Dynamic Marketing Model: The Case of Piece-Wise Constant Pricing

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Abstract

We study a stylized vertical distribution channel where a representative manufacturer sells a single kind of good to a representative retailer. The control of the manufacturer is the price discounts, while the control of the retailer is pass-through. In the classical setting, the arising problem is quadratic with respect to wholesale price discount and pass-through. Thus, the optimal sale price is continuous. It seems elegant mathematically but not adequate economically. Therefore we assume that the controls are constant or piece-wise constant. This way, the optimal control problem reduces to the mathematical programming problem where the profit of the manufacturer is quadratic with respect to price discount level(s), while the profit of the retailer is quadratic with respect to pass-through level(s). We study the concavity property of the profits. This allows getting the optimal behavior strategies of the manufacturer and the retailer.

Original languageEnglish
Title of host publicationOptimization and Applications - 10th International Conference, OPTIMA 2019, Revised Selected Papers
EditorsMilojica Jaćimović, Michael Khachay, Vlasta Malkova, Mikhail Posypkin
PublisherSpringer Gabler
Pages150-163
Number of pages14
ISBN (Print)9783030386023
DOIs
Publication statusPublished - 1 Jan 2020
Event10th International Conference on Optimization and Applications, OPTIMA 2019 - Petrovac, Montenegro
Duration: 30 Sep 20194 Oct 2019

Publication series

NameCommunications in Computer and Information Science
Volume1145 CCIS
ISSN (Print)1865-0929
ISSN (Electronic)1865-0937

Conference

Conference10th International Conference on Optimization and Applications, OPTIMA 2019
CountryMontenegro
CityPetrovac
Period30.09.201904.10.2019

Keywords

  • Concavity
  • Piece-wise constant pricing
  • Retailer
  • Sale motivation

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