l l N l o o h l * * 2 l . " JA I;nnnuUgt 2 1 1 1 ~ 23-32 119731. cOMP43. P. SPIRA, "4 NeM A l g o r l t h n f o r F i n d l n q A l l S h o r t e s t Paths I n a GraDh o f o o s l t l v e A r c s i n

COMPb4. R . TPRJAh. "Oeoth F l r s t S t a r c n 3-d L i n e a r Graph Algor l thms." A w u m Q * 1 f Z l r 146-160 119721.

COHPk5. L.. :AOEn. " T r e o r e t l c a l F f l l c l e n c v o f t h e Edmonds-Karp L l ? o r l t h m f o r ComDutlng Maxlmal Flows." JACflt 19. 184-132 11972) .

c0nP1.6. h . ZAOEH. "More P a t h o l o g l c a l En imoles f o r Network F low Problems." U l t h . kng. . 5. 217-224 119731.

C O H P ~ ~ . h . ~ A O E H . " A dad N e t n o r k Prob lem l o r t h e S i n o l e x Method and O t n e r M l n l n u m Cost F low A l g o r l t n m s , " ul.ts pcp3.. 2. 255-266 119731.

D e s i g n 01 a n O o t i n a l h e t w o r k

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S . K . 4GA44AL. " O o t i m i z l n g I e c h n i aues ( o r t h e Interactive D e s l g n of l r a n s o o r t a t l o n Networks under Wul t ,p le ODlec t ivcs . " Oh.0. Thesls. Oeot. 01 C l v l I Eng. N o r t h n o s t e r n U n l v . 119731.

J. 4. A V O l i l a n J I. 1 . FRISCH. " 0 o t l m a I I v I n v u l n e r a b l e O l r e c t e a C o m r u n l c a t l o n Yetworks," I= I C a ! S r C Q n P r 1srrJnQ.L. * C P k l 1 r 494- 4 9 9 1 1 9 7 U l .

P. BAKSAL and S. JACOBSEM. "An A l g o r i t h m i o r O o t l m l z l n g Network F l o n C a o a c l t v Under E c o n o n l e s o f Scale," JQIA. fi151r 565-586 113751.

G. 3ERGEN09ML. "A Cornblneo L l n a a r a r u Ovnaslc P r o g r a n n l n g Model f o r I n t o r a e c r n j e n t R o a j I n v e s t m e n t Plannlcg." m s A B-. 3, 211-228 119691.

J. SILLWEIMEP and P. GRAY. ' *hetnork O e s l g r n l t h F i x e d and V a r l a b l e Cost Elomonts." -& m.,

F. 3OESCn m c 4 . FELZER. "A Genera l C l a s s 01 I n v u l n e r a b l e GraohS." Unr)ls. 2131. Z t l - 2 8 4

Lq 49-7 - 119731.

119721 .

D. 3 o v C ~ . 4. FARHI, and R. UFISCWEOFL. "ODtimal Network * r o b l e m l A Branch and Bound A l g o r l t h n . " E@ulfmBsnl and E l ~ n l ~ , 2 141. 519-533 119731.

fa. BURSTALL. "Tree S e a r c h l n q Methods n l t h An A o o l l c a t l o n t o a N e t n o r h Oes lgn Prcblem.' Ma- Lnmlhrrm. 1. 65-85 119671.

0. E . BUTLER. "Conmunrcat ion : iets n i t n S o e c i i r m a S u r v l v a b i l i t v . ' C o o r d l n a t e d Scl . L a b o r a t o r v ReDOrt Q-359. Unlv. o i I l l l n o l s I J u l v 19671.

F . c. C A R T E R and J. P. STOUEQS. 'Model f o r Funds A l l o c a t l o n f o r Urban MlphUavS Svstom C a a o c l t v Imerovements." ~ A ~ I U I U mr %$Mcp. f p v 8*-152.

v. P. CHAh. " O o i i n a l T rave l T i n e R e d u c t i o n i n a I r a n s o o r t Network: A n Ioollcatlor 01 NetworM A g g r c 3 a t i o i and Branch ana ?ouno TecPnlauos." Research S e o o r t R 69-34. Oaoar imcnt of C l v l I Engrneer ln3 . H.I.1. 119691.

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Y . CHIN. - C o n f i g w l n g a I r a n s o o r t a t l o n Route Netnork v l a (be Method o t Success lva ADwoxlmatlon." !&nlpr .nP R Q S t 8-q 1 s 385-420 (19741.

P. I . CMIEN. "Synthesis o f a Communlcat lor Netnork.' & E.t M d u. hi 311-320 (19601.

n. CHW and P. FRANK, 'Survivable Communicatlon Netnorks and the Termlna l Caoac l t v M a t r l x r -

N. CMRISlOFIOES ana P. BROOKER, - 0 o t I m a I Exoanrlor, of an E x l s t l n g Netnork,' I(ntL be 197-211 (1974).

A. CLAUS an0 0. J. KLEIlMAN, 'Meur l s t l c Methods t o r S o l v l n g L C g e S c a l e Netnork ROUt!nq PrObIemSI The I e l D a c k l n ~ Problem.' Studl.f AMlld !&(1) 17-29(1975).

J. EOHONOS~ " E ~ r s t e n c e o f k-Edge Connecteo Ord lna rv Graphs n i t n P r e s c r i b e d Oegrees.' 3r BI& b.BS. 68R. 73-74 (19b41.

L . ESAU and K. Y I L L I A M S e 'A H e t M O f o r ADDroxlmat lng the O D t l l a l Netnork.' Sr+t..l &I&* 5. 1 4 2 - 1 4 7 (1966).

L. FOR0 and 0. FULKERSON. -s. P r l n c e t o n Unlv. Pressr P r lnce ton . N. J. 119%?l.

I . 1. FRISCH. "0p t lm iza t ;on o f Communicatlon hots n I t h Snl tchlng," & Ecankllo h&t. * UTI 405-430 (1963) .

ltpsr LhLpLTs C M . 192-197 (1970).

" A n A l g o r l t b m f o r V e r t e x P a l r Connect lv l t v . ' & 579-593

I . FRISCH ana 0. K. SEN. 'A lqor l thms f o r Svn thes l s a t Orlented C o m u n l c s t l o n s Nets.' Ir- f x s U Ib-. E U e 570-379 119t7).

0. R. FULKERSON, " I n c r e a s l n y t h e Caoacr tv o f a N e t n o r k l The Parametric Budpet Problem." !lath Sd.. 5 1 672-483 (1959).

0. FULKERSON and L. SHAPLEY. "Mlnlmal a-Arc Connectad Graohs." 1(1). 91-98 11971).

A. J. GOLOMAL and G. NEHMAUSET. - A I r a n s o o r t Imcrovement Problem Trans tormab le t o a Bes t -Path Proolem.' 1. 295-307 (1967).

R. GOMORv m a I . C. MU, " A n A o o l l c a t l o n o f Generellzea L l n e a r Proqramminq t o Ne tno rk Flons.' A S I M . rp. ZEO-283 11962).

P. GOMORV m a I . C. MUe 'Mu l t l -Termlna l Netnork Flons,' L 9 t 4 ) . 551-570 l l S 6 1 ) .

R. G O O R V and 1. C. MU. "Svnthes ls o f a Comnun lce t lon Netnork." JA S U b 12. 346-369 (1964).

5 . M A K I M I . 'on t h e R e a l l z a t l o n of 3 S e t o f I n t e g e r s as Oewees o f the V e r t l c e s o f a L l n e a r Grooh." J.. pl Barn. , fi, 135-147 (1963).

5 . M A K I H I , 'An A l p o r l t h r f o r C o n s t r u c t i o n o t t h e L e a s t v u l n e r a b l e Communlcatlon Netnork. XEE I r m - 9 afi. 229-230 ( 1 9 6 9 ) .

5 . MAKIHI and A. 4 H f R . "On tne Oeslpn o t R e l l a b l e Ne1nOrkS.- m m r J(31e 241-260 119731.

b . *. HERSHOORFER. "Oot lual 2Out lnq o f Urban Tra f t l c . ' Ph.D. l hes l s . 0-t. o f C l t v an4 RcplOnel Planning. H.I.1. (MaV 1965).

1. C. nu, "Some P r o D l e m S I n D r s c r e t e Ootlrlzationt' mar 1. 102-112. (19711.

T . C. MU. "ODtimum Communication Soannlng Trees.' A m w . 3 ( 3 l . 188-195 (1974).

Y . KIM and R. CHIEN, M a - Aa.lrrlr and nl N.trorb+. Columbla U n l v e r s l r V Press, Nen VOrk (1962) .

0 . J. K L F I I H A N . 'Methods t o r I n v e s t l g a t l n o C o n n e c t l v l t v f o r La rge GraDhSr' ZU po

0 . I(LEITMANI 'Mlnlmal Numbar o f M u l t l o f e Ed.ies IF R e a l l r a t l o n o f 311 I n c l a e n c e Seauence n l t h o u t

S A W 1-s U-A. 232-233 (1969).

LOOOS.- SM J.. 91 a m . . ~ ( t ) . 25-28 (19701 .

