Channel coordination in a HMMS-type supply chain with profit sharing contract

Imre Dobos, Barbara Gobsch, Nadezhda Pakhomova, Grigory Pishchulov, Knut Richter

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We investigate a supply chain with a single supplier and a single manufacturer. The manufacturer is supposed to know the demand for the final product which is produced from a raw material ordered from the supplier just in time—i.e., the manufacturer holds no raw material inventory. Her costs consist of the linear purchasing cost, quadratic production cost and the final product quadratic holding costs. It is assumed that the market price of the final product is known as well, hence the sales of the manufacturer are known in advance. Her goal is to maximize her cumulated profits. The supplier’s costs are the quadratic manufacturing and inventory holding costs; his goal is to maximize the revenues minus the relevant costs.We will not examine the bargaining process that determines the adequate price and quantity. The situation is modeled as a differential game. The decision variables of the supplier are the sales price and the production quantity, while the manufacturer chooses a production plan that minimizes her costs, so maximizing the cumulated profits. The basic problem is a Holt-Modigliani-Muth-Simon (HMMS) problem extended to linear purchasing costs. We examine two cases: the decentralized Nash-solution and a centralized Pareto-solution to optimize the behavior of the players of the game.
Original languageEnglish
Title of host publicationOperations Research Proceedings 2011
Subtitle of host publicationSelected Papers of the International Conference on Operations Research (OR 2011), August 30 - September 2, 2011, Zurich, Switzerland
EditorsDiethard Klatte, Hans-Jakob Lüthi, Karl Schmedders
PublisherSpringer Nature
Number of pages6
ISBN (Electronic)978-3-642-29210-1
ISBN (Print)978-3-642-29209-5
Publication statusPublished - 2012

Publication series

NameOperations Research Proceedings


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