Incorporating Promotional Effects in Sales Planning of the Retail Industry Using Geometric Programming

This paper addresses the challenge faced by managers in the fast-moving consumer goods industry: the joint optimization of promotion prices and the scheduling of promotion vehicles for multiple items to boost total profit. We first propose a general multiplicative demand function that encompasses all crossperiod effects, crossitem effects, promotion vehicle effects, and crossterm effects of promotion vehicles. Then, we formulate the problem of planning sales promotions, simultaneously using price reductions and promotion vehicles, considering several business rules as constraints. To efficiently solve this mixed-integer nonlinear program, we reformulate it as a convex optimization form by using the demand function’s multiplicative structure and the concept of geometric programming. Furthermore, to reduce the running time of the large-scale instances, we develop a Lagrangian decomposition algorithm, dividing the original model into a geometric program and an integer program. The algorithm significantly improves computational efficiency as evidenced by a reduction in running time from 8,125 to 78 seconds for large-scale instances. Finally, utilizing real sales data from a meal delivery company, we demonstrate that applying the convex promotion optimization model allows the company to increase its profits by roughly 21% compared with scenarios where neither price reductions nor promotion vehicles are utilized.