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n. ROTMFAR3, "Comblnator ic Methods f o r Y u l t i c o n n o d l t y Flowst" Ph.0. Thcs l r . U n l v . o f Ca l l ( . . R e r k e l e y 119CBI.

R. SOTHcAR3 and I . 1. FRISCH. "0'1 t h e Three-Comnodltv F l o w Problem." A pII !,.nE.L m.. . * 6 - 5 8 113691.

R. QOTHFARYI N. P. SHFINI and 1. 1. FRISCIi. " C O m l O n T e r n l n a l M u l t l c o m m o d l t v Flon.' Print &.r Ah, 202-205 (19681.

8 . 90TnSCkILt and A. UMINJTOh. " F e a s l b l l l t y o f Two Conmodltv Flows." Uk. l h v 1121-1129 119661.

9. ~ o r n s C n I L D ana A. WHIIISTON, "On Two C o n n o a i t v Network Flows1 p n n ~ m.. 14, 377-387 119661.

n. ROTMSCNILL. A. WHIf<STON. ana J. KEYT. "Comoutlnq Two-Connodltv Flows." Q&!!J.% Bat. 16, 446-450 113611.

1. RUEFLI. "Oecent ra l i r e 0 1ranssh;onent Networks," p n n ~ g a . l9, l b 1 9 - I E 3 1 (19711 .

R . SAIGAL. " H u l t l c o n m o d l t y F l o w s I n O l r c c t e o hetworks." Tech. R e o o r t ORC 69-14. Overs. Res. Center. Univ. o f C a l i f . , R e r k e l e v ISeot . 1969) .

H . SAKIROVIlCH, "The M u l t i c o n r o d l t y Hax F l o n Problem." Tech. R e p o r t ORC 66-25. OO*rS. Rcs. Center. Unlv. o f C a l i f . . RerMelev (19661.

Y . SAUAROVITCH. "The M u l t i c o n n o d l t v F l o w P r o b l e r . " Ph.0. T h e s l s r Opers. Pas. C e n t e r . Unlw. o f c ~ I I ~ . . :3erkel ev f 1 9 t 6 l .

M . SAKAROVITCH. "Two C o n n o l l t v Network Flows and L l n e a r Programmlnq." u. 3. 1-20 119731.

J. F. SHAPIRO. " A h o t e on t h e P r l m a l - D u a l and O u t - o f - K l l t c r A l q o r l t h r s f o r Network O v t l n l z a t l o n Problems.*' m f h I t o a o v e a r l

FLOUISZ. L. 5. SH~PLEV. "On h e t w o r k Flow Funct lons. ' Re+. Memorandum RM-2338. The RAN0 Caro., (March 19591.

FLow133. v . S R I N I V A S A h 3nd c. THOMPSON, " f i l g o r i t h m s f o r M l n l n l z l n q T o t a l Cost. B o t t l e n e c k Tlme and R o t t l e n e c k S h i o i e n t I n T r a n s o o r t a t l o n Problems." Ilat Lop. Q.9 i X l 4 l t 567-596 119761.

FLOWi34. C. SHOVELAID. "A Two-Stage O e c o e o o s l t l o n b l g o r l t h m f o r a G c n e r a l l z e d M u l t l c o m m o d l t y F low

FLOu135. C. SHOVELAYO, "Oecompos l t lon A l j o r l t h n s f o r t h e n u l t l c o m n o a l t v O l s t r l b u t l o n Problem." Y o r k l n q

Problem," ~~r u 1 3 1 1 232-244 119731.

Paver NO. 184. Western Sc l . Man. I n s t h t . . UCLA (June 1975)

FLOWl36. U. SZNARC. " I n s t a n t T r a n s o o r t a t l o n S o l u t l o n s . " UPyI L a Pynrr.9 g 1311 427-450 119751.

FLOu137. U . S i Y A R C . "The T r a n s v o r t a t l o n Paradox," &. I&& Quptt.. id. 185-202 119711.

FLOWl38. W . S Z W A R C . "The l r a n s o o r t a t l o n Prob lem w l t h StoCPaSt lc Demand. MADl SrL.1 fi. 3 3 - 5 0 11964).

FLOU139. 0. 1. TAhG. "Cannents o n F e a s i b l l l t v C o n d i t i o n s o f S I ~ u l t a n e o U S F low i n a Network." pnn.& w.r AJr 143-146 1 1 9 b 5 ) .

1 6 1

F L O Y i 4 0 . 0. 1. TANG. "Comaunlcat lor YetnOCks n l t h S leu l taneous F l o n Repulrements." I;lW Ib.. w r 176-182 (19621.

FLOYl42. N. T O W I Z A Y b . "On Some Techniaums U s e f u l f o r S o l u t l o n o f T r a n s o o r t a t l o n Pr0DIe.S.- a-s. 1. 173-194 (19721.

FLOYl43. J. 4. TOWLIh+ "qlnlmue Cost Mul t l commodl tv Netnark Flon." &&* 45-51 (19661.

FLOY144. J. A. TOWLIN."A Mafhemat ica l Proarammlnq Model f o r t h e Comblnmd O l s t r l D u t l o n - I s s l q n m e n t o f Traffic." m. %* 2, 120-140 (19711.

FLOYl45. 4. U. TUCKER. "Ana lowes o f K l r C h h o f f a S Lansr" Y m U L n o l U r ern= 3. t 195 0 I .

FLOY146. J. VON NEUMA~N. "4 C e r t a i n Zero-Sum Tno-Person Game E o u l v a l e n t t o t h e O o t l m a l 4 s s l q n m e ~ t Problem." I n ~~~~ Lp a 41 f-. Ann. Math Study 28. 5-12 (19531.

FLOY147. 0. F. VOT44 JR.. and 4. OROEh. ' rhe Personnel Assipnment h-oblem.' P r o l e c I SCOOP. Manual 10. 155-163 (13521.

FLOYI48. H. w. IIAGNER. " O n a C lass o f Caoac l ta ted T r a n s o o r t a t l o n ProDlmmS." ma kl., 5. 304-310 (19591.

FLOY11.9. 4. YEINrRllUB. - I Pr lma l A lqo r i t nm t o S o l v e Yetwork F l o n rnroblcms n l t h Convex Costs," ma, 87-37 119741.

FLOYISO. H. YEIGEL m a J. CREMEANS. "The ~ u l t l c o m m o d l t y Netnork F l o n M o d e l Rev1S.d t o I n c l u d e V e h l c l e o e r Tima P e r l o d and Node Constralnts. ' tux, sur & 19, 77-99 (19711.

FLOY151. 1. C. WILLIAMS, - 4 Treatment o f T r a n s o o r t a t l o n ProDlems D V Oecomoositlonr" ,L &I&!l 19. 35-41 (1%2l.

FLOnl52. Y. YnIrE, "Ovnamlc Transshloment hefnorhsl A n A l q o r l t h n and Its 4 o o l l c a t l o n to the D l s t r l b u t l c n o f Emoty Contalners," umtr 2 f 3 l r 211-236 (19721 .

F L O Y l 5 3 . R . YOLLMER. "Mrx imiz inq F l o n t h r o u q h a Netnork n i t h Node and Arc Caoac l t l cs . " I- aa. ,z. 213-232 (13681.

FLOY154. P. a. YOLL*CP. " M u l t l c o i m o d l t v Network F lows n l t h Resource Cons t ra ln t s : The Genm-allzej

FLOY155. R . VIGEO. " W l n l m u m Cost s o u t l ? g f o r S t a t l c Netnork nodeis." ~ r t u . ~ ( 2 1 . 139-172 (1971).

FLOYl56. 0. VAGEO. 'Mlnlaum Cost R o u t l n g l o r Ovnamlc Netnork MoJmls." UQE~. 3, 1 9 3 - t Z 4 l1973I .

FLOY157. N. ZAOEn. "More P a t h o l o q l c a l Examoles f o r NCtwOPk F l o n Problems." Pyp~.. 5(2l. 217-221.

M u l t i c o m m o j l t r F l o n P r O D I C m . " w w . 1 ( 3 l . 245-263 (19721.

(19731.

FLOYl58. N. LAOEM. 'A add h e t n o r k Prob lem l o r t he S I M D ~ ~ I I Methoa and Other M l n l m u m Cost F l o n Algor i thLS." ml&, gcon.. q ( 3 ) . 255-266 (19731.

FLOY159. n. I . ZAhrJUILL, "I f i a c k l o ~ g ~ n t 'lode1 ana a Mul t l -Echmlon Model o f a Ovnamlc E c o r o n l c Lot S I T S P r o a u c t l o r System- I Netnork ADorOaCh." f l h m., G I 9 1 . 506-527 (19691 .

General ReTerencer

162

G F N I Z .

GFN1.3.

I m D l e m e n t r t l o n Issues

I M P I . H. A A W l I A Y I and 1. HAGtdANTI. - S o I v l n P Large S c a l e Netmork O p t l m l z a t l o n Prob lems. ' nu-. 1.1 11). 8 - 7 1 (1975) .

IMPZ. H. A A L I N S K I and R. GOnOSVr -A P r l n a l M e t h o d f o r the L s s l p n m n t and Transportation PrOblOD.' AR s 578-593 1 1 9 6 4 ) .

