Order and exit decisions under non-increasing price curves for products with short life cycles

J. B. G. Frenk (), Canan Pehlivan () and Semih O. Sezer ()
Additional contact information
J. B. G. Frenk: Sabancı University
Canan Pehlivan: Yeditepe University
Semih O. Sezer: Sabancı University

Mathematical Methods of Operations Research, 2019, vol. 90, issue 3, No 3, 365-397

Abstract: Abstract We consider a supplier selling a product with a relatively short life cycle and following a non-increasing price curve. Because of the short cycle, there is a single procurement opportunity at the beginning of the cycle. The objective of the supplier is to determine the initial order quantity and the time to remove the product from the market in order to maximize her profits. We study this problem in a continuous-time framework where the demand is modeled with a non-homogeneous Poisson process having a general intensity function and the pricing strategy is given by an arbitrary non-increasing function. We give a rigorous mathematical analysis for the problem and show how it can be solved in two stages. We also consider the special case with piecewise constant intensity and price functions. For this case, we show that the optimal exit time is included in the set of break points of these functions. This brings a fast method to obtain the optimal solution for this special case.

Keywords: Martingales; Poisson processes; Inventory control; Price discrimination; Primary 60J27; 60J28; Secondary 90B05 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00186-019-00682-w

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