A {0, 1} linear program for fixed-profile load scheduling and demand management in automated irrigation channels

A {0,1} linear program is proposed for scheduling fixed-profile requests to load a dynamical system. The problem involves organizing requested load across time, without modifying the load profile of individual requests, while satisfying constraints on the transient response of the system to change in the load. A time representation of the load is developed and delivery delays, being the differences between requested and scheduled start times, are introduced as the decision variables. Given a linear discrete-time state-space model of the dynamical system and an objective of minimizing a measure of overall delivery delay, the problem is initially formulated as a mixed-integer non-linear program. This is then shown to be equivalent to a more tractable {0,1} linear program. The main ideas are motivated by and applied to the problem of scheduling water off-takes from an automated irrigation channel.