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

Part of the International Series in Operations Research & Management Science book series (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.

Keywords

  • Multi-product newsvendor
  • Complementary products
  • Effects of substitute
  • Single constraint
  • Multiple constraints
  • Future research

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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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  Google Scholar 

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Correspondence to Asoo J. Vakharia .

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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

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