Task Schedule sicstus prolog

Question

I started sicstus prolog recently and have this homework to solve with CLP (constraint logic programing), please help me understand the problem, what I should be looking for and what I'm doing wrong. So,

A building company:

• To get raw material the BC has to rent a truck that takes 6 days to transport 25T of raw materials, and it costs 80$ a day.
• To build above the ground 15T of raw material is needed, it takes 10 days and costs 150$ per floor.
• To build underground 20T of raw material is needed, it takes 23 days (due to excavating), costs 150$ and at least one excavating machine is needed that adds 75$ per day and reduces excavating time by 3 days (two machines max at a time). (1->20days,2->17days)
• If a crane is rented all building time is reduced by 25% and has a cost of 120$ a day.
• The electric team can only advance when 75% of the building is built, it takes 5 days and costs 200$ per floor. And when the building is complete one more week is needed to finish all floors connections.

The BC pretends to build a Skyscrapers with 150 floors above ground and 15 underground, how must the building be organized so profit is maximized and and time required minimized?

Define the problem as a constraint satisfaction problem and solve it with CLP so it is possible to solve it with different parameters (more or less floors, or adjusting teams sobreposition times).

And what I have so far:

:- use_module(library(clpfd)).

start(Fdigs,Floors,Vars):-
    length(Vars,5),

    %S -> start, E -> end, D -> duration
    %t -> transport, e -> excavating, f -> floor (build)

    Vars=[St,Et,Se,Ee,Cost],

    Se #>= Et,
    Ee #= Se + 10,
    Et #>=6,
    Cost #>= Ee * 80,  %transport cost since it starts at 0 Ee will be the days needed

    domain(Vars,0,2000),
    construct(0,Fdigs,Floors,Vars),
    labeling([minimize(Cost)],Vars).

construct(Stock,0,Floors,Vars).

construct(Stock,Fdigs,Floors,[St,Et,Se,Ee,Cost]):-
    Tasks=[
    task(St,6,Et,0,1),  %transport task
        task(Se,10,Ee,5,2)  %dig task, 5 because I'm digging all then building (20-15)
                %10 because build is 10 so dig is 10
    ],
    cumulative(Tasks,[limit(Stock)]),
    Nfdigs is Fdigs - 1,
    Nstock is Stock + 25,
    construct(Nstock,Nfdigs,[Et,_Et,Ee,_Ee,Cost]).

And it doesn't work of course, because I cannot use cumulative with a task requiring 5 resources and a limit of 0 resources is the first of many issues I can't get around...

Answer 1

Here it's what I came up with so far, seems to be a lot easier and getting me the result expected:

:- use_module(library(clpfd)).

start(Floors,Fdigs,Vars):-
    length(Vars,20),
    domain(Vars,0,999999999),   %all vars must be bounded
    Vars=[                      % S-start,D-duration,E-end,C-cost (money)
    St,Dt,Et,Ct,                % transport vars
    Se,De,Ee,Ce,                % excavation vars
    Sb,Db,Eb,Cb,                % building vars
    Sc,Dc,Ec,Cc,                % electricity vars
    Machines,Crane,Cost,Time],
    Machines in 1..2,
    Crane in 0..1,
    St is 0,
    Dt is ceiling(((Floors*15)+(Fdigs*20))/25)*6,
    Et is Dt,
    Ct is 80 * Dt,
    Se is 0,
    De #= (13 - (Machines*3)) * Fdigs,
    Ee #= De,
    Ce #= De * (75*Machines),
    Sb #>=6 #/\ Sb #>= Ee,
    Db #= ((Fdigs * (10-(Crane*3))) + (Floors * (10-(Crane*3)))),
    Eb #= Sb + Db,
    Cb #= (Fdigs + Floors) * 150 + (Crane*Db*120),
    Sc #= (Eb * 75 / 100),
    Dc #>= (Eb * 25 / 100) + 5 #/\ Dc #=((Floors + Fdigs) * 5) + 5,
    Ec #= Sc + Dc #/\ Ec #> Eb,
    Cc is (Fdigs + Floors) * 200,

    %Costs
    Cost #= (Ct + Ce + Cb + Cc),

    %Times (will be end time of final & nonoverlaping task)
    Time #= Ec,

    %labeling([minimize(Cost)],Vars),       % - cost, + time
    labeling([maximize(Cost)],Vars),        % + cost, - time
    writeVars(Vars).

writeVars([St,Dt,Et,Ct,Se,De,Ee,Ce,Sb,Db,Eb,Cb,Sc,Dc,Ec,Cc,Machines,Crane,Cost,Time]):-
    write('1 '),write(St),write(' '),write(Dt),write(' '),write(Et),write(' '),write(Ct),write('\n'),
    write('2 '),write(Se),write(' '),write(De),write(' '),write(Ee),write(' '),write(Ce),write('\n'),
    write('3 '),write(Sb),write(' '),write(Db),write(' '),write(Eb),write(' '),write(Cb),write('\n'),
    write('4 '),write(Sc),write(' '),write(Dc),write(' '),write(Ec),write(' '),write(Cc),write('\n'),
    write('Cost: '),write(Cost),write('\n'),
    write('Time: '),write(Time),write('\n'),
    write('Crane: '),write(Crane),write('\n'),
    write('Machines: '),write(Machines).
    %write('4 ',St,' ', Dt,' ', Et,' ', Ct),
    %write('5 ',St,' ', Dt,' ', Et,' ', Ct).

Any sugestions, comments that improve my answer are very much welcome.