SAMPL

Language Features

SAMPL shares all language features with AMPL, and adds some constructs specifically designed for expressing scenario based stochastic programming and robust optimization.

Stochastic programming features and constructs

To express scenario-based SP problems, additional constructs describe the tree structure and group the decision variable into stages. Moreover, it is possible to specify which parameter stores the probabilities for each branch of the tree and which set represents the scenario set. Other constructs to easily define chance constraints and integrated chance constraint in an SP problem are available as well. Using these language constructs allows to retain the structure of the problem, hence making it available to the solvers, which might exploit it using specialized decomposition methods like Benders' decomposition to speed-up the solution.

Robust optimization constructs

SAMPL supports constructs to describe three types of robust optimization formulations:

Soyster

Bertsimas and Sim

Ben-Tal and Nemirovski

Availability

SAMPL is currently available as a part of the software AMPLDev (distributed by www.optirisk-systems.com). It supports many popular 32- and 64-bit platforms including Windows, Linux and Mac OS X. A free evaluation version with limited functionality is available.

A stochastic programming sample model

The following is the SAMPL version of a simple problem (Dakota), to show the SP related constructs. It does not include the data file, which follows the normal AMPL syntax (see the example provided in the AMPL Wikipedia page for further reference).

set Prod; set Resource; # Scenarios (future possible realizations) scenarioset Scen; # Definition of the problem as a two-stage problem tree Tree := twostage; # Demand for each product in each scenario random param Demand{Prod, Scen}; # Probability of each scenario probability P{Scen}; # Cost of each unit of resource param Cost{Resource}; # Requirement in terms of resources units to produce one unit of each product param ProdReq{Resource,Prod}; # Selling price of each product param Price{Prod}; # Initial budget param Budget; # Amount of resources to buy var buy{r in Resource} >= 0, suffix stage 1; # Amount of each product to produce var amountprod{p in Prod, s in Scen} >= 0, suffix stage 2; # Amount of each product to sell var amountsell{p in Prod, s in Scen} >= 0, suffix stage 2; # Total final wealth, as expected total income from sales minus costs for the resources maximize wealth: sum{s in Scen} P[s] * (sum{p in Prod} Price[p] * amountsell[p,s] - sum{r in Resource} Cost[r] * buy[r]); subject to # Make sure you have enough resources to produce what we intend to balance{r in Resource, s in Scen}: buy[r] >= sum{p in Prod} ProdReq[r,p] * amountprod[p, s]; # Make sure we do not sell what we did not produce production{p in Prod, s in Scen}: amountsell[p,s] <= amountprod[p,s]; # Make sure we do not sell more than the market demand sales{p in Prod, s in Scen}: amountsell[p,s] <= Demand[p,s]; # Respect initial budget budgetres: sum{r in Resource} Cost[r] * buy[r] <= Budget;

Solvers connectivity

SAMPL instance level format for SP problems is SMPS, and therefore the problem can be solved by any solver which supports that standard. One of such solvers (FortSP) is included in the standard SAMPL distribution. Regarding robust optimization problems, the needed solver depend on the specific formulation used, as Ben-Tal and Nemirovski formulation need a second-order cone capable solver.