Deterministic equivalent program

CPLEX, a highly advanced commercial MILP solver based on branch-and-bound with cuts and heuristics, and with automatic parameter adaptation is used to address the problem in the form of the large-scale deterministic equivalent program (DEP). After two minutes, the first feasible solution x = 0 with an objective of +29.7 was found. The next feasible solution was found after approximately 90 minutes. The best solution found after eight hours was -17.74. 

It is noteworthy that sampling techniques can be used to approximate the continuous probability functions included in the stochastic program to discrete functions. Another appropriate technique can be the utilization of quadrature rules (Lafnez-Aguirre and Reklaitis 2013). By doing so, an approximate deterministic equivalent program can be obtained for most stochastic programs. 

The deterministic equivalent program of a multistage stochastic optimization can be formulated in a similar manner to the program (A.22). However, special care should be taken to preserve the so called non-anticipativity principle in such cases. 

Wets RJ-B (1989) Stochastic Programming. In Nemhauser G, Rinnooy Kan AHG, Todd MJ (eds) Optimization. North-Holland Publishing Company, Amsterdam et al., pp 573-629 Wets RJ-B (1974) Stochastic Programs with Fixed Recourse The Equivalent Deterministic Program. SIAM Review 16 309-339 Wilkin S (2000) Why Political Risk is Important to You. World Trade 13 40-44... 

Point and range estimates as well as probabilistic models (Monte Carlo simulation) must show complete reproducibility per programming environment, since the underlying algorithms are deterministic. They should show asymptotic equivalence of results over different software environments and simulation techniques. 

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