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Optimal production, pricing, and substitution policies in continuous review production-inventory systems. (English) Zbl 1403.90066

Summary: We consider the optimal production, pricing, and substitution policies of a continuous-review production-inventory system with two products: a high-end product and a low-end product. Each product has its associated customer stream; however, the demands for the low-end product may be satisfied by the high-end product. We formulate the problem as a Markov decision process and characterize the structure of the optimal control policy, which specifies when to produce for each product, when to use the high-end product as a substitute, and how to set the optimal prices. We show that a base-stock production policy is optimal; however, the optimal base-stock level for each product depends on the inventory level of the other product and it features a monotonic property. We also demonstrate that the optimal substitution policy is a rationing policy with the rationing level depending on the total inventory amount. We find that the optimal prices can be either decreasing or increasing in the inventory levels, depending on the forms of demand functions. Furthermore, we utilize numerical experiments to investigate the impact of different system characteristics on the benefits of using substitution and dynamic pricing. Finally, we investigate when the dynamic pricing strategy and the substitution strategy are complements or substitutes.

MSC:

90B05 Inventory, storage, reservoirs
90B30 Production models
90C40 Markov and semi-Markov decision processes
Full Text: DOI

References:

[1] Akcay, Y.; Natarajan, H.; Xu, S., Joint dynamic pricingof multiple perishable products under consumer choice, Management Science, 56, 8, 1345-1361 (2010) · Zbl 1232.91234
[2] Altman, E.; Gaujal, B.; Hordijk, A., Multimodularity, convexity, and optimization properties, Mathematics of Operations Research, 25, 2, 324-347 (2000) · Zbl 0977.90005
[3] Balakrishnan, A.; Geunes, J., Requirements planning with substitutions: exploiting bill-of-materials flexibility in production planning, Manufacturing & Service Operations Management, 2, 2, 166 (2000)
[4] Bassok, Y.; Anupindi, R.; Akella, R., Single-period multiproduct inventory models with substitution, Operations Research, 47, 4, 632-642 (1999) · Zbl 0979.90005
[5] Bitran, G.; Dasu, S., Ordering policies in an environment of stochastic yields and substitutable demands, Operations Research, 40, 5, 999-1017 (1992) · Zbl 0775.90139
[6] Chen, F. Y.; Ray, S.; Song, Y., Optimal pricing and inventory control policy in periodic-review systems with fixed ordering cost and lost sales, Naval Research Logistics, 53, 117-136 (2006) · Zbl 1106.90008
[7] Chen, L.; Feng, Y.; Ou, J., Joint management of finished goods inventory and demand process for a make-to-stock product: A computational approach, IEEE Transactions on Automatic Control, 51, 258-273 (2006) · Zbl 1366.90003
[8] Chen, X.; Simchi-Levi, D., Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case, Operations Research, 52, 887-896 (2004) · Zbl 1165.90308
[9] Chen, X.; Simchi-Levi, D., The oxfordhandbook of pricing management, 784-822 (2012), Oxford University Press: Oxford University Press Oxford, United Kingdom
[10] Dong, L.; Kouvelis, P.; Tian, Z., Dynamic pricing and inventory control of substitute products, Manufacturing & Service Operations Management, 11, 2, 317-339 (2009)
[11] Elmaghraby, W.; Keskinocak., P., Dynamic pricing in the presence of inventory considerations: Research overview, current practices, and future directions, Management Science, 47, 1287-1309 (2003) · Zbl 1232.90042
[12] Federgruen, A.; Heching, A., Combined pricing and inventory control under uncertainty, Operations Research, 47, 3, 454-457 (1999) · Zbl 0979.90004
[13] Gayon, J.-P.; Benjaafar, S.; De Véricourt, F., Using imperfect advance demand information in production-inventory systems with multiple customer classes, Manufacturing & Service Operations Management, 11, 1, 128-143 (2009)
[14] Ha, A., Optimal dynamic scheduling policy for a make-to-stock production system, Operations Research, 45, 1, 42-53 (1997) · Zbl 0892.90056