IWP3. K. dARR. F. GLOVEQ. and 0 . < L I N G H A N . ~ " A n I m W o v e a VWSLOI ! O f the Out-of-Kllter M e t h o d m d a

IMP4. 6. BEhNlhGlOh. * A n E f f l c i e n t H l n l m a l C o s t Flow Algorithm.' m. u.. -19). 1 ~ 2 1 - 1 0 S l (19751.

IMPS. G. 3RAOLEV. " S u r v e v o f O e t e r m l n i r t l c N e t w o r k s . " I-, Z13l . 222-2Sb 11975).

C o m p a r a t i v e S t u l v o f C o m o u t K C o a e s . m.. 2 (1). 68-87 1197II.

1b3

1 ~ ~ 6 . G . lRAOLEY. G . BROWN. and G . GRAVES, " A Comoarlson o f Some S t r u c t u r e s l o r P r l a a l Network

IHP7. A. CHARNFS a r d Y. COOFERr "The S t e o o l n g Stone Method o r E r p l a r n l n g L l n e a r P r o s r a r a l n g

IHP8. L. CHLRNfS, F. GLOVER, 0. KARNEV. 0. KLINGMAN. and J. STUTZ. "Past, Present . ah3 F u t u r e 0 1 L a r g e S c a l e I r a n s s h l m e n t C o r o u t e r Codes and A o D l l c a t l o n s r " Qn.puUX ml Q R ~ Brtrarrb.

Codes." pBu BJlbtro. 2 , l I l l ~ 119751.

C a l c u l a t l o n s I n T r r n s o o r t a t l o n Problems," .%Ar .l 44-69 119541.

2121. 71-Cl 11975).

IMP9. R. CLASEh. " I h e Numerical S o l u t l o n O f Network Prob lems U s l n g t h e O u t - O f - K l l t e r A lgor l tnm." R A h O Coroorat ,on Memorandum RM-5456-PR. Santa Honlca. C a l l f o r n l a r (March 19681.

IMPIO. 9 . 9EMBO and J. HULVEV. "On t h e A n a l v s l s and ComoMlson o f H a ? h e R a t l c a l P r o g a m n l n g A l q o r l t h m s ano Software." H b r w a r d Y o r k l n q P a o w HOS 76-19 119761.

I M P I I . J. EOHONOS a r o 4. UAPP. " T n e o r e t l c a l Imwowements In A l g o r l t h n l c E f f l c l a n c v l o r Network F low Proo1e.s." m, 19, a d - 2 6 4 119721.

IHPIZ. H. FLOOi). "4 I r a n s o o r t a t i o n A l g o r i t h m and Code." &ah &sr Lpp. 9. p. 257-2161 119611.

IHP13. H. FLORIAh a r d H. KLEIN. "An E x o e r l m e n t a l E w a l u a t l o n o f Some Methods o f Solwlng Asslqnment Problems." Ur Ess. Zs, &uc..A. 1 0 1 - 1 0 8 11970).

IHP14. L. FORD a n j C. FULUERSON. " A p r l m a l - O u a l A l g o r l t h n f o r t h e CaDaCl ta ted H I t c h c o c k Problem." liah 8 ; ~ ~ p b 2.. 4 I 47-54 (19571.

I H P 1 5 . B. L . Fox. - a a t a S t r u c t u r e s and Computer Sc lence I e c h n l o u e s I n O o e r a t i o h s Research," P u b l l c a t l o n E o . 245. Oeoartment O ' l n f o r m a t l o u e . Un lv . l e M o n t r e a l IRcwlsed Oec. 19761.

IHP16. J. GILSItrh a r d C. U1T:GALL. "1 p e r f o r m a n c e Comoarlson o f L a b e l i n g A l 3 0 r l t h m s f o r C a l c u l a t l n a S h o r t e s t P i t h Trees." N a t l o n a l Bureau o f S t a n o a r o r T e c h n l c a l N o t e 772 119731.

IHP17. F. GLOVER, 0 . UARNEY. and 0. ULIYGHAN. "The Auqmentea p r e a a c e s s o r I n d e x Method f o r L o c a t l n a S t e D o i n g Stone P a t h s and A s s l g n l n q Oual o r i c e s I n O l S t r l b u t l o n Problems." Lcmat 6111. 171-100 11372).

IHPl8 . F. GLOWER. 0. UARNEY. and 0. KLNGNAN. " I n o l e m e n t a t l o n and C r l t e r l a f o r a P r l m a l Network Code." b-. 3. lJl-212* (19741.

IHP19. F . GLOVER. 9. KARNEY. 0 . ULINGHAN, and A. NAPIER. "A C o n o u t a t l o P a l S tudy on S t I t Procedures. 9 a s i s Cnanye C r l t e r i a and S o l u t i o n A l g o r l t h m s f o r T r r n s o o r t a t i o r Problems." sl.. Z Q t 5 l . 793-819 l197Ll.

IHPZG.

IHPZ1.

IHP22.

lMP23.

IHP25.

IHP26.

IHP27.

F. GLOVER and D. ULINGtiA!. ":dew Adwances I n t h e S o l u t l o n o f L a r g e S c a l e Network and Network-Re la ted Problems. b1-U- SuLrl.al.ls 3-5 Wynl 12. N o r t h H o l l a n i P u b l l s h l c g Conoanv 119751 .

F. GLOVER dnc 0. ULI?.GHAN, "NetworN A ~ o l l c a t l m s in I n d u s t r y and Governmnt . " U n l w e r s l t y o f Texas I December 19741.

F. GLOVER, o. ULINGHAN. ava A. NLPIER. - A N o t e on F l n d l n g AII S h o r t e s t paths." trl., A l l l . 3 - 1 5 119741.

f. GLOVLR. 0. XLINGNAN. and J. STUTZ. "LupneoteJ Threaded Inaex q e t h o 9 t o r Network O o t l a l z a t l o n . " IblfpB. u I 3 l . 293-290' 119741.

F. GLOVER anc J. HULWEV. " E ~ u l v a l a n c e o f t h e 0 - 1 I n t e g e r Programnlng Prob lem t o O l s c r e t e G e n e r a l l z e j and O l s c r e t e Pure Network Wodels." t o aooear I n

9. GOLOEh. " S h o r t e s t P a t h A l g o r l t t w s l A Comoarlson." b ~ . 24161. 1164-1166 119161.

9. SOLOEL. 1. HAGNANTI. and H. NGUVEN. " I m o l e m e n t l n g WehlcIm R o u t l r ~ A lgor i thms. " f o r t h c o m l r a I n ti-.

9. HARRIS. "A Code f o r 119761.

t h e Transportation Prob lem o f L l n a a r p r ogr ammi nq. " 155-157

IHP2.9. R . HATCH. "Oench H a r k s ComDarlnr T r a n s o o r t a t l o n Codes 9ased on P r l m a l S l r o l e x mnd P r l D a l - D u a l A l g a r i t tms," print hr 23, 1167-1172 (19751.

IHPP9. A. UERSHENjAUH1 U. MSIEH. an6 8. GOLOEN. "Constrained R o u t l n g I n L a r g e Soarse Networks," CQDlarcncS Qf 1926 l a r n c P r mL on b U w L n n r * JUne 14-16. P b l l a d e l o h l e .

InP30. E . JOHNSOL. "NetnOrkS and R a s l c S o l u t l o r s . " u. U l b l . 614-623 11?66l .

IHP31. E. JOHNSOh. -On S h o r t e s t Paths and Sor t lnq . " w u ni &Il CppL-m, R O S t O n . 510-517 IAug. 13721.

A a KERSWEN3LUH. 299-310 (13741.

" C o n w t l n g C a o d c l t a t e d H l n l m a l Soannln 7 T r e e s

InP33. A. KERSHFNSAUH and R. VAN SLVKE. "Comout lng H ln lnum Soann lnq Trees E f f l c l e n t l v . " 81;m & m s . 1972 Annual C o n f e r e n c e o ? t h e L s s o c l a t l o n f o r Comout lng M a c h l n e r y r 518-527 11912 l .

IHP34. 0. ULINGHAN. A. NAPIER. and J. STUTi. "NETGEN- A Program f o r G e n e r a t l n g L a r g e S c a l e I U n I C a ~ a c I t a 1 8 d Assignment. T r a n s o o r t a t l o n aPd HlnlDum Cost F l o w Network Problems.' kA.. 2Qt51. e l4-822 (19741.

InP35. 1. ?IAGNAhII. " O o t l m l r a t l o r f o r Sparse Systems." I n a m m m IJ. P. Bunch 0 . J. Rose. eds.1. A c a d m l c Press. New York 119761.

and

IHP36. J. HULWEV. 'NQtwOPk R e l a x a t l o n s f o r S e t Cowerlna. S e t p a r t r t l o n l n g and Other I n t e q e r P r o g r a m a l n j Problems." Researcn R e p o r t ( t o apoear Center f o r C v b e r n e t l c S t u d l e r . U n l w e r s l t v of Texas, BEE-613. Austln. T e x . 787651.

164

J. HULVEV. ' T e s t l n g o f 3 Larqe-Sca le Network Ootlmlzatlon Program,' H a r v a r d Work lng Paper HBS 75-38, 1975. s u b n l t t e a t o t l a~ p-.

