Jointly pricing and ordering for a multi-product multi-constraint newsvendor problem with supplier quantity discounts. (English) Zbl 1219.90016

Summary: We present an extension to the multi-product newsvendor problem by incorporating the retailer’s pricing decision as well as considering supplier quantity discount. The objective is to maximize the expected profit of the retailer through jointly determining the ordering quantities and selling prices for the products, subject to multiple capacity constraints. We formulate the problem as a generalized disjunctive programming (GDP) model and develop a Lagrangian heuristic approach for its solution. Randomly produced instances involving up to 1000 products are used to test the proposed approach. Computational results show that the Lagrangian heuristic approach can present very good solutions to all instances in reasonable time.


90B05 Inventory, storage, reservoirs
90B06 Transportation, logistics and supply chain management
90C59 Approximation methods and heuristics in mathematical programming
Full Text: DOI


[1] Khouja, M., The single-period (new-vendor) problem: literature review and suggestions for future research, OMEGA Int. J. Manage. Sci., 27, 537-553 (1999)
[2] Hadley, G.; Whitin, T., Analysis of Inventory Systems (1963), Prentice-Hall: Prentice-Hall EnglewoodCliffs, NJ · Zbl 0133.42901
[3] Vairaktarakis, G. L., Robust multi-item newsboy models with a budget constraint, Int. J. Prod. Econ., 66, 213-226 (2000)
[4] Shao, Z.; Ji, X., Fuzzy multi-product constraint newsboy problem, Appl. Math. Comput., 180, 7-15 (2006) · Zbl 1139.90436
[5] Abdel-Malek, L. L.; Areeratchakul, N., A quadratic programming approach to the multi-product newsvendor problem with side constraints, Eur. J. Oper. Res., 176, 1607-1619 (2007) · Zbl 1110.90027
[6] Niederhoff, J. A., Using separable programming to solve the multi-product multiple ex-ante constraint newsvendor problem and extensions, Eur. J. Oper. Res., 176, 941-955 (2007) · Zbl 1103.90019
[7] Abdel-Malek, L.; Montanari, R.; Meneghetti, D., The capacitated newsboy problem with random yield: The Gardener Problem, Int. J. Prod. Econ., 115, 113-127 (2008)
[8] Abdel-Malek, L.; Montanari, R., An analysis of the multi-product newsboy problem with a budget constraint, Int. J. Prod. Econ., 97, 296-307 (2005)
[9] Abdel-Malek, L.; Montanari, R., On the multi-product newsboy problem with two constraints, Comput. Oper. Res., 32, 2095-2116 (2005) · Zbl 1068.90003
[10] Erlebacher, S. J., Optimal and heuristics solutions for the multi-item newsvendor problem with a single capacity constraint, Prod. Oper. Manage., 9, 303-318 (2000)
[11] Moon, I.; Silver, E. A., The multi-item newsvendor problem with a budget constraint and fixed ordering costs, J. Oper. Res. Soc., 51, 602-608 (2000) · Zbl 1055.90505
[12] Abdel-Malek, L.; Montanari, R.; Morales, L. C., Exact, approximate, and generic iterative models for the multi-product Newsboy problem with budget constraint, Int. J. Prod. Econ., 91, 189-198 (2004)
[13] Zhang, B.; Xu, X.; Hua, Z., A binary solution method for the multi-product newsboy problem with budget constraint, Int. J. Prod. Econ., 117, 136-141 (2009)
[14] Lau, H.; Lau, A., The multi-product multi-constraint newsboy problem: application, formulation and solution, J. Oper. Manage., 13, 153-162 (1995)
[15] Lau, H.; Lau, A., The newsstand problem: a capacitated multiple-product single-period inventory problem, Eur. J. Oper. Res., 94, 29-42 (1996) · Zbl 0929.90003
[16] Whitin, T. M., Inventory control and price theory, Manage. Sci., 2, 61-68 (1955)
[17] Petruzzi, N. C.; Data, M., Pricing and the newsvendor problem: a review with extensions, Oper. Res., 47, 183-194 (1999) · Zbl 1005.90546
[18] Petruzzi, N. C.; Dada, M., Information and inventory recourse for a two-market, price setting retailer, Manuf. Serv. Oper. Manage., 3, 242-263 (2001)
[19] Karakul, M., Joint pricing and procurement of fashion products in the existence of clearance markets, Int. J. Prod. Econ., 114, 487-506 (2008)
[20] Granot, D.; Yin, S., Price and order postponement in decentralized newsvendor model with multiplicative and price-dependent demand, Oper. Res., 56, 121-139 (2008) · Zbl 1167.90379
[21] Chen, J.; Bell, P. C., The impact of customer returns on pricing and order decisions, Eur. J. Oper. Res., 195, 280-295 (2009) · Zbl 1159.90362
[22] Pan, K.; Lai, K. K.; Liang, L.; Leung, S. C.H., Two-period pricing and ordering policy for the dominant retailer in a two-echelon supply chain with demand uncertainty, Omega, 37, 919-929 (2009)
[23] He, Y.; Zhao, X.; Zhao, L.; He, J., Coordinating a supply chain with effort and price dependent stochastic demand, Appl. Math. Model., 33, 2777-2790 (2009) · Zbl 1205.90045
[24] Khouja, M., The Newsboy problem with multiple discounts offered by suppliers and retailers, Decis. Sci., 27, 589-599 (1996)
[25] Lin, C.; Kroll, DE., The single-item newsboy problem with dual performance measures and quantity discounts, Eur. J. Oper. Res., 100, 562-565 (1997) · Zbl 0917.90110
[26] Zhang, G.; Ma, L., Optimal acquisition policy with quantity discounts and uncertain demands, Int. J. Prod. Res., 47, 2409-2425 (2009) · Zbl 1171.90388
[27] J. Shi, G. Zhang, The multi-product newsboy pricing problem with supplier quantity discounts and a budget constraint, Technical report, University of Windsor, 2008.; J. Shi, G. Zhang, The multi-product newsboy pricing problem with supplier quantity discounts and a budget constraint, Technical report, University of Windsor, 2008.
[28] Raman, R.; Grossmann, I. E., Modeling and computational techniques for logic based integer programming, Comput. Chem. Eng., 18, 563-578 (1994)
[29] Turkay, M.; Grossmann, I. E., Disjunctive programming techniques for the optimization of process systems with discontinuous investment cost-multiple size regions, Ind. Eng. Chem. Res., 35, 2611-2623 (1996)
[30] Mills, E. S., Uncertainty and price theory, Q. J. Econ., 73, 116-130 (1959)
[31] Wolsey, L. A., Integer Programming (1999), Wiley, pp. 173-177
[32] D’alfanso, T. H.; Ventura, J. A., Assignment of tools to machines in a flexible manufacturing system, Eur. J. Oper. Res., 81, 115-133 (1995) · Zbl 0913.90126
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.