Working?

Author: scheinerman

Project.toml

@@ -1,7 +1,7 @@
 name = "SimplexTableaux"
 uuid = "b49aa546-d643-4829-bb91-bc1e5e539d80"
 authors = ["Ed Scheinerman <ers@jhu.edu>"]
-version = "0.0.7"
+version = "0.0.8"
 
 [deps]
 ChooseOptimizer = "858a232f-1959-5553-8cfc-91e1fd5304e2"

README.md

@@ -16,10 +16,8 @@ See [the documentation](https://docs.juliahub.com/General/SimplexTableaux/stable
 ## Caveats
 
 As a demonstration project, this is not suitable for solving actual linear programming (LP) problems. 
-At present it will fail if:
-* The LP is infeasible.
-* The LP is unbounded.
-* Other unidentified reasons. (In other words, still buggy.)
+
+At present the user needs to specify a starting basis; see the documentation. 
 
 This module is set up for minimization problems only. 
 

development/examples.jl

@@ -49,6 +49,7 @@ function unbounded_example()
     b = [5; 4; -3]
     c = [-1; -2]
     T = Tableau(A, b, c)
+    set_basis!(T, [1, 2, 5])
     return T
 end
 
@@ -118,21 +119,21 @@ end
 
 function deg_picture()
     newdraw()
-    
-    L1 = Line(3,4,8,5)
-    L2 = Line(8,5,6,2)
-    L3 = Line(6,2,1,1)
-    L4 = Line(1,1,3,4)
-    L5 = Line(3,4,4,5)
-
-    p1 = Point(1,1)
-    p2 = Point(3,4)
-    p3 = Point(8,5)
-    p4 = Point(6,2)
-    pp = [p1,p2,p3,p4]
-
-    draw_xaxis(-1,9)
-    draw_yaxis(-1,6)
+
+    L1 = Line(3, 4, 8, 5)
+    L2 = Line(8, 5, 6, 2)
+    L3 = Line(6, 2, 1, 1)
+    L4 = Line(1, 1, 3, 4)
+    L5 = Line(3, 4, 4, 5)
+
+    p1 = Point(1, 1)
+    p2 = Point(3, 4)
+    p3 = Point(8, 5)
+    p4 = Point(6, 2)
+    pp = [p1, p2, p3, p4]
+
+    draw_xaxis(-1, 9)
+    draw_yaxis(-1, 6)
 
     draw_xtick(1:8)
     draw_ytick(1:5)
@@ -141,14 +142,14 @@ function deg_picture()
         draw(p)
     end
 
-
-    LL = [L1,L2,L3,L4,L5]
+    LL = [L1, L2, L3, L4, L5]
 
     for L in LL
         draw(L)
     end
     finish()
-
 end
 
+
+
 nothing

src/SimplexTableaux.jl

@@ -23,6 +23,7 @@ export Tableau,
     find_a_basis,
     find_all_bases,
     find_pivot,
+    find_pivot_column,
     get_Abc,
     get_basis,
     is_feasible,

src/Solver.jl

@@ -57,12 +57,12 @@ function find_pivot(T::Tableau)
 end
 
 function find_pivot_column(T::Tableau)
-    for i in 1:T.n_vars
-        if T.M[1, i + 1] > 0
-            return i
-        end
+    reduced_costs = T.M[1, 2:(end - 1)]   # top row between separators
+    rc, j = findmax(reduced_costs)
+    if rc <= 0
+        return 0   # no pivot possible
     end
-    return 0 # no valid column
+    return j
 end
 
 """
@@ -80,18 +80,21 @@ function simplex_solve!(T::Tableau, verbose::Bool=true)
         println(T)
     end
 
-    pivot_count = 0 
+    pivot_count = 0
 
     while !is_optimal(T)
         p = find_pivot(T)
         if 0 ∈ p
-            @error "Cannot solve this LP. Is it infeasible? Unbounded?"
+            @info "This linear program is unbounded"
+            return nothing
         end
         basis_pivot!(T, p...)
         pivot_count += 1
         if verbose
             in, out = p
-            println("Pivot $(pivot_count): column $out leaves basis and column $in enters\n")
+            println(
+                "Pivot $(pivot_count): column $out leaves basis and column $in enters\n"
+            )
             println(T)
         end
     end