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 personal:blog:2017:0203_jump_for_gams_users [2017/02/03 14:29]antonello personal:blog:2017:0203_jump_for_gams_users [2018/06/18 15:11] (current) Both sides previous revision Previous revision 2017/02/07 10:26 antonello [Declaration of the model] 2017/02/07 10:24 antonello [Definition of the parameters] 2017/02/07 10:21 antonello [Defining the sets] 2017/02/07 10:20 antonello [Importing the libraries] 2017/02/07 10:20 antonello 2017/02/07 10:12 antonello 2017/02/07 09:05 antonello [Complete script] 2017/02/06 11:09 antonello [Human-readable visualisation of the model (optional)] 2017/02/03 16:44 antonello 2017/02/03 15:32 antonello 2017/02/03 14:45 antonello 2017/02/03 14:29 antonello 2017/02/03 14:09 antonello 2017/02/03 14:03 antonello Next revision Previous revision 2017/02/07 10:26 antonello [Declaration of the model] 2017/02/07 10:24 antonello [Definition of the parameters] 2017/02/07 10:21 antonello [Defining the sets] 2017/02/07 10:20 antonello [Importing the libraries] 2017/02/07 10:20 antonello 2017/02/07 10:12 antonello 2017/02/07 09:05 antonello [Complete script] 2017/02/06 11:09 antonello [Human-readable visualisation of the model (optional)] 2017/02/03 16:44 antonello 2017/02/03 15:32 antonello 2017/02/03 14:45 antonello 2017/02/03 14:29 antonello 2017/02/03 14:09 antonello 2017/02/03 14:03 antonello Line 35: Line 35: Pkg.add("​GLPKMathProgInterface"​) ​   # A lineaqr and MIP solver Pkg.add("​GLPKMathProgInterface"​) ​   # A lineaqr and MIP solver Pkg.add("​Ipopt"​) ​                   # A non-linear solver Pkg.add("​Ipopt"​) ​                   # A non-linear solver - Pkg.add("​DataFrames"​) ​              # A library to deal with dataframes (R-like tabular data) + Pkg.add("​DataFrames"​) ​              # A library to deal with dataframes (R like tabular data) ​ Line 44: Line 44: 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''​ 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 + # 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 using JuMP, DataFrames - <​code>​ + ==== Defining the "​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.\\ 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.\\ 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.\\ Line 55: Line 56: - # Sets + # Define sets # + #  ​Sets + #       ​i ​  ​canning plants ​  / seattle, san-diego / + #       ​j ​  ​markets ​         / new-york, chicago, topeka / ; plants ​ = ["​seattle","​san_diego"​] ​         # canning plants plants ​ = ["​seattle","​san_diego"​] ​         # canning plants markets = ["​new_york","​chicago","​topeka"​] ​ # markets markets = ["​new_york","​chicago","​topeka"​] ​ # markets Line 61: Line 65: - ==== Defining ​the "​parameters"​ ==== + ==== Definition of the "​parameters"​ ==== - Capacity of plants and demand of markets are directly defined as dictionaries,​ while the distance is first read from a white-space separated table and then it is converted in a "​(plant,​ market) => value" dictionary. + + Capacity of plants and demand of markets are directly defined as dictionaries,​ while the distance is first read as a DataFrame ​from a white-space separated table and then it is converted in a "​(plant,​ market) => value" dictionary. - # Parameters + # Define parameters # + #   Parameters + #       ​a(i) ​ capacity of plant i in cases + #         / ​   seattle ​    350 + #              san-diego ​  ​600 ​ / a = Dict(              # capacity of plant i in cases a = Dict(              # capacity of plant i in cases "​seattle" ​  => 350, "​seattle" ​  => 350, "​san_diego"​ => 600, "​san_diego"​ => 600, ) ) + + #       ​b(j) ​ demand at market j in cases + #         / ​   new-york ​   325 + #              chicago ​    300 + #              topeka ​     275  / ; b = Dict(              # demand at market j in cases b = Dict(              # demand at market j in cases "​new_york" ​ => 325, "​new_york" ​ => 325, Line 76: Line 90: ) ) - #  distance in thousands of miles + # Table d(i,​j) ​ ​distance in thousands of miles + #                    new-york ​      ​chicago ​     topeka + #      seattle ​         2.5           ​1.7 ​         1.8 + #      san-diego ​       2.5           ​1.8 ​         1.4  ; d_table = wsv"""​ d_table = wsv"""​ plants ​    ​new_york ​ chicago ​ topeka plants ​    ​new_york ​ chicago ​ topeka Line 83: Line 100: """​ """​ d = Dict( (r[:​plants],​m) => r[Symbol(m)] for r in eachrow(d_table),​ m in markets) d = Dict( (r[:​plants],​m) => r[Symbol(m)] for r in eachrow(d_table),​ m in markets) + # Here we are converting the table in a "​(plant,​ market) => distance"​ dictionary # r[:​plants]: ​  the first key, row field using a fixed header # r[:​plants]: ​  the first key, row field using a fixed header # m:            the second key # m:            the second key # r[Symbol(m)]:​ the value, the row field with a dynamic header # r[Symbol(m)]:​ the value, the row field with a dynamic header + # Scalar f  freight in dollars per case per thousand miles  /90/ ; f = 90 # freight in dollars per case per thousand miles f = 90 # freight in dollars per case per thousand miles + # Parameter c(i,​j) ​ transport cost in thousands of dollars per case ; + #            c(i,j) = f * d(i,j) / 1000 ; # We first declare an empty dictionary and then we fill it with the values # We first declare an empty dictionary and then we fill it with the values c = Dict() # transport cost in thousands of dollars per case ; 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] ​ [ c[p,m] = f * d[p,m] / 1000 for p in plants, m in markets] ​ ​ + The above code take advantage of [[http://​docs.julialang.org/​en/​stable/​manual/​arrays/#​comprehensions|List Comprehensions]],​ a powerful feature of the Julia language that provides a concise way to loop over a list. + If we take the creation of the d dictionary as example, without List Comprehensions we would have had to write a nested for loop like: + + d = Dict() + for r in eachrow(d_table) + for m in markets + d = (r[:​plants],​m) => r[Symbol(m)] + end + end + ​ + Using List Comprehension is however quicker to code and more readable. - # Model declaration + ==== Declaration of the model ==== - trmodel ​= Model() # transport ​model + - # Variables + Here we declare a JuML optimisation model and we give it a name. This name will be then passed as first argument to all the subsequent operations, like creation of variables, constraints and objective function.\\ + We can, if we wish, works with several models at the same time.\\ + If we do not specify a solver, we let JuML use a suitable solver for the type of problem. Aside to specify the solver, we can also pass it solver-level options, e.g.: + ''​mymodel = Model(solver=IpoptSolver(print_level=0))''​ + + + # Model declaration (transport model) + trmodel = Model() + + ​ + + ==== Declaration of the model variables ==== + + Variables ​can have multiple-dimensions - that is, being indexed under several indexes -, and bounds are given at the same time as their declaration.\\ + Differently from GAMS, we don't need to define the variable that is on the left hand side of the objective function. + + + ## Define variables ## + #  Variables + #       ​x(i,​j) ​ shipment quantities in cases + #       ​z ​      total transportation costs in thousands of dollars ; + #  Positive Variable x ; @variables trmodel begin @variables trmodel begin x[p in plants, m in markets] >= 0 # shipment quantities in cases x[p in plants, m in markets] >= 0 # shipment quantities in cases end end + ​ - # Constraints + ==== Declaration of the model constraints ==== + + As