Simultaneous-Irrigation Scheduling GA Model with Identical Discharges and Travel Time

Multimachine scheduling problems with earliness/tardiness costs and sequence-dependent setup times are analogous to the simultaneous irrigation scheduling problem with water travel times between outlets in a canal irrigation system where all the farmers are supplied with identical discharges at their requested time, i.e., arranged demand irrigation scheduling. The multimachine scheduling problem with earliness/tardiness costs even without setup consideration is computationally very demanding and optimum solutions are not possible in practical time limits. The addition of the sequence-dependent setup time and the dual goal of minimizing earliness/tardiness and the number of machines makes it even more difficult, complicated, and novel. For practical applications, meta-heuristics such as genetic algorithms, simulated annealing, or tabu search methods need to be used. This study employs the genetic algorithm (GA) model. The model presented here is an improvement over earlier work as it considers travel time in a multimachine or simultaneous irrigation system and resolves the issue of computational time by using an approximate algorithm instead of an exact algorithm. However, no quantitative comparison can be done with earlier models as the current model accommodates travel time; hence, its objective function is numerically different than earlier models. The problem is successfully modeled using GA and its implementation is demonstrated. No comprehensive data set is available that completes the requirements of rigorous testing of the GA model. Therefore, to evaluate the performance of the GA model with travel time, instances were randomly generated from a uniform distribution, for three different values of travel times. The GA model was able to obtain feasible schedules for all the instances tested.