Skip to main content
SpringerLink
Log in

The Multi-product Newsvendor Problem: Review, Extensions, and Directions for Future Research

  • Chapter
  • First Online:
Handbook of Newsvendor Problems

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 176))

Abstract

In this paper, we review the contributions to date for the multi-product newsvendor problem (MPNP). Our focus is on the current literature concerning the mathematical models and the solution methods for the multi-item newsvendor problems with single or multiple constraints, as well as the effects of substitute and complementary products on the stocking decisions and expected profits. We present some extensions to the current work for a stylized setting assuming two products and conclude with directions for future research.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For obvious reasons, it is generally assumed that g i  < v i .

References

  • Abdel-Malek, L., & Areeratchakul, N. (2007). A quadratic programming approach to the multi-product newsvendor problem with side constraints. European Journal of Operational Research, 176(3), 1607–1619.

    Article  Google Scholar 

  • Abdel-Malek, L., & Montanari, R. (2005a). An analysis of the multi-product newsboy problem with a budget constraint. International Journal of Production Economics, 97(3), 296–307.

    Article  Google Scholar 

  • Abdel-Malek, L., & Montanari, R. (2005b). On the multi-product newsboy problem with two constraints. Computers & Operations Research, 32, 2095–2116.

    Article  Google Scholar 

  • Abdel-Malek, L. Montanari, R., & Morales, L. (2004). Exact, approximate, and generic iterative models for the multi-product newsboy problem with budget constraint. International Journal of Production Economics, 91(2), 189–198.

    Article  Google Scholar 

  • Anupindi, R., Dada, M., & Gupta, S. (1998). Estimation of consumer demand with stock-out based substitution: an application to vending machine products. Marketing Science, 17(4), 406–423.

    Article  Google Scholar 

  • Areeratchakul, N., & Abdel-Malek, L. (2006). An approach for solving the multi-product newsboy problem. International Journal of Operational Research, 3(3), 219–227.

    Google Scholar 

  • Arrow, K., Harris, T., & Marshak, J. (1951). Optimal inventory policy. Econometrica, 19(3), 250–272.

    Article  Google Scholar 

  • Aviv, Y., & Federgruen, A. (2001). Capacitated multi-item inventory systems with random and seasonally fluctuating demands: implications for postponement strategies. Management Science, 47(4), 512–531.

    Article  Google Scholar 

  • Bassok, Y., Anupindi, R., & Akella, R. (1999). Single-period multiproduct inventory models with substitution. Operations Research, 47(4), 632–642.

    Article  Google Scholar 

  • Ben-Daya, M., & Raouf, A. (1993). On the constrained multi-tem single-period inventory problem. International Journal of Operations and Production Management, 13(11), 104–112.

    Article  Google Scholar 

  • Cai, L., Chen, J., & Yan, H. (2004). Technical note: single-period two-product inventory model with substitution: solution and properties. Journal of Systems Science and Systems Engineering, 13, 112–123.

    Article  Google Scholar 

  • Carrillo, J., Vakharia, A., & Wang, R. (2011). Environmental implications for online retailing. Working Paper.

    Google Scholar 

  • Casimir, R. (2002). The value of information in the multi-item newsboy problem. Omega, 30(1), 45–50.

    Article  Google Scholar 

  • Chen, L., & Chen, Y. (2010). A multiple-item budget-constraint newsboy problem with a reservation policy. Omega, 38(6), 431–439.

    Article  Google Scholar 

  • Cheng, T.C.E., & Choi, T.M. (2010). Innovative quick response programs in logistics and supply chain management. International handbooks on information systems. Berlin: Springer.

    Google Scholar 

  • Choi, S., Ruszczynski, A., & Zhao, Y. (2011). A multiproduct risk-averse newsvendor with law-invariant coherent measures of risk. Operations Research, 59(2), 346–364.

    Article  Google Scholar 

  • Chung, C., Flynn, J., & Kirca, O. (2008). A multi-item newsvendor problem with preseason production and capacitated reactive production. European Journal of Operational Research, 188(3), 775–792.

