Procurement, Dynamic Pricing, and Early Exit Decisions for Products with Short Life Cycles

• Published in: Methodology and computing in applied probability Vol. 27; no. 3; p. 65
• Main Authors: Ertekin, Elifnas, Frenk, J. B. G., Pehlivan, Canan, Sleptchenko, Andrei
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2025; Springer Nature B.V
• Subjects: Algorithms; Business and Management; Continuous time systems; Costs; Decisions; Dynamic programming; Economics; Electrical Engineering; Life Sciences; Market exit; Mathematics and Statistics; Numerical analysis; Optimization; Order quantity; Pricing; Pricing policies; Procurement; Profits; Statistics; Variables; 60G55; Non-homogeneous poisson processes; Optimal pricing policy; 90C39; 60J28; 90B05; Dynamic programming; Inventory
• DOI: 10.1007/s11009-025-10180-8
• ISSN: 1387-5841

We revisit the finite-horizon profit maximization problem of a supplier selling a product with a short life cycle. Earlier literature on this problem generally assumes that the pricing policy and the initial procurement decision are the main tools to boost revenues. A small number of recent papers bring a third one into the picture: the early exit possibility/time from the market. In the current paper, we study a continuous-time model with Poisson arrivals, which incorporates all three decisions together. To the best of our knowledge, this is the first paper to include all these decisions in a model for a short-life-cycle product. Except for the initial procurement, we assume that pricing and exit decisions are taken dynamically. We give a rigorous treatment of the model, study its dynamic programming equations, and provide a numerical algorithm. We illustrate our algorithm with various examples. In our numerical experiments, we also consider three subproblems to see the marginal contributions of these decisions to the supplier’s profits. In each subproblem, we remove one of the decisions from the optimization framework and simply replace it with a simple rule of thumb. In our experiments, we observe that pricing and the initial-order quantity are the decisions that affect the profits the most.