J. HULVEV. " b Network R e l a x a t l o n Aooroach f o r t h e Set P a t l t l o n l n g and S e t C o v e r l n g Models,' H a r v a r d U o r k l n g Paoer 75-37 119751.

J. MULVFV. " S o e c l a l S t r u c t u r e I n he twork Models and A s r o c l a t e d AooI1cat lons. ' Ph.0. O i s s e r t a t l o n t UCLA I A u g u s t 19751.

U. DlPE. " I m l e r n e n t a t l o n and F f f l c l e n c y o f Hoore-Algorithms f o r t h e S h o r t e s t Route Problem,' y a h ecpg.* z. 212- 222 (19741.

J. JLA. " A n O u t - o f - Y l l t e r Algorithm f o r S o l v l n g H l n l m u n Cost P o t e n t l a l Problems.' e m . , A, 275-290 11971).

H. I . SCIOYS. ' Ihe ComDact R e o r e s e n t a t i o n o f a Rooted f r e e and t h e T r a n s D o r t a t l o n Problem.' 1 n L e m a L ' n a d suapruium nn - m a w ~rgscaaalm LOMon (19641.

V . SRINIVASAL and G. THOMPSON. " L c c e l e r a t e a L I g o r l t h m S f o r L a b e l l n g and R e l a b e l l n g o f Trees m l t h A D o l i c a t l o n f o r O l s t r l b u t l o n ProblemSr" us U 1 4 1 , 712-726 (1972).

V. S R I N I V A S A I . and G. THOHPSOH. "Benefit-Cost A n a l y s l s of COdlng I c c h n l c u e s f o r t h e P r l m a l T r a n s o o r t a t l c n A13or l th r . ' Zp. 194-213 119731.

J. YEh. " F i n o i n g t n e L e n g t h s o f A l l S h o r t e s t P a t h s I n N-Node Nonnegat lve Ols tmnce ConDle te N e t n o r k o U s l r g 1 1 2 tP.3 A o d l t l o n s snd Nxx3 ComDarlsonsr" Jlll;t1. fi(31. 423-424 (19721.

L o c a t l o n o f F a c l l l t l e o on a Network

LOCI. V. 3ALACUANORAN ana S. JAIN. " O o t i n a l F a c l l i t v Location under Random Oomand w i t h General Cost S t r u c t u r e . " MA RedL LoyI Q.. 2313). 421-436 119761.

LOW. 0. A. BABAVEV. "Comments on t h e N o t e o f Fr leze. ' 2 , 245-248 119741.

LOC3. Q . 3ALLOU. "LOCat1n9 Warehouses i n a L o g l + t l c r Svstem." U s W m r 9. 25-50 119b8).

Lock. W . 3AUHOL rnc P. WOLF€* " P Warehouse Problem, 'pp& -. 6. 252-263 ( 1 9 5 0 .

LOCS. R. 3ELLttAh. "An A D o l l c a t i o n o f Dvnamlc P c o q r a m r i n y t o L o c a t l o n - A l l o c a t l o n Problemsr- Rsuga. Z(11. 126-128 (19E51.

LOC6. Y. DROWN. "A G e n e r a l l r e a D l a n t L o c a t l o r Problem.' Ph.0. Thesis. O w a r t m e n t o f O o e r a t l o n s Res3rch. C i s 0 Yesterr R@serve U n l v e r s l t y (Jan. 1973).

LOC7. A. C H A R and C. FRANCIS. " A R o u n d - I r l ~ L o c a t l o n PCObICm on a Tree Graph,' Irpyr mrr 1fl(ll, 35-51 (19761.

L3C8. I . . CHQISTOFIGES and P. VIOLA. " I n e O o t l c u n L o c a t l o n o f M u l t l - C e n t e r on a Graon.' Q u z t r 22. l L5-154 11971).

L029. A . 2HA'I and F . FQANCISt " A R o u n d - I r l o L o c a t i o n PCOLYICm on a I r e e Graoh," 35-51 (19701.

M r .

Lnc io . J. COHEN. "Survey on t h e harehouse L o c a t l o n Problem,- Worklnq Paoer OR 022-73. Sloan Schoo l of Hanagemen t , P. I . I . ( 1973).

LOCl l .

LOCIP.

LOCIS.

LOC14.

LOC15.

LOC16.

LOCI?.

L o c i n .

LOC19.

LOC20.

R. C O h W A v 3nc H. MAXYELL. " A Note OP t h e Asslgnment o f F a c l l l t v Location,' ,& pl fGg.. 12. 34-36 l19t11.

L. COOPER. 'Location-Allocatlon 'roblemst ' Ppmr b. U. 331-343 119631.

L. COOPtR. W e u r i s t l c Metrods fo- L o c a t l o n - A I l o c a t l o n PPOblemS." s m w. 6. 37-53 11964).

G. CORNUEJOLS. H. FISHER, and G. '4EMHLUSER. 'An A n a l v s l s o f n e u r l s t l c s m d R a l a x a t l o n s for thc u n c r o a c l t a t e c L o c a t l o n Problem." I e c h n l c r l Reoor t NO. 271. Deot. o f Oooratlons R - e r c h . C o r n e l l U n A v e r s l t y (August 1975).

G. C U R R Y a n d II. SIEITn. "A Jvriamlc Programmlng A l g o r l t h m f o r F a c l l l t v L o c a t l o n and L l loca t lon . ' A U f ~ L S A ~ At 133-138 (196'41.

P. S. D A V I S and 1. L. RAY " A Rrancn-Bound Algorithm fo r the C a o a c l t a t e d F a c l l l t l e s L o c a t i o n Problem," Yayr !l$.s. 4.. fi!3br 331-344 (1969).

198. Oeot o f Ooero. Pen.. C o r n e l l Unlv. (19731.

0 . H. OEARING. Y. FRAhCIs. ana T. LOWE. T o n v e x L o c a t l o n Prob lems on Tree RSL. Z 4 t L I . 628-642 119761.

G. DIEHI?. " A r A l g o r i t h m f o r t n e ?-Medians Problem. Worklng Paoer No. 191. W e s t o m ( I a ~ 9 8 w n t Sclence I n r t l t u t e . UCLA (June 19721.

5 . F. DREVFUS and R. A. YAGWS. " I n e S t e i r e r Problem I n Graohs.' m-, 3. 195-207 (19721.

P. H . OEAXING and R. L. FRANCIS. "A Minlmax L o c a t l O n PrOble. On a NetwWk.- Tech. Re00rt NO.

165

LoC21. M. A. EFFdJVMSON ana 1. L. RLV. "1 Branch-Round LI?OClthW f o r P l a n t Locat ion . " a m.. f i e 361-3bb (136C:).

LOC22. L. 6. ELLuEIh and P. GRIV. " S o l v l v l F l x e d Charge L o c a t l o n - 4 I I a c a t 1 c n Prob lems w i t h C a o a c l t v an¶ C o n f I . j u r a t i o r C.mst ra ln ts . " U W.. 314). 290-298 11971).

LoC23. 4. N. ELSMlFFI and U. N. MALEV. ' F a c l l i t l e s L o c a t l o n t Some F o r m u l a t i o n s r Ilmthods o f S o l u t i o n . L o p l l c m t l o n s and C o m p u t a t l o n a l Exoer le rce . " OR R e p o r t t40. 91.. N o r t h C a r o l l n a S t a t e Unlv. o f R a l e l o n l 1 3 7 L l .

LOCZ4. 4. 9. EL-SHIIEB. "4 l:Cw A l a o r l t h m f o r L o c a t l n p Sources 4 m ~ n q O m r t l n a t i o r s . " a, a. 221-231 11973)

LOC25. 0. C. ELSON. " S i t e L o c a t i o n V l a M l x e d - I n t c ? e r Proqrammln7." QnnnLI Basr Qm.. 23il). 31-*3

LOCZ6. F. F E L D M A ~ . F. LEMRFR. an* 1. R 4 I . "Warehouse L o c a t l o n m a e r C o n t l n u o u s Economies a t Fcale,'

LOCZ7. R. FRINCIS. "Some A s o e c t r o f a Yln lmax L o c a t i o n Problem." &i.. f i l 6 ) . 1163-1169 11967).

11972).

n a b zr~.. u 670-6b4 (19661.

LoC28. R. L. FRlNCIS and J. H. GOLDSlEIN. ' L o c a t l o n l h e o r v l 4 S e l e c t l v e 9 l b l l o g r a o h v ~ " Q!Ulh !%$.. u v 400-410 (19741.

LOC29. R. L. FRANCIS ana J. A. U M I l E . WlUx L.#tQut MA l.~sal.iQU All kDnlrLlr bnnrwb. P r m t l c e - M a l l . Eng lenoa¶ C l l f f s . N.J. (1974) .

LOC30. *. FRANK, 'Optlnur L o c a t r o n s o n a Graoh w i t h P r O b a b l l l S t I C Demands." pnnr. But., 14. 4 0 9 - 4 2 1 11960).

LOC31. 1. *. FRIEZE. "A Cast F u n c t l o n D r o a e r t v t o r P l a n t L o c a t l o n Problems," w. ecppr. 2 , 245-249 (1974).