    Article  Google Scholar 

  • Dutta, P., & Chakraborty, D. (2010). Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand. European Journal of Operational Research, 200(1), 99–110.

    Article  Google Scholar 

  • Erlebacher, S. (2000). Optimal and heuristic solutions for the multi-item newsvendor problem with a single capacity constraint. Production and Operations Management, 9(3), 303–318.

    Article  Google Scholar 

  • Gallego, G., & Moon, I. (1993). The distribution free newsboy problem: review and extensions. The Journal of the Operational Research Society, 44(8), 825–834.

    Google Scholar 

  • Hadley, G., & Whitin, T. (1963). Analysis of inventory systems. New jersey: Prentice-Hall.

    Google Scholar 

  • Khouja, M., & Mehrez, A. (1996). A multi-product constrained newsboy problem with progressive multiple discounts. Computers and Industrial Engineering, 30(1), 95–101.

    Article  Google Scholar 

  • Khouja, M., Mehrez, A., & Rabinowitz, G. (1996). A two-item newsboy problem with substitutability. International Journal of Production Economics, 44(3), 267–275.

    Article  Google Scholar 

  • Lau, A., & Lau, H. (1988). Maximizing the probability of achieving a target profit in a two-product newsboy problem. Decision Sciences, 19(2), 392–409.

    Article  Google Scholar 

  • Lau, H., & Lau, A. (1995). The multi-product multi-constraint newsboy problem: applications, formulation and solution. Journal of Operations Management, 13(2), 153–162.

    Article  Google Scholar 

  • Lau, H., & Lau, A. (1996). The newsstand problem: a capacitated multiple-product single-period inventory problem. European Journal of Operational Research, 94(1), 29–42.

    Article  Google Scholar 

  • Lau, H., & Lau, A. (1997). Some results on implementing a multi-item multi-constraint single-period inventory model. International Journal of Production Economics, 48(2), 121–128.

    Article  Google Scholar 

  • Mahajan, S., & van Ryzin, G. (2001). Stocking retail assortments under dynamic consumer substitution. Operations Research, 49(3), 334–351.

    Article  Google Scholar 

  • McGillivray, A. R., & Silver, E. A. (1978). Some concepts for inventory control under substitutable demand. INFOR, 16(1), 47–63.

    Article  Google Scholar 

  • Mieghem, J. V., & Rudi, N. (2002). Newsvendor networks: inventory management and capacity investment with discretionary activities. Manuacturing Service Operations Management, 4(4), 313–335.

    Article  Google Scholar 

  • Moon, I., & Silver, E. A. (2000). The multi-item newsvendor problem with a budget constraint and fixed ordering costs. The Journal of the Operational Research Society, 51(5), 602–608.

    Google Scholar 

  • Nagarajan, M., & Rajagopalan, S. (2008). Inventory models for substitutable products: optimal policies and heuristics. Management Science, 54(8), 1453–1466.

    Article  Google Scholar 

  • Nahmias, S., & Schmidt, C. P. (1984). An efficient heuristic for the multi-item newsboy problem with a single constraint. Naval Research Logistics Quarterly, 31(3), 463–474.

    Article  Google Scholar 

  • Netessine, S., & Rudi, N. (2003). Centralized and competitive inventory models with demand substitution. Operations Research, 51(2), 329–335.

    Article  Google Scholar 

  • Niederhoff, J. (2007). Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions. European Journal of Operational Research, 176(2), 941–955.

    Article  Google Scholar 

  • Ozler, A., Tan, B., & Karaesmen, F. (2009). Multi-product newsvendor problem with value-at-risk considerations. International Journal of Production Economics, 117(2), 244–255.

    Article  Google Scholar 

  • Parlar, M., & Goyal, S. (1984). Optimal ordering decisions for two substitutable products with stochastic demands. OpSearch, 21, 1–15.

