A genetic algorithm approach on a deterministic inventory model for deteriorating items with shortages

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 algorithm (GA) with Random Stochastic Sampling selection (with replacement), whole arithmetic crossover and mutation has been developed. In the algorithm, mutation is carried out for the fine 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.