×

zbMATH — the first resource for mathematics

A possibilistic multiple objective pricing and lot-sizing model with multiple demand classes. (English) Zbl 1284.91294
Summary: We address an inventory-marketing system to determine the production lot size, marketing expenditure and selling prices where a firm faces demand from two or more market segments in which the firm can set different prices. Considering pricing, marketing and lot-sizing decisions simultaneously, the model maximizes the profit and return on inventory investment under multiple time varying demand classes. The model is formulated as a fuzzy non-linear multi-objective one where some parameters are ill-known and modeled by fuzzy numbers. A hybrid possibilistic-flexible programming approach is proposed to handle imprecise data and soft constraints concurrently. After transforming the original model into an equivalent multi-objective crisp model, it is then converted to a classical mono-objective one by a fuzzy goal programming method. An efficient solution procedure using particle swarm optimization (PSO) is also provided to solve the resulting nonlinear problem.

MSC:
91B38 Production theory, theory of the firm
90B05 Inventory, storage, reservoirs
90C29 Multi-objective and goal programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Freeland, J. R., Coordination strategies for production and marketing in a functionally decentralized firm, ABE Trans., 12, 2, 126-132, (1982)
[2] Kotler, P., Marketing decision makinga model building approach, (1971), Holt, Rinehart and Winston New York
[3] Porteus, E. L.; Whang, S., On manufacturing/marketing incentives, Manage. Sci., 37, 9, 1166-1181, (1991) · Zbl 0729.90871
[4] Kunreuther, H.; Richard, J. F., Optimal pricing and inventory decisions for non-seasonal items, Econometrica, 39, 1, 173-175, (1971) · Zbl 0209.51701
[5] Lee, W. J.; Kim, D., Optimal and heuristic decision strategies for integrated production and marketing planning, Decision Sci., 24, 6, 1203-1213, (1993)
[6] Kim, D.; Lee, W. J., Optimal joint pricing and lot sizing with fixed and variable capacity, Eur. J. Oper. Res., 109, 1, 212-227, (1998) · Zbl 0951.90031
[7] Huang, Z.; Li, S. X., Co-op advertising models in manufacturer-retailer supply chainsa game theory approach, Eur. J. Oper. Res., 135, 527-544, (2001) · Zbl 0989.90083
[8] Phillips, R. L., Pricing and revenue optimization, (2005), Stanford University Press Stanford, CA
[9] Schroeder, R. G.; Krishnan, R., Return on investment as a criterion for inventory model, Decision Sci., 7, 697-704, (1976)
[10] Otake, T.; Min, K. J.; Chen, C., Inventory and investment in setup operations under return on investment maximization, Comput. Oper. Res., 26, 883-899, (1999) · Zbl 0957.90006
[11] Otake, T.; Min, K. J., Inventory and investment in quality improvement under return on investment maximization, Comput. Oper. Res., 28, 113-124, (2001) · Zbl 1017.90003
[12] Li, J.; Min, K. J.; Otake, T.; Voorhis, T. M., Inventory and investment in setup and quality operations under return on investment maximization, Eur. J. Oper. Res., 185, 593-605, (2008) · Zbl 1137.90315
[13] Wee, H.; Lo, C.; Hsu, P., A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment, Eur. J. Oper. Res., 197, 620-631, (2009) · Zbl 1159.90532
[14] Mandal, N. K.; Roy, T. K.; Maiti, M., Multi-objective fuzzy inventory model with three constraintsa geometric programming approach, Fuzzy Sets Syst., 150, 87-106, (2005) · Zbl 1075.90005
[15] Whitin, T. M., Inventory control and price theory, Manage. Sci., 2, 6l-68, (1955)
[16] Lee, W. J., Determining order quantity and selling price by geometric programming optimal solution, bounds, and sensitivity, Decision Sci., 24, 76-87, (1993)
[17] Esmaeili, M.; Abad, P. L.; Aryanezhad, M. B., Seller-buyer relationship when end demand is sensitive to price and promotion, Asia-Pac. J. Oper. Res., 26, 5, 605-621, (2009) · Zbl 1178.90206
