implement least cost method for transportation problems

Author: jbytecode

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 - Add new tests for CPM
 - Feed an initial feasible solution (with North-West Corner Method) to a Transportation Problem. That makes it 10x faster
+- Implement least cost method for constructing a feasible initial solution to the transportation problems.
 
 
 ### 0.2.4

src/OperationsResearchModels.jl

@@ -42,7 +42,12 @@ import .TravelingSalesman
 
 
 import .Transportation:
-    TransportationProblem, TransportationResult, balance, isbalanced, northwestcorner
+    TransportationProblem, 
+    TransportationResult, 
+    balance, isbalanced, 
+    northwestcorner, 
+    leastcost
+
 import .ShortestPath: ShortestPathResult, ShortestPathProblem
 
 import .Network: Connection, nodes
@@ -60,7 +65,7 @@ import .RandomKeyGA: Chromosome, run_ga
 import .TravelingSalesman: TravelinSalesmenResult, travelingsalesman
 import .Simplex: SimplexProblem, simplexiterations, createsimplexproblem, gaussjordan
 
-export TransportationProblem, TransportationResult, balance, isbalanced, northwestcorner
+export TransportationProblem, TransportationResult, balance, isbalanced, northwestcorner, leastcost
 export Connection, ShortestPathResult, MaximumFlowResult, nodes
 export ShortestPathProblem, MaximumFlowProblem
 export AssignmentProblem, AssignmentResult

src/transportation.jl

@@ -6,6 +6,10 @@ using JuMP, HiGHS
 
 export TransportationProblem
 export TransportationResult
+export northwestcorner
+export leastcost
+export isbalanced
+export balance
 
 import ..OperationsResearchModels: solve
 
@@ -151,7 +155,7 @@ function solve(t::TransportationProblem)::TransportationResult
     @constraint(model, sum(x[1:n, j] for j = 1:p) .== newt.supply)
     @constraint(model, sum(x[i, 1:p] for i = 1:n) .== newt.demand)
 
-    initial_solution = northwestcorner(newt).solution 
+    initial_solution = northwestcorner(newt).solution
     JuMP.set_start_value.(x, initial_solution)
 
     optimize!(model)
@@ -198,6 +202,33 @@ function northwestcorner(t::TransportationProblem)::TransportationResult
     return result
 end
 
+function leastcost(t::TransportationProblem)::TransportationResult
+    problem = t
+    if !isbalanced(t)
+        problem = balance(t)
+    end
+    supply = Base.copy(problem.supply)
+    demand = Base.copy(problem.demand)
+    n, m = size(problem.costs)
+    asgnmatrix = zeros(Float64, n, m)
+    cost = 0.0
+    while (sum(supply) > 0) && (sum(demand) > 0)
+        mincost = minimum(problem.costs)
+        mincostrow, mincostcol = argmin(problem.costs).I
+        amount = min(supply[mincostrow], demand[mincostcol])
+        asgnmatrix[mincostrow, mincostcol] = amount
+        supply[mincostrow] -= amount
+        demand[mincostcol] -= amount
+        if supply[mincostrow] == 0
+            problem.costs[mincostrow, :] .= Inf
+        elseif demand[mincostcol] == 0
+            problem.costs[:, mincostcol] .= Inf
+        end
+        cost += amount * mincost
+    end
+    result = TransportationResult(t, problem, asgnmatrix, cost)
+    return result
+end
 
 
 end # end of module  

test/runtests.jl

@@ -3,12 +3,12 @@ using OperationsResearchModels
 using OperationsResearchModels.Simplex
 
 
+include("testtransportation.jl")
 include("testrandomkeyga.jl")
 include("testtravelingsalesman.jl")
 include("testjohnsons.jl")
 include("testutility.jl")
 include("testjump.jl")
-include("testtransportation.jl")
 include("testassignment.jl")
 include("testshortestpath.jl")
 include("testmaximumflow.jl")
@@ -21,3 +21,4 @@ include("testlatex.jl")
 include("testknapsack.jl")
 include("testsimplex.jl")
 
+

test/testtransportation.jl

@@ -77,7 +77,7 @@
         ]
     end
 
-    @testset "Solution - 2" begin 
+    @testset "Solution - 2" begin
         t = TransportationProblem(
             Float64[10 20 25; 12 15 7],
             Float64[190, 40, 20],
@@ -87,7 +87,7 @@
 
         @test result.cost == 2720.0
         @test result.solution == [150.0 0.0 0.0; 40.0 40.0 20.0]
-    end 
+    end
 
     @testset "North-West Corner" begin
         @testset "Example 1" begin
@@ -134,9 +134,49 @@
             @test result.cost == 3510
         end
     end
-    
+
+
+
+
+    @testset "Least Cost Method" begin
+        @testset "Example 1" begin
+            t = TransportationProblem(
+                Float64[1 2 8 10; 7 3 4 5; 12 11 9 6],
+                Float64[50, 60, 30, 130],
+                Float64[90, 110, 70]
+            )
+            result = leastcost(t)
+            expected = Float64[
+                50 40 0 0;
+                0 20 30 60;
+                0 0 0 70
+            ]
+            @test result.solution == expected
+            @test result.cost == 1030
+        end
+
+        @testset "Example 2" begin
+            t = TransportationProblem(
+                Float64[10 2 20 11; 12 7 9 20; 4 14 16 18],
+                Float64[5, 15, 15, 15],
+                Float64[15, 25, 10]
+            )
+            
+            result = leastcost(t)
+            
+            expected = Float64[0 15 0 0; 0 0 15 10; 5 0 0 5]
+            
+            @test result.solution == expected
+            
+            @test result.cost == 475
+        end
+    end
+
+
+
+
     @testset "Big Example - Check if it is solved in reasonable times" verbose = true begin
-        
+
         t = TransportationProblem(
             rand(10:1000, 350, 450) * 1.0,
             rand(1:100, 450) * 1.0,
@@ -145,7 +185,7 @@
 
 
         result = solve(t)
-        
+
         @test result.cost > 0
 
     end