Chance constraints

This problem was taken from King [1] who attributes it to Prékopa and Szántai [2]. It represents a water management problem, whereby a number of reservoirs must be designed in order to control flooding due to random stream inflows.

where I is a set of inflows into the system,

J is a set of reservoirs,

x_j is the capacity of reservoir j,

u_j is an upper bound on the capacity of reservoir j,

c_j is the cost per unit capacity of reservoir j,

x_i is the random inflow from source i,

K is the number of simple constraints used to represent the no-flood condition,

and are incidence matrices for the no-flood condition,

p is the desired probability of confidence that the river system will not be flooded.

Time file

Core file

Stoch file

References

1. A.J. King, “Stochastic programming problems: Examples from the literature”, in: Yu. Ermoliev and R.J-B Wets (eds.), Numerical Techniques for Stochastic Optimization, Springer Verlag, Berlin–New York–London, 1988.

2. A. Prékopa and T. Szántai, “Flood control reservoir system design using stochastic programming”, Mathematical Programming Study 9 (1978) 138–151.