The purpose of this research is to determine an optimal solution of a deterministic inventory model of single deteriorating items with a constant rate of deterioration. In this model, the demand rate is a ramp type function of time. Shortages are allowed and partially backlogged. During the shortage period, the backlogging rate is a variable which depends on the length of the waiting time over the replenishment period. The mathematical formulation of the problem indicates that the model is a non-linear constrained optimization problem. Considering the complexity of solving such a model (for getting global optima, not local optima, as it is a decision making problem.), a real-coded genetic algorithms (GAs) with Random Stochastic Sampling selection {with replacement), whole arithmetic crossover and mutation has been developed. In the algorithm, mutation is c;uTied out for the tine tuning capabilities of the system by non-uniform operators whose action depends on the age of the population. The proposed model has been solved using this real-coded GA as well as Generalised Reduced Gradient (GRG) Method. Finally, the results are illustrated with the help of a numerical example and sensitivity analysis of the optimal solution with respect to the different parameters of the system is carried out.