An application of genetic algorithm in a marketing oriented inventory model with interval valued inventory costs and three-component demand rate dependent on displayed stock level

Abstract

The objective of this research is to investigate an inventory model for a single item with imprecise inventory costs, by considering the impact of marketing strategies such as pricing and advertising on three component demand rate. This rate is dependent on selling price, frequency of advertisement and displayed stock level (DSL) in a show room/shop. Here, the impreciseness of inventory costs like carrying cost, purchase cost, ordering cost and advertisement cost has been represented by interval valued numbers. Analyzing the relative size of the storage capacity of the show room/shop and the stock level dependency parameters of demand, different scenarios with sub scenarios of each have been mentioned. Then, for each sub scenario, the model has been formulated as a constrained optimization problem with interval objective. To solve these problems, an advanced genetic algorithm (GA) for mixed integer non-linear programming has been developed with interval valued fitness function. In this developed GA, the order relations of interval valued numbers have been used with respect to pessimistic decision maker’s point of view. This approach has been used in the ranked based selection process for selecting better chromosomes/individuals for the next generation and also for finding the best chromosomes/individuals in each generation. Finally, the model has been illustrated with some numerical examples and the performance of the GA has been tested by computing appropriate statistical measures and the computing time.