Multi-period price optimization problem for omnichannel retailers accounting for customer heterogeneity

In recent times many brick and mortar retailers have considered adding online channels to compete with e-tailers. These retailers have further enabled omnichannel features into their businesses considering customer's channel switching behavior. This article presents a price optimization problem for such a retailer who already had many offline stores but then added an online channel to improve its digital presence. The retailer has a distribution center that replenishes these stores periodically. Furthermore, the retailer uses either the distribution center or any of the offline stores to fulfill online orders. The paper takes an integrated approach to price optimization, inventory control, and e-fulfillment problem and developed a decision support model for such a retailer having multiple objectives of profit maximization and lost sales minimization. The lost sales minimization is achieved either by decreasing the probability of no-purchase option (by reducing the posted price) or by fulfilling online demands at relatively higher costs (it is not optimal to meet all the demand). The paper tests the efficacy of conventional Non-dominated sorting genetic algorithm-II (NSGA-II) and recently proposed direct Zigzag search in order to solve the resulting NP-hard discrete multi-objective optimization problem. We offer a new algorithm that exploits the neighborhood search feature of the Zigzag method to extend the NSGA-II front further. Furthermore, using realistic and real-world inspired data, we generated some useful insights for omnichannel retailers.