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The “Hub” and “Wheel” Scheduling Problems

Author

Listed:
  • Sanji Arisawa

    (Mitsubishi Petrochemical Co., Ltd., Tokyo, Japan)

  • Salah E. Elmaghraby

    (The Catholic University of Leuven and the European Institute for Advanced Studies in Management, Brussels)

Abstract

We pursue the analysis of the Hub Operation Scheduling Problem (HOSP) over the finite and infinite horizons. The demand is assumed deterministic and stationary. We deduce the minimum fleet size V T that satisfies all demands for 1 (le) T (le) (infinity), as well as the optimal schedule that minimizes lost sales for a given fleet size smaller than V T . Reintroducing the costs of empties and of delayed sales or, equivalently, the cost of empties and the gains from shipments, we resolve the issues of optimal allocation and optimal schedule over a horizon T (le) (infinity). Finally, we generalise the above results---still under the assumption of deterministic, stationary demands---first to the case in which each city communicates with its two “adjacent” cities (this is the “Wheel” problem) and then to the general network problem in which each terminal may communicate with any other terminal.

Suggested Citation

  • Sanji Arisawa & Salah E. Elmaghraby, 1977. "The “Hub” and “Wheel” Scheduling Problems," Transportation Science, INFORMS, vol. 11(2), pages 147-165, May.
    • Handle: RePEc:inm:ortrsc:v:11:y:1977:i:2:p:147-165
    DOI: 10.1287/trsc.11.2.147
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