in GAMS, each constraint can actually be a "​family"​ of constraints:​ + + + ## Define contrains ## + # supply(i) ​  ​observe supply limit at plant i + # supply(i) .. sum (j, x(i,j)) =l= a(i) + # demand(j) ​  ​satisfy demand at market j ; + # demand(j) .. sum(i, x(i,j)) =g= b(j); @constraints trmodel begin @constraints trmodel begin supply[p in plants], ​  # observe supply limit at plant p supply[p in plants], ​  # observe supply limit at plant p Line 110: Line 172: sum(x[p,m] for p in plants) ​ >=  b[m] sum(x[p,m] for p in plants) ​ >=  b[m] end end + ​ + ==== Declaration of the model objective ==== + + Contrary to constraints and variables, the objective is always a unique function. Note that it is at this point that we specify the direction of the optimisation. ​ + + # Objective # Objective @objective trmodel Min begin @objective trmodel Min begin sum(c[p,​m]*x[p,​m] for p in plants, m in markets) sum(c[p,​m]*x[p,​m] for p in plants, m in markets) end end + ​ + ==== Human-readable visualisation of the model (optional) ==== + + If we wish we can get the optimisation model printed in a human-readable fashion, so we can expect all is like it should be + + print(trmodel) print(trmodel) + ​ + ==== Resolution of the model ==== + + It is at this point that the solver is called and the model is passed to the solver engine for its solution. The return value is the status of the optimisation (":​Optimal"​ if all went fine) + + status = solve(trmodel) status = solve(trmodel) + ​ + ==== Visualisation of the results ==== + While you can do any fancy output you may wish after you retrieve the optimal value of the variables with ''​getvalue(var_name)'',​ you can just ''​println(getvalue(x))''​ to get a basic output.\\ + Notice that you can also easily retrieve the dual value associated to the constraint with ''​getdual(constraint_name)''​. + + if status == :Optimal if status == :Optimal println("​Objective value: ", getobjectivevalue(trmodel)) println("​Objective value: ", getobjectivevalue(trmodel)) println(getvalue(x)) 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 else println("​Model didn't solved"​) println("​Model didn't solved"​) Line 129: Line 219: ​ - ==== Set definition ==== - Sets are created as attributes object of the main model objects and all the information is given as parameter in the constructor function. Specifically,​ we are passing to the constructor the initial elements of the set and a documentation string to keep track on what our set represents: - - ## Define sets ## - #  Sets - #       ​i ​  ​canning plants ​  / seattle, san-diego / - #       ​j ​  ​markets ​         / new-york, chicago, topeka / ; - model.i = Set(initialize=['​seattle','​san-diego'​],​ doc='​Canning plans'​) - model.j = Set(initialize=['​new-york','​chicago',​ '​topeka'​],​ doc='​Markets'​) - ​ - ==== Parameters ​==== + ==== Editing and running the script ​==== - Parameter objects are created specifying the sets over which they are defined and are initialised with either a python dictionary or a scalar: + Differently from GAMS you can use whatever editor environment you wish to code a JuMP script. If you don't need debugging features, ​a simple text editor like Notepad++ ​(in windows), gedit or kate (in Linux) will suffice. They already have syntax highlight for Julia.\\ - ​ + If you want advanced features and debugging capabilities you can use a dedicated Julia IDE, like e.g. [[http://junolab.org/|Juno]]. - ## Define parameters ## + - #   ​Parameters + - #       a(i)  capacity of plant i in cases + - #         / ​   seattle ​    350 + - #              san-diego ​  ​600 ​ / + - #       ​b(j) ​ demand at market j in cases + - #         / ​   new-york ​   325 + - #              chicago ​    300 + - #              topeka ​     275  / ; + - model.a = Param(model.i, initialize={'​seattle':​350,'​san-diego':​600},​ doc='​Capacity of plant i in cases') + - model.b = Param(model.j, initialize={'​new-york':​325,'​chicago':​300,'​topeka':​275},​ doc='​Demand at market j in cases'​) + - #  Table d(i,j)  distance ​in thousands of miles + - #                    new-york ​      ​chicago ​     topeka + - #      seattle ​         2.5           ​1.7 ​         1.8 + - #      san-diego ​       2.5           ​1.8 ​         1.4  ; + - dtab = { + - ('​seattle', ​ '​new-york'​) : 2.5, + - ('​seattle', ​ '​chicago'​) ​ : 1.7, + - ​('​seattle'​,  '​topeka'​) ​  : 1.8, + - ('​san-diego','​new-york'​) : 2.5, + - ('​san-diego','​chicago'​)  ​: 1.8, + - ('​san-diego','​topeka'​) ​  : 1.4, + - } + - model.d = Param(model.i,​ model.j, initialize=dtab,​ doc='​Distance in thousands of miles'​) + - #  Scalar f  freight in dollars per case per thousand miles  ​/90/ ; + - model.f = Param(initialize=90,​ doc='​Freight in dollars per case per thousand miles'​) + - + - A third, powerful way to initialize a parameter is using a user-defined function.\\ + - This function will be automatically called by pyomo with any possible (i,j) set. In this case pyomo will actually call c_init() six times in order to initialize the model.c parameter. + - ​ + - #  Parameter c(i,​j) ​ transport cost in thousands of dollars per case ; + - #            c(i,j) = f * d(i,j) / 1000 ; + - def c_init(model,​ i, j): + - return model.f * model.d[i,j] / 1000 + - model.c = Param(model.i,​ model.j, initialize=c_init,​ doc='​Transport cost in thousands of dollar per case'​) + - ​ + - ==== Variables ==== + If you are using instead the Julia console,  ​you ​can run the script as ''julia transport.jl''​. - Similar to parameters, variables are created specifying their domain(s). For variables we can also specify ​the upper/lower bounds in the constructor.\\ + - Differently from GAMS, we don't need to define the variable that is on the left hand side of the objective function. + - ​ + - ## Define variables ## + - #  Variables + - #       ​x(i,​j) ​ shipment quantities in cases + - #       ​z ​      total transportation costs in thousands of dollars ; + - #  Positive Variable x ; + - model.x = Var(model.i,​ model.j, bounds=(0.0,​None),​ doc='Shipment quantities in case') + - ​ + - ==== Constrains ​==== + ===== Further help ===== - At this point, it should not be a surprise that constrains are again defined as model objects with the required information passed as parameter in the constructor function. ​ + Documentation ​of JuMP is available from [[https://jump.readthedocs.io/en/latest/|this page]]. However if you want to do serious things with juMP, it is most likely that you will have to either look at the source ​code or consult the [[https://discourse.julialang.org/​c/​domain/​opt|discussion forum]]. - ​ + - ## Define contrains ## + - # supply(i) ​  ​observe supply limit at plant i + - # supply(i) .. sum (j, x(i,​j)) ​=l= a(i) + - def supply_rule(model,​ i): + - return sum(model.x[i,​j] for j in model.j) <= model.a[i] + - model.supply = Constraint(model.i,​ rule=supply_rule,​ doc='​Observe supply limit at plant i') + - # demand(j) ​  ​satisfy demand at market j ; + - # demand(j) .. sum(i, x(i,j)) =g= b(j); + - def demand_rule(model,​ j): + - return sum(model.x[i,​j] for i in model.i) >= model.b[j] ​ + - model.demand = Constraint(model.j,​ rule=demand_rule,​ doc='​Satisfy demand at market j') + - ​ + - The above code take advantage ​of [[https://docs.python.org/2/tutorial/datastructures.html#​list-comprehensions|List Comprehensions]], a powerful feature of the python language that provides a concise way to loop over a list. + - If we take the supply_rule as example, this is actually called two times by pyomo (once for each of the elements of i). Without