An application of real-coded genetic algorithm (RCGA) for mixed integer non-linear programming in two-storage multi-item inventory model with discount policy

The purpose of this research work is to solve mixed-integer non-linear programming problem with constraints by a real-coded genetic algorithm (RCGA). This GA is based on Roulette wheel selection, whole arithmetic crossover and non-uniform mutation. Here, mutation is carried out for the fine-tuning capabilities of the system by non-uniform operator whose action depends on the age of the population. This methodology has been applied in solving multiple price break structure and implemented for multi-item deterministic inventory control system having two separate storage facilities (owned and rented warehouse) due to limited capacity of the existing storage (owned warehouse). Also, demand rate is a linear function of selling price, time and non-linearly on the frequency of advertisement. The model is formulated with infinite replenishment and shortages are not allowed. The stocks of rented warehouse (RW) are transported to the owned warehouse (OW) in bulk-release rule. So, the mathematical model becomes a constrained non-linear mixed-integer problem. Our aim is to determine the optimal shipments, lot size of the two warehouses (OW and RW), shipment size and maximum profit by maximizing the profit function. The model is illustrated with numerical example and sensitivity analyses are performed with respect to different parameters.