### Abstract

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 language | English |
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Title of host publication | OPERATIONS RESEARCH PROCEEDINGS 2011 |

Editors | D Klatte, HJ Luthi, K Schmedders |

Publisher | Springer |

Pages | 445-450 |

Number of pages | 6 |

ISBN (Print) | 978-3-642-29209-5 |

DOIs | |

Publication status | Published - 2012 |

Event | International Conference on Operations Research (OR) - Zurich Duration: 30 Aug 2011 → 2 Sep 2011 |

### Publication series

Name | Operations Research Proceedings |
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Publisher | SPRINGER-VERLAG BERLIN |

ISSN (Print) | 0721-5924 |

### Conference

Conference | International Conference on Operations Research (OR) |
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Country | Switzerland |

City | Zurich |

Period | 30/08/11 → 2/09/11 |

### Cite this

*OPERATIONS RESEARCH PROCEEDINGS 2011*(pp. 445-450). (Operations Research Proceedings). Springer. https://doi.org/10.1007/978-3-642-29210-1_71

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*OPERATIONS RESEARCH PROCEEDINGS 2011.*Operations Research Proceedings, Springer, pp. 445-450, Zurich, 30/08/11. https://doi.org/10.1007/978-3-642-29210-1_71

**Channel coordination in a HMMS-type supply chain with profit sharing contract.** / Dobos, Imre; Gobsch, Barbara; Pakhomova, Nadezhda; Pishchulov, Grigory; Richter, Knut.

Research output

TY - GEN

T1 - Channel coordination in a HMMS-type supply chain with profit sharing contract

AU - Dobos, Imre

AU - Gobsch, Barbara

AU - Pakhomova, Nadezhda

AU - Pishchulov, Grigory

AU - Richter, Knut

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-642-29210-1_71

DO - 10.1007/978-3-642-29210-1_71

M3 - статья в сборнике материалов конференции

SN - 978-3-642-29209-5

T3 - Operations Research Proceedings

SP - 445

EP - 450

BT - OPERATIONS RESEARCH PROCEEDINGS 2011

A2 - Klatte, D

A2 - Luthi, HJ

A2 - Schmedders, K

PB - Springer

ER -