LOC32. M. FRLNU a r d 1. 1. FPISCHI G m l l ~ Q I l s I cMXLkih I MI T m S W f l n n WQCkL Addlson-Weslev. R e a d l n j . H a s . l l q 7 l ) .

LOC33. R. S. GPLtFINKEL, A. W. NCEBF, an¶ M. R. 010. "The m-Center Prob leml B o t t l e n e c k F a c i l l t v LOCdtlOn.' Wark lnq P a w r N O . 7414. Grad. Schoo l a t Mmaqement. Unlv. o f R o c n e s t e r (1974).

LOC34. Y. GAI(FILKEL. A. NEF4E. avd M. RA9. "Pn I l q o r l t n r f o r t h e H - n e d l a n P l a n t L o c a t r a p Problem," J . c ~ . S & l r . 3, 217-236 (1974).

Lnc35. 4 , 9. GEOFFRION. "4 Gulae t o C a m o u t e r - A s s i s t e d Methods f o r O r s t r t b u t l o n Svstem Plannlnq." UQa@ npaan.lro1 & X i - + U ( 2 l (13751.

LOC36. 4. M. GEOFFfiION and G. U. GRLVES. ' M ~ I t i c ~ m m ~ Q i t v 3 i s t r i b u t l o n Svsten 0es19r Rv Sanaers Oecomoos i t io r , " !IanA u., t p t 5 ) . 022-844 119741.

LOC37. c. M. GILLCSPIE JR. ."Lacat.n3 4 0 ~ 0 I u t e 2 -Centers o f U n d l r e c t e d t r a o h s , M. 5 . TheSlS. Nava l ~ O S t g r a J U a t e Scnoo l . Monterev. C a l l f ( 1 9 6 9 1 .

~ 0 ~ 3 1 3 . . 4 . J. ~ o ~ n ~ 4 t . "Mlnlmax L o c a t i o n o f F a c l l l t l e s on a Yetworhr " Ssl . . 514). 407-419 119721.

LOC39. 4 . J. GOLUM4t. "Ootrmal C e n t e r L a c a t l o n I n S lmole Y e t w l r h s . J.msL %lr. 5 i 2 ) . 212-221 11971).

LOCSO. A . J. GOLOPPI.. "Ootlmum ~ o c a t l o n s f o r C e n t e r s r n a '4etwOrk." kn, Srl. . 5121. 252-360 (19691.

LOC41. S . MLLFIN. 'On F i n d r n g t n e . . ~ s o I ~ t e and V e r t e x Centers o f a l r e e w l t h O ls ta rces . " Icam W e .

11 75-77 11974).

LOC42. 5 . L. HAKIAI. "dotlmum O i s t r l o u t l o n o f S w l t c h l n q C e n t e r s I n a Comnunlca t lon Network and Some R e l a t e d GreoP l n e o r e t i c Problems." ws Bs.. u. 462-475 11965).

LOC43. s. L. n41(IlIl "Oot lma l L o c a t i o n s o f S w i t c r l n q C e n t e r s an4 t h e l b s o l u t e C e n t e r s and I l e j l m s o f a Cra0h.- Qam -r LZ. 450-459. 11964).

LOC1.4. 5 . L. MANIMI. " S t c l n e r ' r Droblem r n a G r a m and I t s I m o l i c a t i o n s . " m-. LiZlr 113-1331 I197 1).

LOC45. s. r(4uI9I an0 S. YAHESMUPRI . "opt I m u m L o c a t l o n s a t C e n t e r s i n Networks," err.. 967-973 (1972).

~ 0 ~ 4 6 . G . v. n4hO~Ea. "Min lnaa ~ o c a t l o n a t a F a c i l i t y I n an U n d l r e c t e d l r e e Graoh." 1-s. 2. 287-293 113731.

LOCr7. G. r. HlNOLEP. "Pllnlmaa N e t m r k L o c a t l o n r h e o r v and 4DOI1CdtlOnS." Tech. ReDWt NO. 107, O O W S . Pes. Center , M I 1 INov. 1974).

LOC4b. G . I . HAhOLEP. "The M-Center P r m I e n t 4 R e l a a a t l o n ADDPOaCh.' Work lnq Paoer No. 58/6. The I s r a e l Institute o f n u s l n e s s Research. Tel-4v.v (Jan. 1977).

LOC1.9. P. JIRVIhEY, J. RLJILI . and n. SINERVO. "4 Branch and Sound 4 1 q o r l t h m f o r Smeklnq t h e 0-Median." Brr.. z p l l ) . 173-182 11972).

LOC50. I. U412 a n ¶ L. COOPER, "Oot lmal F a c I I I t v L o c a t l o n t o r Y o r n a l l v and E a o o n e n t l a l l v n l s t r l b u t e l po in ts . " ~pyulal nl w m YES %-fil. q O o l 1 ) . 53-72 (1976).

LOC51. B. H. KMUMPU1LI. " A n E t f l c r e n t B r a n c h and Bound 4 l p o r I t n m f o r t h e Warehousm L o c a t i o n ProOIem." Ub %&* 1 p 1 1 2 ) ~ B718-H731 (1972) .

LOC52. 4 . A. W E W ~ I and M. J. M4MBURGER. "4 H e u r l s t l c Prow-am fa r L o c a t l n q Warehousesr" L I f i rsir. 9.

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LOC53. J. LEVY, "An Extended Theorem f o r L o c a t l o r on a Network.' opanlr 8 . t pultmh. u d ( C I . 433-422 (19671.

LOC54.

LOC55.

LUC56.

LOC57.

LCJCSB.

LUC59.

LOCbO.

LOCCI.

LCC62.

LOC63.

LOC64.

LOC65.

LOC66.

LOCb7.

LOCb8.

LOC69.

LOC7O.

LOC71.

LOC72.

LOC73.

LOC7k.

LOC75.

LOC7t.

LOC77.

LOC7.3.

LOC74.

LOCSD.

Locn i .

I I . S. H A ~ . \ E . "P lan t L o c a t i o n Unacr Economles o f S c a l e - J e c e n t r a l l r a t l o n and Comoutatlons."

F. E . MAQAYZbNAl "On the Loca t ion o f S U D D ~ V p o i n t s t o H l n i a l r e Transoor t Costs.' pnnrlr Q u a y , fifit 261-270 (1964).

SSi., Ll. 213-235 (1964) .

R. E. MARSTEN. "an A l g o r i t h m f o r F i n d i n g Almost A l l o f t he Medlans of a Nmtwork." O l r c u r t l o n Paper NO. 23. Center l o r Hathemat I c a I S t u o l e s I n Economics and Management Sclence. Nor thwestern unlw. 1 1 9 7 2 ) .

E. H I N I E K A . "rne a-Center Proolem." U ti.Ylm. a. 138-139 119701.

p. a. HIRCHALDI~I. "Ana lvs l s o f S t o c h a s t l c He1*orks I n Emergencv S r v l c m Svrteas.' Tach. R e D O r t TP-15-75. noers. Res. Center. H I T (March 19751.

4. 9. 000hI. ' Loca t lon 01 F a c l l l t l e s on a Network1 A Survmv o f Rasults. ' Tech. Reoort NO. 3-74. Ooers. Qcs. Ceqter. H I T 11974).

A . PRIThKE3 an5 P. GHARE. "Loca t lng New F a c l l l t l e s w l t h ResDeCt t o E x l s t l r g F a c l l l t l e s . ' U E

J. J. REED. " T Y O 4 lgOr l thRS f o r ' i n d l n g the Abso lu te n - C e n t a o f a Graph." M.S. TCesIs. Nava l P o s t g r a a u i t e School, Monterevr C a l l f . (19711.

I E U ' 0s. 290-297 (19701.

C. 5. QEVELLE. ,I. HARKS. and J. C. LIFBMlh. "An A n a l v s l s O f Prlk'ate and Pub l lC SOC1OP LOCOtlOn M O O ~ ~ S . " mjDa S d . . U. 692-707 (19701.

C. S. 2EVELLf ana R. SWAIh. "Cent ra l F a c l l l t l e s Loeatlon." h,nwnplrrl b m s . f t l l . 38-42 I 1 9 7 01.

P . J. SCOTT. 'Location-Allocation Svstems: a Revlen." ~SQscmhkaL La.lvrls. 95-119 (19701.

A . J. Sc'Jr l , "Ovnaalc L o c a t l o n - 4 l l o c a t l o n S v S t e M s J Some Bas lc P IannJng S t r ~ t m q l e s . " L n m u a f aal 3. 73-83 (19711.

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I(. sP t ILOt? t . "Algor;tnns f a r the S l a o l e P l a n t L o c a t l o n P rob lea wlth Soar f l d e C o n s t r a l n t s r " p p ~ ~ s ~ . , K. $5-111 (1969).

K. ;PEILdt?G. "Plan? L o c a t i o n w l t h t e n e r a l l r e a Search Orlqln." &,b 165-178 (19C9l.

k . Y . SN41'4. " A OecomDostion A l g o r l t h m f o r a C lass o f F a c l l i t v I O C O t l O n PPoblea5.- Ph. 0. ! l i sser ta t lon , Corne l l Univ. (June 1971) .

