Scheduling Promotion Vehicles to Boost Profits

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 model is motivated and calibrated using actual data in collaboration with Oracle Retail. We introduce and study a class of models for which the boost effects of promotion vehicles on demand are multiplicative. We show that the general setting of the promotion vehicle scheduling problem is computationally intractable. Nevertheless, we develop approximation algorithms and propose a compact integer programming formulation. In particular, we show how to obtain a (1-e) - approximation using an integer program of polynomial size and derive an efficient polynomial time algorithm under a mild assumption on one of the input parameters. In addition, we investigate analytically and computationally the performance of a greedy procedure. Then, we discuss an interesting extension that includes cross-term effects to capture the cannibalization aspect of using several vehicles simultaneously. Finally, we validate and test our methods on actual data and quantify the impact of our models.