### Abstract

An economic model is developed for exploring optimal internal pricing and capacity planning for service facility with finite buffer capacity. Because of the limited buffer capacity, jobs finding the system full upon their arrival would be rejected. Such rejections create a gap between the value collectively perceived by users and the actual achievement of the organizational value. This gap, called a loss externality, has never been studied before and plays an important role for designing optimal pricing scheme. In general, the underlying economic structure may involve multiple equilibria and it is unclear whether or not the system can be controlled through internal pricing. In this regard, a sufficient condition is given under which the system administrator can find two separate prices for accepted and rejected users at any demand level to be desired so that the desired demand level becomes the unique equilibrium of the system. For a short-run problem, it is shown that the optimal pricing scheme can be expressed as the sum of the congestion and the loss externalities. For a long-run problem, the optimal pricing scheme is expressed in a unified manner so that a structural relationship between the short-run problem and the long-run problem at optimality can be readily observed. A necessary and sufficient condition is also given for the marginal capacity pricing to be optimal, i.e., the optimal long-run pricing consists of the marginal cost for processing capacity and the marginal cost for buffer capacity without involving any externality at all.

Original language | English |
---|---|

Pages (from-to) | 192-205 |

Number of pages | 14 |

Journal | European Journal of Operational Research |

Volume | 128 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

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### ASJC Scopus subject areas

- Information Systems and Management
- Management Science and Operations Research
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Modelling and Simulation
- Transportation

### Cite this

*European Journal of Operational Research*,

*128*(1), 192-205. https://doi.org/10.1016/S0377-2217(99)00355-0

**Optimal internal pricing and capacity planning for service facility with finite buffer.** / Sumita, Ushio; Masuda, Yasushi; Yamakawa, Shigetaka.

Research output: Contribution to journal › Article

*European Journal of Operational Research*, vol. 128, no. 1, pp. 192-205. https://doi.org/10.1016/S0377-2217(99)00355-0

}

TY - JOUR

T1 - Optimal internal pricing and capacity planning for service facility with finite buffer

AU - Sumita, Ushio

AU - Masuda, Yasushi

AU - Yamakawa, Shigetaka

PY - 2001/1/1

Y1 - 2001/1/1

N2 - An economic model is developed for exploring optimal internal pricing and capacity planning for service facility with finite buffer capacity. Because of the limited buffer capacity, jobs finding the system full upon their arrival would be rejected. Such rejections create a gap between the value collectively perceived by users and the actual achievement of the organizational value. This gap, called a loss externality, has never been studied before and plays an important role for designing optimal pricing scheme. In general, the underlying economic structure may involve multiple equilibria and it is unclear whether or not the system can be controlled through internal pricing. In this regard, a sufficient condition is given under which the system administrator can find two separate prices for accepted and rejected users at any demand level to be desired so that the desired demand level becomes the unique equilibrium of the system. For a short-run problem, it is shown that the optimal pricing scheme can be expressed as the sum of the congestion and the loss externalities. For a long-run problem, the optimal pricing scheme is expressed in a unified manner so that a structural relationship between the short-run problem and the long-run problem at optimality can be readily observed. A necessary and sufficient condition is also given for the marginal capacity pricing to be optimal, i.e., the optimal long-run pricing consists of the marginal cost for processing capacity and the marginal cost for buffer capacity without involving any externality at all.

AB - An economic model is developed for exploring optimal internal pricing and capacity planning for service facility with finite buffer capacity. Because of the limited buffer capacity, jobs finding the system full upon their arrival would be rejected. Such rejections create a gap between the value collectively perceived by users and the actual achievement of the organizational value. This gap, called a loss externality, has never been studied before and plays an important role for designing optimal pricing scheme. In general, the underlying economic structure may involve multiple equilibria and it is unclear whether or not the system can be controlled through internal pricing. In this regard, a sufficient condition is given under which the system administrator can find two separate prices for accepted and rejected users at any demand level to be desired so that the desired demand level becomes the unique equilibrium of the system. For a short-run problem, it is shown that the optimal pricing scheme can be expressed as the sum of the congestion and the loss externalities. For a long-run problem, the optimal pricing scheme is expressed in a unified manner so that a structural relationship between the short-run problem and the long-run problem at optimality can be readily observed. A necessary and sufficient condition is also given for the marginal capacity pricing to be optimal, i.e., the optimal long-run pricing consists of the marginal cost for processing capacity and the marginal cost for buffer capacity without involving any externality at all.

UR - http://www.scopus.com/inward/record.url?scp=0035200204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035200204&partnerID=8YFLogxK

U2 - 10.1016/S0377-2217(99)00355-0

DO - 10.1016/S0377-2217(99)00355-0

M3 - Article

AN - SCOPUS:0035200204

VL - 128

SP - 192

EP - 205

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -