Scheduling Promotion Vehicles to Boost Profits

In addition to setting price discounts, retailers need to decide how to schedule promotion vehicles, such as flyers and TV commercials. Unlike the promotion pricing problem that received great attention from both academics and practitioners, the promotion vehicle scheduling problem was largely overlooked, and our goal is to study this problem both theoretically and in practice. We model the problem of scheduling promotion vehicles to maximize profits as a non-linear bipartite matching-type problem, where promotion vehicles should be assigned to time periods, subject to capacity constraints. Our modeling approach is motivated and calibrated using actual data in collaboration with Oracle Retail, leading us to introduce and study a class of models for which the boost effects of promotion vehicles on demand are multiplicative.From a technical perspective, we prove that the general setting considered is computationally intractable. Nevertheless, we develop approximation algorithms and propose a compact integer programming formulation. In particular, we show how to obtain a ($1-\epsilon$)-approximation using an integer program of polynomial size, and investigate the performance of a greedy procedure, both analytically and computationally. We also discuss an extension that includes cross-term effects to capture the cannibalization aspect of using several vehicles simultaneously. From a practical perspective, we test our methods on actual data through a case study, and quantify the impact of our models. Our tests suggest that a rigorous optimization approach to the promotion vehicle scheduling problem allows the retailer to increase its profit by 2% to 9%