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in each computer as discussed in Chaprer 3. Thus, only small sized vectors are exchanged in order
to rninimize communication load When the algorithm is executed to the end of the cycle and the
ciifference between the upper bound and the lower bound of the original problem is still larger
than a predetetmined small tolerance. then the algorithm will start another cycle with a new cut
using the CPXaddrows() routine and a new proposal using the CPXaddcols() routine from the
CPLEX Callable Libnry.
Since the size of the whole C codes of WSET and WATPAR are very large. only the core
parts of the codes are presented with detailed explmation in appendix A.
5.2 The Test Problems and Results of the Experiment
In order CO make sure that our dilgoxithm converges to an optimal solution in a finite
number of itentions. we have tested seved rnodels such as the small 'Toy Energy Planning"
model (TEP) enplained in the previous section (Figure 5.1). a North Amencan Energy Planning
modei (NEP) [Fuller. 19921, a Hydro-Electric Power Generaion model (HEPG 1) pirge et ai.,
19991 and a huge Financial Planning mode1 (FP) [Fragniere et al., 1998b1. Because TEP and
NXP are multi-regional energy planning models. they can be natunlly phtioned into re@ons.
HEPGL and FP ye stochastic linear p mmng models. so they can be divided into scenarios.
HEFW is rewrinen with different formulation and data, in the format of a scenario formulation
with the nonuiticipativity constnints as linking constraînts: this is called HEPGî. The NI details
of models except N A3 (whose description is very len-@y and complex) are available in
Appendix B.