Some general properties for the newsboy problem with an extraordinary order

  1. V. Pando 1
  2. L.A. San-José 1
  3. J. García-Laguna 1
  4. J. Sicilia 2
  1. 1 Universidad de Valladolid, España
  2. 2 Universidad de La Laguna, España
Revista:
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ISSN: 1863-8279,  1134-5764

Año de publicación: 2014

Volumen: 22

Número: 2

Páginas: 674-693

Tipo: Artículo

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Resumen

In this paper, an extension of the standard newsboy problem is presented, involving an extraordinary order and a variable mixture of backorders and lost sales. The backlogged demand ratio is given by a nonincreasing function of the quantity of shortage. Some general properties for the expected cost are derived under weak assumptions about the backorder rate function. When the backorder rate is a linear function, some sufficient conditions for the global convexity of the expected cost are derived. A sufficient condition for the local concavity of this function is also provided. Numerical examples are presented to illustrate the theoretical results and a specific practical case is proposed and solved. Moreover, a sensitivity analysis of the optimal solution with respect to the parameters of the backorder rate function is included. Finally, some extensions of the proposed model are suggested as possible directions for future research.

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Acknowledgements The authors would like to thank the anonymous referees for their useful suggestions and comments. This work is partly supported by the Spanish Ministry of Science and Innovation through the research project MTM2010-18591.

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