Discounted multi-item inventory model via genetic algorithm with Roulette wheel selection, arithmetic crossover and uniform mutation in constraints bounded domains

Abstract

Genetic Algorithm (GA) with different logic structures for price breaks has been developed and implemented for a multi-item inventory control system of breakable items like the items made of glass, mud, porcelain, etc. with all unit discount (AUD), incremental quantity discount (IQD) and a combination of these discounts. Here, AUD and IQD on purchasing price with two price breaks are allowed. Also, demand and breakability of the items are stock-dependent. Shortages are not allowed. Replenishment is instantaneous. Selling price is a mark-up of the purchasing cost. For storage, warehouse capacity is limited. For the present model, GA has been developed in real code representation using Roulette wheel selection, arithmetic crossover and uniform mutation. This algorithm has been implemented successfully to find the optimum order quantities for the above inventory control system to achieve the maximum possible profit. The algorithm and the inventory model have been illustrated numerically and some sensitivity analyses with respect to breakability and demand are presented.

Keywords:

• inventory
• breakability
• all unit discount
• incremental quantity discount
• genetic algorithm

2000 AMS Subject Classification :

• 90B05

Acknowledgements

Department of Science and Technology, Govt. of India supports this work under the research grant III.5 (70)/2000-ET (PRU).