tr20.gms : Extended transport model with stochastic demand and costs

Description

In some of these models we have huge scenario trees. DECIS will solve this by
some internal sampling routines, while DE and LINDO should terminate with a
useful error message.


Large Model of Type : SP


Category : GAMS EMP library


Main file : tr20.gms

$title Extended transport model with stochastic demand and costs (tr20,SEQ=84)

* In some of these models we have huge scenario trees. DECIS will solve this by
* some internal sampling routines, while DE and LINDO should terminate with a
* useful error message.


set c
    ck(c)    Center
    cc(c)    Cities
    stoch  / val, prob /
    r      / l, m, h /;

parameter coord(c,*);
parameter dist(c,c);
parameter b(c,c);
parameter rv(stoch,r)
alias (c,cp);

$gdxin tr20_scen
$load c ck cc coord dist b rv

Parameters cap    Maximum capacity of one truck / 10.0 /
           cf     Transportation cost per mile and per truck - full run / 0.2 /
           ce     Transportation cost per mile and per truck - empty run / 0.18 /
           b(c,c) Demand of center and cities
           maxt   Maximum amount of trucks;

set dnet(c,c); dnet(ck,cc) = yes; dnet(cc,ck) = yes;
set enet(c,c); enet(c,cp) = not sameas(c,cp);


maxt=sum(dnet(c,cp), b(dnet));

Parameter
      df(c,c)  random demand factor
      cr(c,c)  Recourse cost (rent-a-truck) per mile
      crr(c,r) stochastic outcome of cr;

$load crr

* -----------------------------------------------
* define the core model
* -----------------------------------------------

Free Variable z total cost;

Positive Variables f(c,c)    Full runs
                   e(c,c)    Empty runs
                   y(c,c)    Recourse
                   a(c)      Allocation
                   stayat(c) Trucks staying at c - i.e. no full or empty runs;

Equations
         tcosts       define objective function
         demand(c,c)  serve demand of center and all cities
         node(c)      node constraint for the trucks
         maxtruck     maximum number of trucks to be allocated;

tcosts .. z =e=    sum(dnet(c,cp), dist(dnet)*(cf*f(dnet) + cr(dnet)*y(dnet)))
                 + sum(enet(c,cp), ce*dist(enet)*e(enet));

demand(dnet(c,cp))..  f(dnet)*cap + y(dnet) =g= df(dnet)*b(dnet);

node(c) .. sum(dnet(c,cp), f(c,cp)) + sum(enet(c,cp), e(enet)) + stayat(c)
           =e= a(c) + sum(enet(cp,c), e(enet));

maxtruck.. cap*sum(c, a(c)) =l= 0.9*maxt;


Model transport /tcosts,demand,node,maxtruck/;

Set s            scenarios / s1*s100 /;

parameters s_df(s,c,c);
Set dict / s     .scenario.''
           df    .randvar. s_df/;

df(dnet)       = 1;
cr(dnet(c,cp)) = crr(c,'m');

file emp / '%emp.info%' /; put emp '* problem %gams.i%';
loop(dnet,
   put / 'randvar ' df.tn(dnet) ' discrete '
   loop(r, put rv('prob',r):5:2 rv('val',r):5:2));
   put / 'stage 2 df f e y stayat demand node';
putclose;

solve transport min z using emp scenario dict;

* Sampling
Scalar h1;

loop(s,
  loop(dnet,
    h1=uniform(0,1);
    if( h1<rv('prob','l') ,
      s_df(s,dnet)=rv('val','l');
    elseif h1<=(rv('prob','l')+rv('prob','m')),
      s_df(s,dnet)=rv('val','m');
    else
      s_df(s,dnet)=rv('val','h');
    );
  );
);

put emp '* problem %gams.i%';
put / 'jrandvar '
loop(dnet, put df.tn(dnet));
loop(s,
  put (1/card(s)):8:6;
  loop(dnet, put s_df(s,dnet):5:2; );
);
put / 'stage 2 df f e y stayat demand node';
putclose;

solve transport min z using emp scenario dict;

parameters s_cr(s,c,c);

Set dict2 / s     .scenario.''
            df    .randvar. s_df
            cr    .randvar. s_cr/;

put emp '* problem %gams.i%';
loop(dnet(c,cp),
   put / 'jrandvar ' df.tn(dnet) ' ' cr.tn(dnet)
   loop(r, put rv('prob',r):5:2 rv('val',r):5:2 crr(c,r):6:3));
   put / 'stage 2 df cr f e y stayat demand node';
putclose;

solve transport min z using emp scenario dict2;