Optimal pricing and lot-sizing policies under promotional expense for some Veblen products

The desire for social status motivates people to possess rare and exclusive luxury products. People like to consume expensive product and service in order to associate themselves with the elite class and build a distinct image of self in society. The demand of luxury products increases with the increase in the price. This phenomenon is also known as Veblen effect, and products with such characteristics are called Veblen products. The demand for products, in general, is positively influenced by promotional expenses. Research suggests that the promotional effort may provide an opportunity to charge more of selling price without sacrificing the demand. With this aspect, the paper focuses on determining the optimal sales price, lot-size as well as promotional expenses for Veblen products. The promotional expense for the two different markets; niche as well as the mass market has been considered. A mathematical model has been proposed for obtaining the optimal price, lot-size and promotional expenses for such product. Some illustrative numerical examples have been taken for both the markets and solved with the help of LINGO optimization software. The sensitivity analysis was also carried out and observed that ordering cost and holding cost rate has almost no impact on optimal inventory policy, but the unit cost has. The proposed formulation of the considered problem is a non-linear integer programming mathematical model and is thus NP-hard. Therefore, genetic algorithm and teaching–learning-based optimization (TLBO) based heuristics have been proposed for solving the problem in a computationally efficient manner. However, these methods were found to take more CPU time compared to LINGO optimization software. TLBO takes the highest CPU time but is rendering solutions like the ones from LINGO.