0 . *. S W A I Y . h~ Paramet r ic 7ecompos i t lon ADbPOaCh f o r t h e S o l u t i o n o f UnCODaCltatmd Location Prooleas.*' 0ec.t. o f I n d u s t r i a l EnG. Ohlo S t a t e Unlv. ( 0 . C . 1971) .

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c. T O R R E G A J . e. SIIAIr.. C. WVELLE. and L. BERG MA^. "Tne L o c a t l o n o f ~ m e r q e n c v Service F a c i l l t l e s . ' pPosA m., 19, 1366-1373 119711.

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H A T R l 7 .

H A T R I B .

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HATP36.

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MATR41.

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REL2. H. 9ALL an0 R. VAN SLVKE. " S a c h t r a c k l n g A l ? o r i t h w s f o r N e t i o r k R e l l a b l l l t v Analysls." B U U . &j(ll, 8-73 119751.

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REL 3.

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H . CORLEY an0 ti. CHANG. " F l n a i n J t h e I. M o s t V l t a l Nodes I n a F l o w Network," !hh u, 362-364 (19741.

P. DOULLIEZ and M. RAO. "CaDacl tv o t J Y e t n o r k n l t h I n c r e a s l n q Oemads and A r c s S u b l e c t t o F a i l u r e , " QpcsJ Basrr n, 905-915 11971).

H . FRANK and U. CHOW, " T o o o I o g 1 c ~ I O o t l n l z a t l o n o f Comouter Netnorks." b w l n n r u. U. 1385-1397 11972I.

H , FPANK and I. FRISCH. " A n a l y s i s and Des iqn 01 S u r v l v a b l e Netb8OrkS." 1 - m Ism.. CnnziB(3l. 502-503 (19701.

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S. . I A K I M I . "An Algorithm f o r C o n s t r u c t l o n o t t h e L e a s t V u l n e r a b l e Communlcat lon Netnork." IfOnti C A C U A ~ ~ a n r v r C . I Z ~ ~ . 229-230 ( 1 9 6 9 ) .

S. L. H A K I H I an2 A. A M I N , "On t n e D e s l g n o f Q e l . l a b l e Netnorks." b m r p(31, 241-260 119731.

E. HAI.ISLfQ. "A F a s t R e c u r s l v e A l q o r i t h n t o C a l c u l a t e t h e R e l l a b l l l t v o t a C o n n u n l c a t l o n Letnork." IELE ICPUL an Camudcailans. Ca1=Zn(3lr 637-640 (19721.

E. HANSLER. G. WCAULIFFE. a n i R. WILYOV. "Exact C a l c u l a t l o n o f C o n w t e r N e t n o r k R o l l a b l l l t v . " c l s a k s . !tl21. 95-112 (19741,

J . HoFCROFT and R. 1ARJANI " D i v l a i n g a G r a m i n t o T r l c o n n e c t e d Comoonents.' J. mu.. z ( 3 ) (Seot . 19731.

J. HOPCROFT a n l R. TARJAh. " E t f i c i e n t A l g o r i t h m s t o p Graoh ManlDulat lon." B ( 1 6 l (June 13731.

T . C. MU, "Most R e l i a b l e Routes I n a hetnork,.. UM m. nI21, 261 (19€6l.

P. JENSEN rnc H . BELLMORE. "An A O o r l t h a t o Oetermlne t h e R e l l a b l l l t v o f a ConDlcx Svstem." IELL I C d ~ & Z l Q U Pn E S U P A l L b . k u L ( 4 1 (19641 .

P. JENSEh. "A Graoh O e c o n o o s l t i o n Techn laue f o r t e e Oes lgn o f Redundant E l e c t r o n l c Netnorks." Ph.0. D l s s a r t a t i o n . Johns t iook ln r U n l v e r s l t v . 9 a l t . . Mary land (19671.

A. KERSHENdAUY and R. V A l r SLYCE. " R e c u r s l v e A n a l v s l s o t Y e t n o r k R e l l a b l l l t v . " w b z . pill. 8 1 - 9 4 119731.

V. K I M , K. CASE. an0 P. GHASE. "4 Method f o r Comout lnq Cono lex Svstem R c l l a b i l 1 t v . - 1- pn a l L . & l & . g-fl(41, 215-219 119721.

J. L F G G E T I . " S v n t h e s l s o f Re1 l a b l e Comnun.cat I o n Netnorks. Ph.0. d l s s e r t a t l o n . U n l v e r s l t v o t Pennsy l v m i a l lY6.31.

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P. MIRCHAfi9AkI. " A n d l v s l s o f St0:hast ic N e t n o r k s I n Ernergencv S e r v i c e Svstems." I n n o v a t l v e Q e s o u r c e p l a n n i n g I n Urban P u B l I c S a t e t v Svstems. Tech. ReDort TR-15-75. ODerS. Res. Center , H . I . 1 , IMdrcb 19751.

K . HISRA. "AP A l g o r l t h n f o r t h e S e l l a b l l l t v C v a l u a t l o n of Redundant Networks," pn B S u U i r X . q a l 4 l r 146-151 (1970).

I(. M I S R A and 1. QAO. " R e l i a D I I I t v A n a l v s l s o f Redundant Netnorks U s l n p F low GraDhs." I C - r M &EllahllllYt U 9 ( 1 l * 19-24 (19701.

E. MOORE and C. SHANNON. " R e l i a b l e C l r c u l t s U s i n g Less R e l l a b l e Relavs." ,h af&.lln Inmu&, f62. 191-208 ( P a r t I1 and 281-297 ( P a r t IIl119561.

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J. HURCHLAYO. " C a l c u l a t l n g the P r o B a b l l l t v t h a t a t r a D h 1s Olsconnccted.' Q e p o r t JOW-102. P l a n n l n p and r r m s o o r t Research and C o n e u t a t i o n Co.. London (Fob. 19731.

J. HURCHLANO. "Fundamentdl S e l a t l o n s f o r Q e o a l r a b l e Items." RCDOrt JOtI-177. P l a n n l n q and T r a n s p o r t 2esearch and C o n o u t a t i o n Co.. London IFeb. 1973).

J. HURCHLANO and 0. SHIERt ' C a l c u l a t l n q t h e p r o b a b i l l t v t h a t an U n d l r e c t e d 6 r a o h Is Olsconnected." Reoor t JOM-186. P l a n n i n g and T r a n s o o r t Research and C o m o u t a t l o n Co.. LondoP (19731.

S. PAQIKH and I . FRISCM. " F l n d l n g t h e H o s t R c l l a b l e Routes I n Communlcat lon Svstem." I C d L L h m l M L Z y r m r ==fir 4 0 2 - 4 0 7 119631.

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RELSI. s. SESHU and I. REED. u ~ p mc~rlc.l mr A d d l ~ o n - Y e S I ~ v (19711.

REL38. J. SWRaALLE. ' 0 l s )o ln t Paths I n a Protnork.' m. h(2). 125-146 (19741.

REL39. N. TAINIltR. 'A New Ooto rm ln i s t l c Wotnork RellaOllltv Hoaswo." u.flpr)u. f i ( 3 ) . 191-204 (19761.

RELIO. R. TARJAk. ' tcoth F i r s t Soarch and L lnoa r G r a m Alqorlthrs.' UIll C M R U . . (June 1972).

RELI.1. A. SHOCAY. "Soouantlal Ooundlng o f t he Rollabllltv o f a S tochas t i c NotmOrk." QM& Esk ,

RELI.2. R. VAN SLYC and W. FRANU. ' 9 o l r a O l l l t y o f Cornoutor-Communlcation Notnorks." Ecab Ttb EQnL &(b). 1027-1044 (19761.

-. AFIPS Pross, Provldoncm. 71-82. (19711.

REL13. R. V A h SLVKE and M. FRANK. "NOtwDrk R ~ l l 8 b i l l t V A n 8 l v S l S l P a r t 1.' U o f h t . A ( 3 l r 279-290 (1971).

RELI.4. R. VrN SLY<€. H. FRAIHK. and A. KERSMENBAUH. 'hotnork 9 o l l a b l l l t v A n a l v s l s l Par t 2.' 8 u k S C t O 00 DUO1 I s h o J l .

REL45. 9. Y ILKOV, "Analvs ls ma Ooslgn o f Rollablo Com~uto r Notnorks." X E E Lcnru an Cn..ualc.fh~. Cparzp ( 3 ) . 660-678 (1972) .

RELS6. 0. YINC. 'Algori thms t o F l n g tho Host Re l l ab lO P a t h I n a Notwork." IBE. kM% W U- - 1 78-73 (19611.

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SP3. R. BELL'IAh. 'On a Rout ing ProbIom,' py.ct bnnL. m.. U. 87-90 (1958).

sP4. J. BROWN. 'Shortost A l t w n a t i n g P a t h Algorithms.' me. k ( 4 I . 311-134 (197Sl .

SP5. L. RUTAS. 'A O l r c c t i o n a l l v Orlmntod Shor tos t Path A l q o r l t h m . " 1.I..rrr. 2, 253-268 (19681,

SP7. 5 . CWAN and Y . CHW. 'An O D t i a l z a t l o n Problem I n Coamunlcatlon Mots." a m . fa, 79-¶6 (19711.

