2018/02/15 by S. Rosa, Paulo Rebelo, Rosa, S. +11
Business, Management and Accounting · Mathematics · #34C60 #49M05 #91C99 #Consumer Market Behavior and Pricing #Customer churn and segmentation #FOS: Mathematics #Optimization and Control (math.OC) #Supply Chain and Inventory Management #math.OC #msc:34C60 #msc:49M05 #msc:91C99
paper · pdf · doi:10.48550/arxiv.1802.05489
This is a preprint of a paper whose final and definite form is with Appl. Math. Comput. [https://www.journals.elsevier.com/applied-mathematics-and-computation]
arxiv created 2018/02/15 · openalex publication_date 2018/02/15 · arxiv updated 2018/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider an optimal control problem for a non-autonomous model of ODEs that describes the evolution of the number of customers in some firm. Namely we study the best marketing strategy. Considering a L2 cost functional, we establish the existence and uniqueness of optimal solutions, using an inductive argument to obtain uniqueness on the whole interval from local uniqueness. We also present some simulation results, based on our model, and compare them with results we obtain for an L1 cost functional. For the L1 cost functional the optimal solutions are of bang-bang type and thus easier to implement, because at every moment possible actions are chosen from a finite set of possibilities. For the autonomous case of L2 problem, we show the effectiveness of the optimal control strategy against other formulations of the problem with simpler controls.