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--- home_test_julia [2017/02/07 09:33]
antonello
+++ home_test_julia [2017/02/07 10:15]
antonello
@@ Line 1: / Line 1: @@
-not in code
+===== Installation =====
-<code julia>
+**Step 1:**
+  * Option a: Get an account on [[https://juliabox.com|JuliaBox.com]] to run julia/JuMP script without installing anything on the local computer
+  * Option b: Install Julia for your platform ([[http://julialang.org/downloads/|http://julialang.org/downloads/]])
+**Step 2:**
-Transposition in JuMP of the basic transport model used in the GAMS tutorial
+Run, only once, the following code to install JuMP language and a couple of open source solvers:
+<code julia>
+Pkg.update()                        # To refresh the list of newest packages
+Pkg.add("JuMP")                     # The mathematical optimisation library
+Pkg.add("GLPKMathProgInterface")    # A lineaqr and MIP solver
+Pkg.add("Ipopt")                    # A non-linear solver
+Pkg.add("DataFrames")               # A library to deal with dataframes (R-like tabular data)
+</code>
-This problem finds a least cost shipping schedule that meets
+===== Model components =====
-requirements at markets and supplies at factories.
-- Original formulation: Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
+==== Importing the libraries ====
-Princeton University Press, Princeton, New Jersey, 1963.
-- Gams implementation: This formulation is described in detail in:
-Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide.
-The Scientific Press, Redwood City, California, 1988.
-- JuMP implementation: Antonello Lobianco
+You will need to import as a minima the ''JuMP'' module. If you wish to specify a solver engine rather than letting JuMP select a suitable one, you will need to import also the module relative to the solver, e.g. ''Ipopt'' or  ''GLPKMathProgInterface''
+<code julia>
+# Import of the JuMP and DataFrames modules (the latter one just to import the data from a header-based table, as in the original trasnport example in GAMS
 using JuMP, DataFrames
+</code>
-# Sets
+==== Defining the "sets" ====
+JuMP doesn't really have a concept of sets, but it uses the native containers available in the core Julia language\\Variables, parameters and constraints can be indexed using these containers.\\
+While many works with position-based lists, I find more readable using dictionaries instead. So the "sets" are represented as lists, but then everything else is a dictionary with the elements of the list as keys.\\
+One note: it seems that Julia/JuMP don't like much the "-" symbol, so I replaced it to "_".\\
+<code julia>
+## Define sets ##
+#  Sets
+#       i   canning plants   / seattle, san-diego /
+#       j   markets          / new-york, chicago, topeka / ;
 plants  = ["seattle","san_diego"]          # canning plants
 markets = ["new_york","chicago","topeka"]  # markets
-# Parameters
-a = Dict(              # capacity of plant i in cases
-  "seattle"   => 350,
-  "san_diego" => 600,
-)
-b = Dict(              # demand at market j in cases
-  "new_york"  => 325,
-  "chicago"   => 300,
-  "topeka"    => 275,
-)
-#  distance in thousands of miles
-d_table = wsv"""
-plants     new_york  chicago  topeka
-seattle    2.5       1.7      1.8
-san_diego  2.5       1.8      1.4
-"""
-d = Dict( (r[:plants],m) => r[Symbol(m)] for r in eachrow(d_table), m in markets)
-f = 90 # freight in dollars per case per thousand miles
-c = Dict() # transport cost in thousands of dollars per case ;
-[ c[p,m] = f * d[p,m] / 1000 for p in plants, m in markets]
-# Model declaration
-trmodel = Model() # transport model
-# Variables
-@variables trmodel begin
-    x[p in plants, m in markets] >= 0 # shipment quantities in cases
-end
-# Constraints
-@constraints trmodel begin
-    supply[p in plants],   # observe supply limit at plant p
-        sum(x[p,m] for m in markets)  <=  a[p]
-    demand[m in markets],  # satisfy demand at market m
-        sum(x[p,m] for p in plants)  >=  b[m]
-end
-# Objective
-@objective trmodel Min begin
-    sum(c[p,m]*x[p,m] for p in plants, m in markets)
-end
-print(trmodel)
-status = solve(trmodel)
-if status == :Optimal
-    println("Objective value: ", getobjectivevalue(trmodel))
-    println("Shipped quantities: ")
-    println(getvalue(x))
-    println("Shadow prices of supply:")
-    [println("$p = $(getdual(supply[p]))") for p in plants]
-    println("Shadow prices of demand:")
-    [println("$m = $(getdual(demand[m]))") for m in markets]
-else
-    println("Model didn't solved")
-    println(status)
-end
-# Expected result:
-# obj= 153.675
-#['seattle','new-york']   = 50
-#['seattle','chicago']    = 300
-#['seattle','topeka']     = 0
-#['san-diego','new-york'] = 275
-#['san-diego','chicago']  = 0
-#['san-diego','topeka']   = 275
 </code>