SP8. 5. CLARICE, R. UQIUORIAN. end J. RAUSE).. "Conoutin9 the N Best Loooless Paths In a N.t*Or(r.' A S n h InpyIL - 9 U, 109f -1102 (19631.

SP9. K. COOUE and E: HALSEv. "Tho Shor tos t Rout. t k o u 9 h a Notwork w i th 11.0-Oa~endont I n t o r n o d a l Trmslt Tlros. J. W AorL. u m.. 14. 493-490 (19bbl .

SP10. G. D A k l Z I G s 'On the S h o r t o s t SOU10 Throu9h a hOtWOTkr' h mq 6r 187-190 (19601.

SPll. E. UIJKSTRA. -1 Not. on T w o Problems I n Connactlon w l t h Craohs." m-9 1. 219-271 (1959).

SP12. S. OREIFUS. 'An 4DDralS.l O f SOMO Shortest -Path 4l9Orlthes.' U ( 3 l . 395-412 (19691.

SP13. H. FLORIAh r d P. ROOERT. 'A O l r o c t Searcb Hethoa t o Locate Neqat lvo CvcIos I n a Graoh." W U ( 5 l t 307-310 (19711.

S P l h H. FLORIAA ma P. ROBERT. "Rc lo lnoo r l O l r o c t Saarch f o r F i n d i n g N o w t l v o Cvclos." a. AS* 315-336 (19721.

SP15. R. FLOYD. 'AlpOPlth. 971 S n o r t ~ s t Path.' pi m. S t b l . 345 (19621.

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SP17. 8 . FOX. 'Ca l cu l r t l np U th Shor tost Paths.' L m . fi, b6-70 (19711.

SPl8. 8. FOX. 'nor. an K t h U lo r tms t Parhs.' id. 279 119751.

SP19. W. FRANK. "Shortost Paths I n P r o o a b l l i s t l c Graons. " pnnt. m.. U t 4 ) . 963-594 (19691.

SPZO. A. G ILL and I . TRAIGER. 'Comuta t l on o t OotlmaI Paths I n F l v l t a Graphs.' ( I n m g a&&& An QnU~AzaUno -9. . d l t m d bv L. Zadoh. L. Noustaat. m a A. Balokrlshnan. k a d o m l c Press. ~ e w York. 19691.

S P Z t . A. FRIEZE, 'Shor tes t P a t h L l g o r l t n m s f o r Unaosack Tvoe Problams," bLh. &as.. ll(2). 150-157

SPZZ. J. CILSIht . a r 1 C. YITZCALL. "A Per fo rmance C o n o a r i s o n o f L a b a l l n g L l v w l t h o s f o r C a l c u l a t l n g

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SP23. F. GLOVER, 0. UL1E;GMhL. ano A. NAPIER. " h N o t e on F l n d l n p A l l S h o r t e s t Paths," m.. dill. 3-13 (19741.

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SP25. A . GOLOHAh ard G. NEHHLUSER. " L T r a n s o o r t Imorovement ProDIam Transformable t o a Bast -Path Droolem." If& 1. 295-307 119671.

SP26. S . HAUIHI. " S h o r t e s t P a t h s I n Grams-A Revlew." hL fm. WyLt w. 368-369 119721.

SP27. J. wALPEPN a r d I . PRIESS. " S h o r t e s t P a t h w i t h T l n e C o n s t r a i n t s o n Hovemont and P r h l r r q , " u ~ w a p . 313) . 241-253 (1974).

~ ~ 2 8 . P. .(AT(T, h. f.ILESOh. and n. RLPHIEL. "4 Formal Basls f o r t he H e u r l s t l c O e t a r n l n a t l o n o f Mln laum Cost PdthSr" Iffi - & P O S m P Q S U S J dn9 c w u . ( 2 ) r 100 -107 (19681.

~ ~ 2 9 . L. MITCH~EP. " A Compara t ive I n v e s t l p a t l o n o t t h e C o m o u t a t l o n a l E f f l c l e n c v o t S h o r t e s t P a t h A l g o r l t P m s . Tach P 8 p o r t oRC 68-17. Ooers. Res. Center , Unlv. o f C a l l f . a t B e r k e l e v ( J u l y 1968).

SPJO. A. HOFFM4h a r j ti. HARUOnIT;. - A Note on S n o r t a s t Path, Asslpnmont. and l r e n s o o r t a t l o n Prob lens . " B u r W r L p p ~ 2.. Upl 375-380 119631.

SP31. n. HOFFHAk a r a R. PAVLEY, "A Hethod f o r t he S o l u t l O n O f the N t h B O S t P a t h Problem, "-9 6. 506-514 119591.

S P S Z . A . H O F F ~ A N a r d s. YIhOCRAOt ' 'F lnd lng A l l shortast O l s t a n c e s In a O l r 8 c t e d Network.' UIl ,& ~ p p ~ u L ~ . 16. 412-414 (1972).

sP33. 1. c. nu. '*Revised n a t r l x A l p o r l t h m s f o r S h o r t e s t Paths," SLAB J1 hl2.l.. Wrt 207-219 119671.

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SP36. H. JOKSCH. "The S n o r t e s t Route Prob lem Wi th Const r r1n ts . - A ur .nQ &&&, 14. 191

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0. S M I E R . " C ~ ~ ~ ~ t i t l o n a l E x o e r l e n c e w l t h an A l g o r l t h u f o r F l n d l n g t h e K Shor test P a t h s I n a Network," Jpyuld a IBf. m r 139-165 119741.

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P. SPIRA. "A Nan A l g o r l t h w f o r F l n d l n q A l l S h o r t e s t Paths I n a Graoh o f P o s l t l v e Arcs In Average T l n e O ( l n l o g r 1 + 0 2 1 r " a 1 ,L !&muling. Z l l l . 23-32 (19731.

P. SPIRA and A. PAN. "On F l n d l n q and UoOat ln ) Scann ln? Trees and S h o r t e s t Paths." mfl A C a m , 4C31. 375-380 (19751.

R. YAGNER. "A S n o r t e s t P a t h Algorithm t o r E jge-SparSe Graohs." Ufl. Z J l l ) . 50-57 (19761.

A. YEIYTRAUB. "The S h o r t e s t and I ( -Shor tes t Routes as Asslgnment Problems," 3el&nc?crt 3(11, 61-71. 119731.

L. A . YOLSEV. " G e n e r a l i z e d Oynamlc Programming Nethods In I n t e g e r Pro i ranmln?. " 9- E ~ ~ J A * 222-232 11973).

k . YONGSEELASMOTE. - A n A l g e b r a f o r O e t e r u i n l n g a l l P a t h - V a l u e s In e Network w l t h A o o I I c e t l o n t o K - S n o r t e s t - P a t h s P r o b l e u r . w b . hl' . ) , 307-33b (19761.

1. YILLIAHS. "An I u w o v e d S h o r t e s t P a t h A l g a l t h w f o r N e t w o r k s I n w h l c h t h e Maxlmun Outward Degree Is Less t h a n n/Z." P r e s e n t e d a t t h e 1975 O R S A / T I M S Meet lng . Las Vesas. Nevaaa.

J. VEN. "An A l g o r l t h u f o r F l n o l n j S h o r t e s t Routes f r o m A l l Source Nodes t o a G l v e n O e s t l n a t l o n I n Genera l N e t n o r k s r " PyKt~h 4- 01 &R.l&d HAih lM- ZLt 526-530 119701

J. YEN. "On W U ' S Oecomoos l t lon A l g o r l t h m f o r S h o r t e s t P a t h s I n a Network. "wr m.9 1pCl.I. 983-985 119711.

J. VEN. 'F lna ina t h e K S h o r t e s t LoODless P a t h s I n a Metwork." !j& klr 12. 712-716 (19711.

J. YEN. " F l n o l n j t h e L e n g t h s o f A l l S h o r t e s t P a t h s In %-Node Nonneaat ivC r l l s t a n c e Comolete Networks U s l v g 1/2Ne*3 A d a l t i o n s an0 So.3 Comoaris lons." Jm. 19131. 423-424 11972).

J. YEh. "On t h e E f f l c i e n c v o f a J l r e c t Search Method t o L o c a t e N e g a t i v e C v c I e s In a Net ro rk . " u. B, 333-335 (19721.

T r a v e l 1 I n 9 Sa lesuan PPObI*IS and E r t e n s l o n s (Veh lc I e R o u t l n g l

5. ASHOUR, J. v E G A . and R. PARK€*. " A n e u r l r t l c Algorltnn t o r t h e Travelling Salesman Problem."

n. JALINSKI. and R. QUANOT. "On a n I n t e g e r P r o q r a u tor a O e l l v e r v Problem." QML 9nsl. 1212). 3 0 0 - 3 0 6 119641.

L. BARACWET. " t r a o h l c S o l u t l o n o f t h e T r a v e l i n g Sa lesuan Probleu." B.nr. 5161. 841-845 I 1957 I .

- 9 6 , 187-195 (19721.

