September 2017 Update

Task/Vogels-approximation-method/Zkl/vogels-approximation-method-1.zkl

@@ -0,0 +1,7 @@
+costs:=Dictionary(
+   "W",Dictionary("A",16, "B",16, "C",13, "D",22, "E",17),
+   "X",Dictionary("A",14, "B",14, "C",13, "D",19, "E",15),
+   "Y",Dictionary("A",19, "B",19, "C",20, "D",23, "E",50),
+   "Z",Dictionary("A",50, "B",12, "C",50, "D",15, "E",11)).makeReadOnly();
+demand:=Dictionary("A",30, "B",20, "C",70, "D",30, "E",60);  // gonna be modified
+supply:=Dictionary("W",50, "X",60, "Y",50, "Z",50);	    // gonna be modified

Task/Vogels-approximation-method/Zkl/vogels-approximation-method-2.zkl

@@ -0,0 +1,14 @@
+cols:=demand.keys.sort();
+res :=vogel(costs,supply,demand);
+cost:=0;
+println("\t",cols.concat("\t"));
+foreach g in (costs.keys.sort()){
+   print(g,"\t");
+   foreach n in (cols){
+      y:=res[g].find(n);
+      if(y){ y=y[0]; print(y); cost+=y*costs[g][n]; }
+      print("\t");
+   }
+   println();
+}
+println("\nTotal Cost = ",cost);

Task/Vogels-approximation-method/Zkl/vogels-approximation-method-3.zkl

@@ -0,0 +1,30 @@
+fcn vogel(costs,supply,demand){
+   // a Dictionary can be created via a list of (k,v) pairs
+   res:= Dictionary(costs.pump(List,fcn([(k,_)]){ return(k,D()) }));
+   g  := Dictionary(); // cross index costs and make writable
+   supply.pump(Void,'wrap([(k,_)]){ g[k] =
+      costs[k].keys.sort('wrap(a,b){ costs[k][a]<costs[k][b] }).copy() });
+   demand.pump(Void,'wrap([(k,_)]){ g[k] =
+      costs.keys.sort('wrap(a,b){ costs[a][k]<costs[b][k] }).copy() });
+
+   while(g){
+      d:=Dictionary(demand.pump(List,'wrap([(k,_)]){ return(k,
+	 g[k][0,2].apply('wrap(gk){ costs[gk][k] }).reverse().reduce('-)) }));
+      s:=Dictionary(supply.pump(List,'wrap([(k,_)]){ return(k,
+	 g[k][0,2].apply('wrap(gk){ costs[k][gk] }).reverse().reduce('-)) }));
+      f:=(0).max(d.values); f=d.filter('wrap([(_,v)]){ v==f })[-1][0];
+      t:=(0).max(s.values); t=s.filter('wrap([(_,v)]){ v==t })[-1][0];
+      t,f=(if(d[f]>s[t]) T(f,g[f][0]) else T(g[t][0],t));
+      v:=supply[f].min(demand[t]);
+      res[f].appendV(t,v);  // create t:(v) or append v to t:(...)
+      if(0 == (demand[t]-=v)){
+	 supply.pump(Void,'wrap([(k,n)]){ if(n!=0) g[k].remove(t) });
+	 g.del(t); demand.del(t);
+      }
+      if(0 == (supply[f]-=v)){
+	 demand.pump(Void,'wrap([(k,n)]){ if(n!=0) g[k].remove(f) });
+	 g.del(f); supply.del(f);
+      }
+   }//while
+   res
+}