    Google Scholar 

  • Pasternack, B. A., & Drezner, Z. (1991). Optimal inventory policies for substitutable commodities with stochastic demand. Naval Research Logistics (NRL), 38(2), 221–240.

    Article  Google Scholar 

  • Qin, Y., Wang, R., Vakharia, A., Chen, Y., & Hanna-Seref, M. (2011). The newsvendor problem: review and directions for future research. European Journal of Operational Research, 213, 361–374.

    Article  Google Scholar 

  • Rajaram, K., & Tang, C. (2001). The impact of product substitution on retail merchandising. European Journal of Operational Research, 135(3), 582–601.

    Article  Google Scholar 

  • Shah, J., & Avittathur, B. (2007). The retailer multi-item inventory problem with demand cannibalization and substitution. International Journal of Production Economics, 106(1), 104–114.

    Article  Google Scholar 

  • Shao, Z., & Ji, X. (2006). Fuzzy multi-product constraint newsboy problem. Applied Mathematics and Computation, 180(1), 7–15.

    Article  Google Scholar 

  • Shi, J., & Zhang, G. (2010). Multi-product budget-constrained acquisition and pricing with uncertain demand and supplier quantity discounts. International Journal of Production Economics, 128(1), 322–331.

    Article  Google Scholar 

  • Shi, J., Zhang, G., & Sha, J. (2011). Jointly pricing and ordering for a multi-product multi-constraint newsvendor problem with supplier quantity discounts. Applied Mathematical Modelling, 35(6), 3001–3011.

    Article  Google Scholar 

  • Silver, E., Pyke, D., & Peterson, R. (1998). Inventory management and production planning and scheduling. New York: Wiley.

    Google Scholar 

  • Smith, S., & Agrawal, N. (2000). Management of multi-item retail inventory systems with demand substitution. Operations Research, 48(1), 50–64.

    Article  Google Scholar 

  • Vaagen, H., & Wallace, S. W. (2008). Product variety arising from hedging in the fashion supply chains. International Journal of Production Economics, 114(2), 431–455.

    Article  Google Scholar 

  • Vairaktarakis, G. (2000). Robust multi-item newsboy models with a budget constraint. International Journal of Production Economics, 66(3), 213–226.

    Article  Google Scholar 

  • Zhang, B., & Du, S. (2010). Multi-product newsboy problem with limited capacity and outsourcing. European Journal of Operational Research, 202(1), 107–113.

    Article  Google Scholar 

  • Zhang, B., & Hua, Z. (2010). A portfolio approach to multi-product newsboy problem with budget constraint. Computers & Industrial Engineering, 58, 759–765.

    Article  Google Scholar 

  • Zhang, B., Xu, X., & Hua, Z. (2009). A binary solution method for the multi-product newsboy problem with budget constraint. International Journal of Production Economics, 117(1), 136–141.

    Article  Google Scholar 

  • Zhang, G. (2010). The multi-product newsboy problem with supplier quantity discounts and a budget constraint. European Journal of Operational Research, 206(2), 350–360.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Information Systems & Operations Management, University of Florida, Gainesville, FL, 32611–7169, USA

    Nazli Turken, Yinliang Tan, Asoo J. Vakharia, Lan Wang, Ruoxuan Wang & Arda Yenipazarli

Authors
  1. Nazli Turken
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yinliang Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Asoo J. Vakharia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ruoxuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Arda Yenipazarli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Asoo J. Vakharia .

Editor information

Editors and Affiliations

  1. , Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR

    Tsan-Ming Choi

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media New York

About this chapter

Cite this chapter

Turken, N., Tan, Y., Vakharia, A.J., Wang, L., Wang, R., Yenipazarli, A. (2012). The Multi-product Newsvendor Problem: Review, Extensions, and Directions for Future Research. In: Choi, TM. (eds) Handbook of Newsvendor Problems. International Series in Operations Research & Management Science, vol 176. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3600-3_1

Download citation

Publish with us

Policies and ethics

Search

Navigation