176

TSP4. J. BEAROYOOD. J. HALTON, and J. MAMMERSLEV. "The S h o r t e s t P a t h Through Ran* Points*'

TSP5. 0. BELL, "The Resolution o f O d a l l t v Gaos I n O l s c r e t e O D t l m l r a t l o n Tech. R e D O r t No. 81. ODers.

W a %Gat 55. 299 (1959).

Res. Center. M . I . T . (Aug. 19731.

TSP6. R. SELLMAN. "Ovnamlc Programmlng Treatment o f t h e 61-63 (1962) .

T r a v e l l n g Salesman PrOb I eRv" 9111.

TSP7. 8 . BELLHORE and S. HONGr ' l r a n s f o r m a t l o n o f M u l t l s a l e s m e n Prob lem t o the S t a n d a r d T r a v e l l n g

TSPB. H. BELLHORE e n d J. HALONE. "Patno logy o f Trave l lng-Sa lesman S u b t o u r - E l l m l n a t l o n Algorlthmsr"

Salesman Problem." .!&I, ZA. (3). 500-504 (197c I .

QPQ$s 8gs.e f i ( Z l . 275-307 (19711.

TSP9. M . BELLHORE and G. LEHHAUSER. "The T r a v e l i n g Salesman Problem: 538-558 (1960).

TsPto. E. BELTSARI and L. BOOIN. 'NetnOrkS and V e h l k l e R o u t l n 3 f o r n u n l c l o a l Waste Collection." l g u r t r r . h(1) . 65-94 (19741.

TSPl l . 8. RENNETT, and 0. GALIS* 'School flus R o u t l n g b v ComDuter." Blr.rcn. 614).

1 ~ ~ 1 2 . n. RILES acd J. BRAOFORO. -a H e u r l s t l c Aooroach t o ~ o n l c ~ e S c h e d u l l n g n l t h h e - o a t e

317-325 (19721.

C o n s t r a i n t s . P r e s e n t e d a t the 1975 ORSA/TIW I e e t l n g , Chicago. X I I l n o l s .

TSP13.

TSP14.

TSP15.

TSPIIY.

~ S P I S .

TSPZO.

TSP21.

TSP22.

TSP23.

TSPZb.

TSPZ5.

TSPZB.

TSP29.

TSPJO.

TSP31.

TSP32.

TSP33.

TSP34.

TSP35.

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P. C A S S I O V I and H. BENNETT, "TRAMP - A HUl t l -deDo1 Y e n l c l e S c h e d u l l n q System." Brslarrn Q W p r l u . i 3 ( 2 I r 151-163 119721.

J. CHISHPIN. "The C l u s t e r e o Trave l Ing Salesman Problem;" f i m A a. z(21, 115-119 (19751.

N . CHRISTOFIDES. '*The S h o r t e s t r a m l l t o n l a n C h a l n 0 1 a Graoh." U M A p p L tlm.. U. 689-696 (1970).

N. CHRISTOFIDES, "Bounds f o r t h e T r a v e l l l r g Salesman Prob lem Pp- m.. Zp, 1044-1056 11072).

N. CYSISTOFIDES. "The V e h l c l c R o u t l n g Problem," NATO Conference on C o m b l n a t o r l a l O o t l m l z a t l o n ~ P a r l s , ( S c o t . 19741.

N. CnRISTOFIDES1 " H a m l t t o n i a n c i r c u i t s ana t h e ~ r a v e 1 1 1 n 9 S a i e s e a n Problem8 A Survev." In

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C n . P l w l a l k t m (0. R O V . ed.8. 9. R e l d l PUbl. CO..

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N. CHRISTOFIOESI and S. EILON. " A l g o r l t h m s f O C L a r g e S c a l e TSP'S*" Q u U h . 23. D . 5 1 1 (1972).

G. CLARKE 3na J. Y R I G H T . " S c h e a u l l n g o f V e h I c I e s from a C e n t r a l OeDot t o a Number o f O e l l v e r v P o l n t r . " QMS. as. t U ( 4 1 r 560-501 ( 1 9 6 4 ) .

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G. O A N T L I G . 0 . FULKERSOh. and S. JOHNSON. "On a L l n e a r Programmlng, C o m b l n a t o r l a l AoDrOach t o t h e T r a v e l I l n 3 Salesman Problem,- Q- &&* Z l l ) . 58-66 (19591.

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R. GARFINKEL, "On P a r t l t l o n l n g the Feas lb le S e t I n a Branch-and-Bound A l g o r l t h m f o r t h e Asymmetric Trmvel lng-Salesman Probtem." Qmt 815.. Z ( l ) r 340-342 (1913).

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Y . GARVINr M. CRaNOALL. J. JOHN. and R. SPELLMAN. " A D o l l c a t l o n s O f L l n e a r Proprammlng I F t h e 011 Indus t ry , " S & L 3 1 4 ) . 487-430 (1957).

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Problem."

TSP37.

TSP38.

TSP39.

TSP40.

TSP41.

r s p u .

TSP43.

TSP44.

TSP45.

TSP46.

TSP47.

TSP48.

TSP49.

TSPSO.

TSP51.

fSP52.

TSP53.

TSP54.

TSP55.

TSP56.

TSP57.

TSP58.

TSP59.

TSPKO.

TSP61.

TSP67.

R. GILLETT and L. MILLER, 'a M e u r l s t l c A l q o r l t h m f o r t h e V e h l C I e O l s o a t c h PPOblem,' Q m S 8 s . . 22. 340-349 (19741-

P. GILMORE and R. COMORY. ":eauenclng a One-Sta te Variable Mach lnc : A S o l v a b l e Case o f t h e T r a v e l l n q S a l e s e m Problem. m.. 121 655-679 (1964) .

8. GOLDEN. ' veh&cIe R o u t i n g P r o b l e e s : F o r m u l a t l o n s and M e u r l s t l c S o l u t l o r Tec lmlauesr " Tech. R e p o r t No. 113. uoers. Res. Canter , M.1.T. (Lug. 1975).

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8. GOLDEN. 'Large-Scale V e h l c l e R o u t l n g and R a l a t e d C o m b l n a t o r l a l ProBlems.' Pn.0. O I s s e r t a t l m . Ooeratlons Research Center. M . 1 . T . (June 19761.

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W . nAROCRAVE and G. NEMMAUSER. 'On t h e R e l a t l o n Between t h e T r a v e l l n g S a l e s r a n and t h e Congest P a t h Problem," ppat m.. Ipt5). 6 4 7 - 6 5 7 ( 1 q 6 2 ~ .

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M . HELD an3 R . KARP, "A Ovnaa lc P r o p r a r m l n q Aooroach t o Seouenc lnq P r o b l e m s ~ ' S U d Jaurr.l* U p 1

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M . HELO and P. YOLFE, and M . CROYOER. ' V a l l d a t l o n o t S u b q r a d l m t O o t i m l r a t l o n r " mh E m s . .

J. MINSON and 5 . MULMERKAR. ' Imcrovemenfs t o t h e C l a r k e and wrlqnt A l q o r l t h m as A~oIled' t o an A l r l l n e S c n e a u l l n g Problem." o r e s e n t e a a t the M l a r l O R S A I T I M S M e e t l n g ( F a l l 1976).

R. MOLMES and 9 . PARKER, 'A v e h i c l e Schcdu1;nq P r o c e d u r e 9ased Uoon S a v l n q s and a S o l u t l o n P e r t u r b a t i o n Scneme." u -1 5. U t l I r 83-92 (19761.

J. HUOSOh. 0. GROSSMAht and 0 . MARKS. ' A n a I v s I s Models f o r S o l l a Waste C o l l e c t l o n . " W I T C l V l l E n ~ l n e e r l n g R e o o r t No. R73-47 ( S e o t . 1973).

L. KARG and G. TMORPSON. 'A n e u r l s t l c AoDPOKh t o S o l v l n q T r a v e l l n g Salesman Problems." fS1.v U p 1 225-248 (19641.

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P. UROLAK. Y. FELTS, a n d J. NELSJh. " L Man-Machlne Aooroach Toward S o l v l n g t h t C e n e r a l l t e d Truck-D1soatch lng Problem." %. 612) 9 149-170 (1972).

J. KRUSKAL. " O n the S h o r t e s t S o a n n l n g S u b t r e e o f a Graoh and t h e Traveling Salesman Problem.'

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R. NEYrOtlr a m Y. THOMAS. "Our Rout lng I n a tIult l -School Svstem." B r W . 1 4 2 l . 213-222 (19741.

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C. ORLOFF. "Poutlnq A F loe? O f M. Veh1Cl.S t o l f r o n Centra l Fac i l i t y , " &-. &(Zl. 147-162 ( 1 974 I .

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nab. u i k i . 400-407 t i ~ 6 9 1 .

lSP69.

TSP70.

TSP74.

lSP75.

TSP76.

TSP77.

TSPTn.

lSP79.

TSP80.

fSP81.

TSP82.

TSP83.

TSP64.

lSP85.

TSP86.

TSP87.

rspna.

lSP91.

TSPSZ.

TSP93.

TSP94.

lSP95.

TSP96.

TSP97.

lSP98 .

lSP99.

5. 2OOERTS a r a 9. FLORES. " In Enqineor ing Aooroach t o the T rauc l l ng Salosman Problem." !lxu

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xL* La131 269-288 (19661.

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