List Comprehensions we would have had to write our function using a for loop, like: + - ​ + - def supply_rule(model,​ i): + - supply = 0.0 + - for j in model.j: + - supply += model.x[i,j] + - return supply <= model.a[i] + - ​ + - Using List Comprehension is however quicker to code and more readable. + - ==== Objective & solving ==== + Happy modelling with JuMP ;-) - The definition of the objective is similar to those of the constrains, except that most solvers require a scalar objective function, hence a unique function, and we can specify the sense (direction) of the optimisation. + - ​ + - ## Define Objective and solve ## + - #  cost        define objective function + - #  cost ..        z  =e=  sum((i,j), c(i,​j)*x(i,​j)) ​; + - #  Model transport /all/ ; + - #  Solve transport using lp minimizing z ; + - def objective_rule(model):​ + - return sum(model.c[i,​j]*model.x[i,​j] for i in model.i for j in model.j) + - model.objective = Objective(rule=objective_rule,​ sense=minimize,​ doc='​Define objective function'​) + - ​ + - As we are here looping over two distinct sets, we can see how List Comprehension really simplifies the code. The objective function could have being written without List Comprehension as: + - ​ + - def objective_rule(model): + - obj = 0.0 + - for ki in model.i: + - for kj in model.j: + - obj += model.c[ki,​kj]*model.x[ki,​kj] + - return obj + - ​ + - ==== Retrieving the output ​==== + ===== Complete script ​===== - To retrieve the output and do something with it (either to just display it -like we do here-, to plot a graph with [[http://​matplotlib.org|matplotlib]] or to save it in a csv file) we use the ''​pyomo_postprocess()''​ function.\\ + - This function is called by pyomo after the solver has finished. + - ​ + - ## Display of the output ## + - # Display x.l, x.m ; + - def pyomo_postprocess(options=None, instance=None, results=None):​ + - model.x.display() + - ​ + - We can print model structure information with ''​model.pprint()''​ ("​pprint"​ stand for "​pretty print"​).\\ + - Results are also by default saved in a results.json file or, if PyYAML is installed in the system, in results.yml. + - ==== Editing and running ​the script ​==== + Here is the complete ​script: ​ - Differently from GAMS you can use whatever editor environment you wish to code a pyomo script. If you don't need debugging features, a simple text editor like Notepad++ (in windows), gedit or kate (in Linux) will suffice. They already have syntax highlight for python.\\ + - If you want advanced features and debugging capabilities you can use a dedicated Python IDE, like e.g. [[https://​code.google.com/​p/​spyderlib/​|Spyder]]. + - You will normally run the script as ''​pyomo solve --solver=glpk transport.py''​. You can output solver specific output adding the option ''​--stream-output''​.\\ + - If you want to run the script as ''​python ​transport.py''​ add the following lines at the end:\\ + # Transposition in JuMP of the basic transport ​model used in the GAMS tutorial - + # - # This is an optional code path that allows the script to be run outside of + # This problem finds a least cost shipping schedule ​that meets - # pyomo command-line.  For example: ​ python transport.py + # requirements at markets and supplies at factories. - if __name__ == '​__main__':​ + # - #This replicates what the pyomo command-line tools does + # - Original formulation:​ Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. - from pyomo.opt import SolverFactory + # Princeton University Press, Princeton, New Jersey, 1963. - import pyomo.environ + # - Gams implementation:​ This formulation is described in detail in: - opt = SolverFactory("​glpk"​) + # Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. - instance = model.create() + # The Scientific Press, Redwood City, California, 1988. - ​results = opt.solve(instance) + # - JuMP implementation:​ Antonello Lobianco - #sends results to stdout + - ​results.write() + - ​pyomo_postprocess(None, instance, results) + - ​ + - Finally, if you are very lazy and want to run the script with just ./​transport.py (and you are in Linux) add the following lines at the top: + using JuMP, DataFrames - ​ + - #​!/​usr/​bin/​env python + - # -*- coding: utf-8 -*- + - ​ + - ===== Further help ===== + # Sets - Documentation of pyomo is available from [[https://​software.sandia.gov/​trac/​coopr/​wiki/​Documentation|this page]]. However if you want to do serious things with pyomo, it is most likely that you will have to either look at the source code or consult the [[https://​groups.google.com/​forum/​#!forum/​coopr-forum|mailing list]]. + plants  ​= ["​seattle","​san_diego"​] ​         # canning plants + markets ​= ["​new_york","​chicago","​topeka"​]  # markets - Happy modelling with pyomo ;-) + # Parameters - ===== Complete script ===== + 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, + ) - Here is the complete script: ​ + #  distance in thousands of miles - + d_table = wsv"""​ - + plants ​    ​new_york ​ chicago ​ topeka - #​!/​usr/​bin/​env python + seattle ​   2.5       ​1.7 ​     1.8 - # -*- coding: utf-8 -*- + san_diego ​ 2.5       1.8      1.4 - + """​ """​ - Basic example of transport model from GAMS model library translated to Pyomo + d = Dict( (r[:plants],m) => r[Symbol(m)] for r in eachrow(d_table), m in markets) - + - To run this you need pyomo and a linear solver installed. + - When these dependencies are installed you can solve this example in one of + - this ways (glpk is the default solver): + - + - ./​transport.py ​(Linux only) + - python transport.py + - pyomo solve transport.py + - pyomo solve --solver=glpk transport.py + - + - To display the results: + - + - cat results.json + - cat results.yml (if PyYAML is installed on your system) + - + - GAMS equivalent code is inserted as single-dash comments. The original GAMS code + - needs slighly different ordering of the commands and it's available at + - http://​www.gams.com/​mccarl/​trnsport.gms + - + - Original problem formulation:​ + - Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. + - Princeton University Press, Princeton, New Jersey, 1963. + - GAMS implementation:​ + - Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. + - The Scientific Press, Redwood City, California, 1988. + - Pyomo translation:​ + - Antonello Lobianco + - + - This file is in the Public Domain + - """​ + - + - # Import + - from pyomo.environ import * + - + - # Creation of a Concrete Model + - model = ConcreteModel() + - + - ## Define sets ## + - #  Sets + - #       ​i ​  ​canning ​plants ​  / seattle, san-diego / + - #       ​j ​  ​markets ​         / new-york, chicago, topeka / ; + - model.i = Set(initialize=['​seattle','​san-diego'​], doc='​Canning plans') + - model.j = Set(initialize=['​new-york','​chicago',​ '​topeka'​],​ doc='​Markets'​) + - + - ## Define parameters ## + - #   ​Parameters + - #       a(i)  ​capacity of plant i in cases + - #         / ​   seattle ​    350 + - #              san-diego ​  ​600 ​ / + - #       ​b(j) ​ demand at market j in cases + - #         / ​   new-york ​   325 + - #              chicago ​    300 + - #              topeka ​     275  / ; + - model.a = Param(model.i,​ initialize={'​seattle':​350,'​san-diego':​600},​ doc='​Capacity of plant i in cases'​) + - model.b = Param(model.j,​ initialize={'​new-york':​325,'​chicago':​300,'​topeka':​275},​ doc='​Demand at market j in cases'​) + - #  Table d(i,​j) ​ distance in thousands of miles + - #                    new-york ​      ​chicago ​     topeka + - #      seattle ​         2.5           ​1.7 ​         1.8 + - #      san-diego ​       2.5           ​1.8 ​         1.4  ; + - dtab = { + - ('​seattle', ​ '​new-york'​) : 2.5, + - ('​seattle', ​ '​chicago'​) ​ : 1.7, + - ('​seattle', ​ '​topeka'​) ​  : 1.8, + - ('​san-diego','​new-york'​) : 2.5, + - ('​san-diego','​chicago'​) ​ : 1.8, + - ('​san-diego','​topeka'​) ​  : 1.4, + - } + - model.d = Param(model.i,​ model.j, initialize=dtab,​ doc='​Distance in thousands of miles'​) + - #  Scalar f  freight in dollars per case per thousand miles  /90/ ; + - model.f = Param(initialize=90,​ doc='​Freight in dollars per case per thousand miles'​) + - #  Parameter c(i,​j) ​ transport cost in thousands of dollars per case ; + - #            c(i,j) = f * d(i,j) / 1000 ; + - def c_init(model,​ i, j): + - return model.f * model.d[i,​j] / 1000 + - model.c = Param(model.i,​ model.j, initialize=c_init,​ doc='​Transport cost in thousands of dollar per case'​) + - + - ## Define variables ## + - #  Variables + - #       ​x(i,​j) ​ shipment quantities in cases + - #       ​z ​      total transportation costs in thousands of dollars ; + - #  Positive Variable x ; + - model.x = Var(model.i,​ model.j, bounds=(0.0,​None),​ doc='​Shipment quantities in case'​) + - + - ## Define contrains ## + - # supply(i) ​  ​observe supply limit at plant i + - # supply(i) .. sum (j, x(i,j)) =l= a(i) + - def supply_rule(model,​ i): + - return sum(model.x[i,​j] for j in model.j) <= model.a[i] + - model.supply = Constraint(model.i, rule=supply_rule,​ doc='​Observe supply limit at plant i') + - # demand(j) ​  ​satisfy demand at market j ; + - # demand(j) .. sum(i, x(i,j)) =g= b(j); + - def demand_rule(model,​ j): + - return sum(model.x[i,​j] for i in model.i) >= model.b[j] ​ + - model.demand = Constraint(model.j,​ rule=demand_rule,​ doc='​Satisfy demand at market j') + - ## Define Objective and solve ## + f = 90 # freight ​in dollars per case per thousand miles - #  cost        define objective function + - #  cost ..        z  ​=e=  sum((i,j), c(i,​j)*x(i,​j)) ; + - #  Model transport /all/ ; + - #  Solve transport using lp minimizing z ; + - def objective_rule(model):​ + - return sum(model.c[i,​j]*model.x[i,​j] for i in model.i for j in model.j) + - model.objective = Objective(rule=objective_rule,​ sense=minimize,​ doc='​Define objective function'​) + - + c = Dict() ​# transport cost in thousands ​of dollars per case ; - ## Display ​of the output ​## + [ c[p,m] = f * d[p,m] / 1000 for p in plants, m in markets] - # Display ​x.l, x.m ; + - def pyomo_postprocess(options=None, instance=None, results=None):​ + # Model declaration - ​model.x.display() + trmodel = Model() ​# transport model - + - # This is an optional code path that allows the script to be run outside of + # Variables - # pyomo command-line. ​ For example: ​ python transport.py + @variables trmodel begin - if __name__ ​== '​__main__'​: + ​x[p in plants, m in markets] >= 0 # shipment quantities in cases - + end - ​#This replicates what the pyomo command-line tools does + - ​from pyomo.opt import SolverFactory + # Constraints - ​import pyomo.environ + @constraints trmodel begin - ​opt = SolverFactory("glpk") + supply[p in plants], ​  # observe supply limit at plant p - ​instance ​= model.create() + sum(x[p,m] for m in markets) ​ <=  ​a[p] - ​results = opt.solve(instance) + demand[m in markets],  # satisfy demand at market m - ​#sends results to stdout + ​sum(x[p,​m] for p in plants) ​ >=  b[m] - ​results.write() + end - ​pyomo_postprocess(None, instance, results) + + # 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: # Expected result: Line 426: Line 326: #​['​san-diego','​topeka'​] ​  = 275 #​['​san-diego','​topeka'​] ​  = 275 ​ - - - - ~~DISCUSSION~~ - - - ~~DISCUSSION~~ ~~DISCUSSION~~
personal/blog/2017/0203_jump_for_gams_users.1486128594.txt.gz · Last modified: 2018/06/18 15:10 (external edit)