Hi Zvonko, Here's an article concerning this particular application -- http://www.opf.slu.cz/vvr/akce/turecko/pdf/SLGazda.pdf
Jeff Kantor On Wed, Sep 5, 2012 at 10:53 AM, glpk xypron <[email protected]> wrote: > Hello Zvonko, > > this is a pure LP problem: > > # partners > set S; > # given flows; > set F, dimen 3; > # minimized flows > var f{S,S}, >=0; > > minimize obj : > sum{i in S, j in S} f[i,j]; > > s.t. c1{i in S} : > sum{(j,i,x) in F} x - sum{(i,j,x) in F} x = > sum{j in S} f[j,i] - sum{j in S} f[i,j]; > > solve; > > display f; > > data; > > set S := A B C; > set F := > A B 7000 > B C 5000 > C A 2000; > end; > > Best regards > > Xypron > > -------- Original-Nachricht -------- >> Datum: Wed, 5 Sep 2012 08:13:18 +0000 >> Von: Zvonko Bregar <[email protected]> >> An: "[email protected]" <[email protected]> >> Betreff: [Help-glpk] financial compensation > >> Hello everyone, >> I came across a certain combinatorial problem. >> Of a mandatory debt compensation between firms. >> The problem can be stated as: >> You have a directed graph. >> Each vortex presents a firm (a company). >> Each (directed) link from A to B presents the money amount that the A-firm >> must pay to the B-firm. >> And the problem is to reduce all the redundant cycles, >> For example if A owes 7000 to B and B owes 5000 to C and C owes 2000 back >> to A then this cycle could be reduced by 2000 and the link between C and A >> becomes obsolete. >> My question is whether or not this problem can be formulated as a mixed >> integer linear program. >> If Yes, does it makes sense or it would be much better to apply some graph >> theory alghoritms for minimal trees, cycles etc. >> If it does make sense to apply MILP please point me to the literature. >> Thank you in advance >> Zvonko >> >> OPOZORILO: To elektronsko sporo?ilo in vse njegove morebitne priloge lahko >> vsebujejo zaupne in/ali privilegirane informacije, ki so last >> Elektroin?tituta Milan Vidmar in so namenjene izklju?no naslovniku. ?e ste >> sporo?ilo >> prejeli pomotoma zaradi napake v naslovu ali pri prenosu sporo?ila, Vas >> prosimo, da nas o tem obvestite s povratno po?to. V tem primeru vsebine >> prejetega sporo?ila ne smete uporabiti, kopirati, tiskati, objaviti ali >> distribuirati, ampak ga morate takoj uni?iti. >> >> DISCLAIMER: This e-mail is for the intended recipient only. It contains >> proprietary information some or all of which may be legally privileged. If >> you received this e-mail by mistake please notify us by replying to this >> e-mail. Consequently, the contents of this e-mail must be deleted and not be >> used, copied, printed, disclosed or distributed. >> > > _______________________________________________ > Help-glpk mailing list > [email protected] > https://lists.gnu.org/mailman/listinfo/help-glpk _______________________________________________ Help-glpk mailing list [email protected] https://lists.gnu.org/mailman/listinfo/help-glpk
