×

Joint decisions on product line selection, purchasing, and pricing. (English) Zbl 1403.90426

Summary: When creating a product line, a retailer must make several decisions simultaneously: the selection of the product types to include in the product line as well as the order quantity and price of each selected product type. This study investigates joint product line decisions by considering the dynamic substitutions of products as driven by the valuations that customers place on the products and the availability of each product type, which changes as consumers purchase a product. An integer programming model was developed for joint decisions of product selection, price, and order quantity in the product line problem to maximize the total profit of the retailer. To solve the model, we propose a hybrid genetic algorithm (HGA) that uses special genetic operators and heuristic algorithms to ensure the feasibility and efficiency of solutions. Computational experiments demonstrate the superiority of the proposed HGA over the solution obtained by CPLEX for large scale problems. Useful managerial insights on the joint product line decisions are also derived from the numerical results.

MSC:

90B50 Management decision making, including multiple objectives
90B05 Inventory, storage, reservoirs
90B06 Transportation, logistics and supply chain management
90C59 Approximation methods and heuristics in mathematical programming

Software:

CPLEX
Full Text: DOI

References:

[1] Aydin, G.; Porteus, E., Joint inventory and pricing decisions for a selection, Operations Research, 56, 1247-1255 (2008) · Zbl 1167.90478
[2] Burkart, W. R.; Klein, R.; Mayer, S., Product line pricing for services with capacity constraints and dynamic substitution, European Journal of Operational Research, 219, 347-359 (2012) · Zbl 1244.90169
[3] Deif, S.; Kamal, H. A.; Tawfik, M., Enhancing genetic algorithms using a dynamic mutation value approach: An application to the control of flexible Robot Systems, International Journal of Artificial Intelligent Systems and Machine Learning, 4, 1, 9-16 (2012)
[4] Dobson, G.; Kalish, S., Positioning and pricing a product line, Marketing Science, 7, 2, 107-125 (1988)
[5] Dobson, G.; Kalish, S., Heuristics for pricing and positioning a product-line using conjoint and cost data, Management Science, 39, 2, 160-175 (1993)
[6] Gajjar, H. K.; Adil, G. K., A piecewise linearization for retail shelf space allocation problem and a local search heuristic, Annals of Operations Research, 179, 149-167 (2010) · Zbl 1201.90136
[7] Holland, J. H., Adaptation in natural and artificial systems (1975), University of Michigan Press · Zbl 0317.68006
[8] Green, P. E.; Krieger, A. M., Models and heuristics for product line selection, Marketing Science, 4, 1, 1-19 (1985)
[9] Irion, J.; Lu, J.-C.; Al-Khayyal, F.; Tsao, Y.-C., A piecewise linearization framework for retail shelf space management models, European Journal of Operational Research, 222, 122-136 (2012) · Zbl 1253.90126
[10] Jin, X.; Li, Z., Genetic-catastrophic algorithms and its application in nonlinear control system, Journal of System Simulation, 9, 2, 111-115 (1997)
[11] Kraus, U. G.; Yano, C. A., Product line selection and pricing under a share-of-surplus choice model, European Journal of Operational Research, 150, 653-671 (2003) · Zbl 1033.90062
[12] Li, Z., A single-period assortment optimization model, Production and Operations Management, 16, 369-380 (2007)
[13] Maddah, B.; Bish, E. K., Joint pricing, assortment, and inventory decisions for a retailer’s product line, Naval Research Logistics, 54, 3, 315-330 (2007) · Zbl 1149.90305
[14] Mahajan, S.; van Ryzin, G., Stocking retail assortments under dynamic consumer substitution, Operations Research, 49, 3, 334-351 (2001) · Zbl 1163.90339
[15] Mayer, S.; Klein, R.; Seiermann, S., A simulation-based approach to price optimization of the mixed bundling problem with capacity constraints, International Journal of Production Economics, 145, 2, 584-598 (2013)
[16] Mayer, S.; Steinhardt, C., Optimal product line pricing in the presence of budget-constrained consumers, European Journal of Operational Research, 248, 219-233 (2016) · Zbl 1348.90357
[17] Monroe, K. B.; Sunder, S.; Wells, W. A.; Zoltners, A. A., A multi-period integer programming approach to the product mix problems, (Bernhardt, K., Proceedings of the American marketing Association Meeting (1976)), 493-497
[18] Shugan, S. M.; Balachandran, V., Working paper (1977), University of Rochester
[19] van Ryzin, G.; Mahajan, S., On the relationship between inventory costs and variety benefits in retail selections, Management Science, 45, 1496-1509 (1999) · Zbl 0953.90002
[20] Yücel, E.; Karaesmen, F.; Salman, F.; Türkay, M., Optimizing product selection under customer-driven demand substitution, European Journal of Operational Research, 199, 759-768 (2009) · Zbl 1176.90042
[21] Zufryden, F. S., Product line optimization by integer programming, (Presented at the Spring 1982 ORSA/TI MS Conference. Presented at the Spring 1982 ORSA/TI MS Conference, San Diego, California (1982))
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.