Bilevel Programming for Manufacturers Operating in an Omnichannel Retailing Environment

In this article, we present a joint production, pricing, and inventory control problem that can help manufacturers manage revenue in an omnichannel environment. This article puts forward a multiperiod Stackelberg game between a manufacturer and a retailer, assuming the former to be the leader. The leader-follower game is formulated as a mixed-integer nonlinear bilevel optimization problem wherein both players seek to maximize their respective profits. The article envisions an omnichannel retailing environment where online, offline, direct, and drop-shipping channels coexist. It then investigates how enabling showrooming and webrooming on the drop-shipping channel account can affect the supply-chain profitabilities. The analyses suggest that when the customers are aided with showrooming and webrooming services and are allowed to place drop-shipping orders from retailers' stores, additional profit can be generated in the supply chain. To solve the proposed bilevel optimization problem, we investigate single-level reduction using Karush-Kuhn-Tucker conditions and hierarchical optimization technique based on the simulated annealing and randomized decomposition solver. To assess the efficacy of the solution techniques, a comparative analysis is carried out. Thereafter, with the aid of numerical experiments and sensitivity analyses, this article draws the key managerial insights for manufacturers.