Is the system reliability profitable for retailing and consumer service of a dynamical system under cross-price elasticity of demand?

Abstract

Retailing strategy is one of the most crucial factors for industries. A proper retailing strategy can help to enhance consumer service and increase the industry's profit. An improved approach to retailing is suggested in this research to deliver superior customer service while maximizing profits in a dynamic system. The study analyzes a retailing strategy for a demand with cross-price elasticity upon the retail price. A product's cross-price elasticity and the system reliability are critical factors in retailing. Understanding the cross-price elasticity of demand between products helps retailers to make pricing decisions that maximize profits by maintaining demand. Imperfect products are produced due to an imperfect production system. The imperfect ones must be adjusted with some costs to make them perfect for better retailing. The system failure rate is crucial for retailing under cross-price elasticity of demand patterns. Production system reliability, cross-price elasticity of demand, and consumer service are all essential factors that can impact a company's success in the market. The production rate is considered time- and system failure rate-dependent. Contradictory to the literature, a dynamical system is proposed for improved retail management, which is solved using the Euler-Lagrange theory. Finally, one can achieve the expected maximum profit for this retail system with optimum selling prices for different products by reducing the system failure rate. Some numerical illustrations with graphical representations are provided to validate the current study. Numerical examples show that applying cross-price elasticity of demand for more than two identical products provides 35% more profit for the retail industry than a single type of product.