add test from a textbook to Minimum Cost Flow

Author: jbytecode

src/maximumflow.jl

@@ -217,7 +217,7 @@ function solve(problem::MinimumCostFlowProblem, flow::Float64)::MinimumCostFlowR
     @variable(model, x[1:n, 1:n] .>= 0)
 
     # Objective Function
-    @objective(model, Max, sum(x[conn.from, conn.to] * conn.value for conn in costs))
+    @objective(model, Min, sum(x[conn.from, conn.to] * conn.value for conn in costs))
 
     # Constraints 
     for nextnode in mynodes

test/testminimumcostflow.jl

@@ -44,7 +44,46 @@
         result = solve(problem)
 
         @test result isa MinimumCostFlowResult
-        @test result.cost == 95.0
+        @test result.cost == 65.0
+    end
+
+    @testset "Book example - 1" verbose = true begin
+
+        # Example is given from the url:
+        # https://www.ams.jhu.edu/~castello/625.414/Handouts/WV8.5.pdf
+
+        conns = Connection[
+            Connection(1,2,800),
+            Connection(1,3,600),
+            Connection(2,5,100),
+            Connection(2,4,600),
+            Connection(5,6,600),
+            Connection(4,5,600),
+            Connection(4,6,400),
+            Connection(3,5,400),
+            Connection(3,4,300)
+        ]
+
+        costs = Connection[
+            Connection(1,2,10),
+            Connection(1,3,50),
+            Connection(2,5,70),
+            Connection(2,4,30),
+            Connection(5,6,30),
+            Connection(4,5,30),
+            Connection(4,6,60),
+            Connection(3,5,60),
+            Connection(3,4,10)
+        ]
+
+        definedflow = 900.0
+
+        problem = MinimumCostFlowProblem(conns, costs)
+        
+        result = solve(problem, definedflow)
+
+        @test result isa MinimumCostFlowResult
+        @test result.cost == 95000.0
 
     end
 end