This example demonstrates a sequential implementation of a simple Benders decomposition method for a stochastic linear program. More...
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Variables | |
| str | benders_2stage.GAMS_DATA |
| str | benders_2stage.GAMS_MASTER_MODEL |
| str | benders_2stage.GAMS_SUB_MODEL |
| sys | benders_2stage.sys_dir = sys.argv[1] if len(sys.argv) > 1 else None |
| GamsWorkspace | benders_2stage.ws = GamsWorkspace(system_directory=sys_dir) |
| GamsWorkspace | benders_2stage.data = ws.add_job_from_string(GAMS_DATA) |
| GamsWorkspace | benders_2stage.opt_data = ws.add_options() |
| GamsWorkspace | benders_2stage.scenario_data = data.out_db["ScenarioData"] |
| GamsWorkspace | benders_2stage.opt = ws.add_options() |
| int | benders_2stage.max_iter = 40 |
| benders_2stage.all_model_types | |
| GamsWorkspace | benders_2stage.cp_master = ws.add_checkpoint() |
| GamsWorkspace | benders_2stage.cp_sub = ws.add_checkpoint() |
| GamsWorkspace | benders_2stage.master = ws.add_job_from_string(GAMS_MASTER_MODEL) |
| benders_2stage.databases | |
| GamsWorkspace | benders_2stage.mi_master = cp_master.add_modelinstance() |
| GamsWorkspace | benders_2stage.cutconst |
| GamsWorkspace | benders_2stage.cutcoeff |
| GamsWorkspace | benders_2stage.theta |
| GamsWorkspace | benders_2stage.theta_fix = mi_master.sync_db.add_parameter("thetaFix", 0) |
| GamsWorkspace | benders_2stage.sub = ws.add_job_from_string(GAMS_SUB_MODEL) |
| GamsWorkspace | benders_2stage.mi_sub = cp_sub.add_modelinstance() |
| GamsWorkspace | benders_2stage.received = mi_sub.sync_db.add_parameter("received", 1, "units received from master") |
| GamsWorkspace | benders_2stage.demand = mi_sub.sync_db.add_parameter("demand", 1, "stochastic demand") |
| float | benders_2stage.lower_bound = float("-inf") |
| float | benders_2stage.upper_bound = float("inf") |
| float | benders_2stage.obj_master = float("inf") |
| int | benders_2stage.it = 1 |
| benders_2stage.value | |
| float | benders_2stage.obj_sub = 0.0 |
| GamsWorkspace | benders_2stage.probability = scenario_data.find_record((s.key(0), "prob")).value |
Detailed Description
This example demonstrates a sequential implementation of a simple Benders decomposition method for a stochastic linear program.
The underlying model implements a simple distribution system with stochastic demand data. Both the master and the sub problems are implemented with the GamsModelInstance which allows resolving the model with modified input without regenerating the model. A GamsModelInstance has a fixed model rim, so this provides a challenge for Benders master problem because every iteration adds new constraints (the Benders cuts) to the master. We get around this limitation of GamsModelInstance by initializing the GamsModelInstance of the master with a fixed number of empty (i.e. non-binding) placeholder constraints and turn them into valid Benders cuts during the run of the algorithm.
Definition in file benders_2stage.py.