[15] Honhon, D.; Gaur, V.; Seshadri, S., Assortment planning and inventory decisions under stock-out based substitution, Operations Research, 58, 5, 1364-1379 (2010) · Zbl 1233.90022
[16] Hopp, W.; Xu, X., A static approximation for dynamic demand substitution with applications in a competitive market, Operations Research, 56, 3, 630-645 (2008) · Zbl 1167.90330
[17] Hsu, V.; Li, C.; Xiao, W., Dynamic lot size problems with one-way product substitution, IIE Transactions, 37, 3, 201-215 (2005)
[18] Huang, D.; Zhao, Q.; Fan, C., Simulation-basedoptimization of inventory model with products substitution, Innovative quick response programs in logistics and supply chain management, 297-312 (2010), Springer: Springer Heidelberg
[19] Koole, G., Convexity in tandem queues, Probability in the Engineering and Informational Sciences, 18, 1, 13-31 (2004) · Zbl 1048.60070
[20] Li, L., A stochastic theory of the firm, Mathematics of Operations Research, 13, 447-465 (1988) · Zbl 0651.90040
[21] Lippman, S., Applyinga new device in the optimization of exponential queuing systems, Operations Research, 23, 4, 687-710 (1975) · Zbl 0312.60048
[22] Mahajan, S.; van Ryzin, G., Stocking retail assortments under dynamic consumer substitution, Operations Research, 49, 3, 334-351 (2001) · Zbl 1163.90339
[23] Murota, K., Note on multimodularity and L-convexity, Mathematics of Operations Research, 30, 3, 658-661 (2005) · Zbl 1082.90071
[24] Netessine, S.; Dobson, G.; Shumsky, R., Flexible service capacity: Optimal investment and the impact of demand correlation, Operations Research, 50, 2, 375-388 (2002) · Zbl 1163.90343
[25] Netessine, S.; Rudi, N., Centralized and competitive inventory models with demand substitution, Operations Research, 51, 2, 329-335 (2003) · Zbl 1163.90344
[26] Pentico, D., The assortment problem: A survey, European Journal of Operational Research, 190, 2, 295-309 (2008)
[27] Robinson, L., Optimal and approximate policies in multiperiod, multilocation inventory models with transshipments, Operations Research, 38, 2, 278-295 (1990) · Zbl 0716.90031
[28] Sadowski, W., A few remarks on the assortment problem, Management Science, 6, 1, 13-24 (1959) · Zbl 0995.90559
[29] Shumsky, R.; Zhang, F., Dynamic capacity management with substitution, Operations research, 57, 3, 671-684 (2009) · Zbl 1233.90046
[30] Smith, S.; Agrawal, N., Management of multi-item retail inventory systems with demand substitution, Operations Research, 48, 1, 50-64 (2000) · Zbl 1106.90306
[31] Song, J.; Xue, Z., Demand management and inventory control for substitutable products, Working Paper (2007), Duke University
[32] Tomlin, B.; Wang, Y., Pricing and operational recourse in coproduction systems, Management Science, 54, 3, 522-537 (2008)
[33] Van Ryzin, G.; Mahajan, S., On the relationship between inventory costs and variety benefits in retail assortments, Management Science, 45, 11, 1496-1509 (1999) · Zbl 0953.90002
[34] de Vericourt, F.; Karaesmen, F.; Dallery, Y., Optimal stock allocation for a capacitated supply system, Management Science, 49, 11, 1486-1501 (2002) · Zbl 1232.90039
[35] Weber, R. R.; Stidham Jr, S., Optimal control of service rates in networks of queues, Advances in Applied Probability, 19, 1, 202-218 (1987) · Zbl 0617.60090
[36] Xu, H.; Yao, D. D.; Zheng, S., Optimal policies for a two-product inventory system under a flexible substitution scheme, Production and Operations Management, 25, 6, 1088-1105 (2016)
[37] Yano, C. A.; Gilbert, S. M., Coordinated pricing and production/procurement decisions: A review, (Chakravarty, A.; Eliashberg, J., Managing business interfaces: Marketing, engineering and manufacturing perspectives (2003), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, MA)
[38] Zhao, H.; Ryan, J.; Deshpande, V., Optimal dynamic production and inventory transshipment policies for multi-location make-to-stock systems, Operations Research, 56, 2, 400-410 (2008) · Zbl 1167.90365
[39] Zipkin, P. H., Foundations of inventory management, vol. 2 (2000), McGraw-Hill: McGraw-Hill New York · Zbl 1370.90005
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