[18] Esmaeili, M.; Aryanezhad, M. B.; Zeephongsekul, P., A game theory approach in seller-buyer supply chain, Eur. J. Oper. Res., 195, 442-448, (2009) · Zbl 1159.91330
[19] Esmaeili, M., Optimal selling price, marketing expenditure and lot size under general demand function, Int. J. Adv. Manuf. Tech., 45, 191-198, (2009)
[20] Abad, P. L., Determining optimal selling price and the lot size when the supplier offers all-unit quantity discounts, Decision Sci., 3, 19, 622-634, (1988)
[21] Dye, C.; Hsieh, T., A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and unit purchasing cost, Comput. Math. Appl., 60, 1895-1907, (2010) · Zbl 1205.90030
[22] Talluri, K. T.; Van Ryzin, G. J., The theory and practice of revenue management, (2004), Kluwer Academic Publishers Boston, MA, USA · Zbl 1083.90024
[23] M.J. Kleijn, R. Dekker, An overview of inventory systems with several demand classes, Econometric Institute Report 9838/A. Erasmus University, Rotterdam, The Netherlands, 1998. · Zbl 0969.90004
[24] Sen, A.; Zhang, A., The newsboy problem with multiple demand classes, IIE Trans., 31, 431-444, (1999)
[25] Zhang, M.; Bell, P. C., The effect of market segmentation with demand leakage between market segments on a Firm’s price and inventory decisions, Eur. J. Oper. Res., 182, 738-754, (2007) · Zbl 1121.90383
[26] Zhang, M.; Bell, P.; Cai, G.; Chen, X., Optimal fences and joint price and inventory decisions in distinct markets with demand leakage, Eur. J. Oper. Res., 204, 589-596, (2010) · Zbl 1181.90029
[27] M. Fadiloglu, M. Bulut, An Embedded Markov Chain Approach to the Analysis of Inventory Systems with Backordering Under Rationing, Working Paper, Department of Industrial Engineering, Bilkent University, Ankara, Turkey, 2005.
[28] Frank, K. C.; Zhang, R. Q.; Duenyas, I., Optimal policies for inventory systems with priority demand classes, Oper. Res., 51, 6, 993-1002, (2003) · Zbl 1165.90313
[29] Deshpande, V.; Cohen, M. A.; Donohue, K., A threshold inventory rationing policy for service-differentiated demand classes, Manage. Sci., 49, 6, 683-703, (2003) · Zbl 1232.90273
[30] Islam, S., Multi-objective marketing planning inventory modela geometric programming approach, Appl. Math. Comput., 205, 238-246, (2008) · Zbl 1151.90313
[31] Sadjadi, S. J.; Ghazanfari, M.; Yousefli, A., Fuzzy pricing and marketing planning modela possibilistic geometric programming approach, Expert Syst. Appl., 37, 3392-3397, (2010)
[32] Dubois, D.; Fargier, H.; Fortemps, P., Fuzzy schedulingmodelling flexible constraints vs. coping with incomplete knowledge, Eur. J. Oper. Res., 147, 231-252, (2003) · Zbl 1037.90028
[33] Peidro, D.; Mula, J.; Poler, R.; Verdegay, J. L., Fuzzy optimization for supply chain planning under supply, demand and process uncertainties, Fuzzy Sets Syst., 160, 2640-2657, (2009) · Zbl 1279.90206
[34] Torabi, S. A.; Hassini, E., An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets Syst., 159, 193-214, (2008) · Zbl 1168.90352
[35] Zimmermann, H. J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets Syst., 1, 45-55, (1978) · Zbl 0364.90065
[36] Bell, P. C.; Chen, J., Enhancing revenues and profits for a multi-product firm with impatient customers through revenue management, J. Oper. Res. Soc., 57, 4, 443-449, (2006) · Zbl 1086.90505
[37] Tersine, R. J., Principles of inventory and materials management, (1994), Prentice Hall PTR NJ, USA
[38] Inuiguchi, M.; Ramik, J., Possibilistic linear programminga brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem, Fuzzy Sets Syst., 111, 3-28, (2000) · Zbl 0938.90074
[39] Torabi, S. A.; Ebadian, M.; Tanha, R., Fuzzy hierarchical production planning (with a case study), Fuzzy Sets Syst., 161, 1511-1529, (2010) · Zbl 1186.90046
[40] Baykasoglu, A.; Göçken, T., A review and classification of fuzzy mathematical programs, J. Intell. Fuzzy Syst., 19, 205-229, (2008) · Zbl 1151.90601
[41] Cadenas, J. M.; Verdegay, J. L., Using fuzzy numbers in linear programming, IEEE Trans. Syst. Man Cybernet. BCybernet., 27, 1016-1022, (1997)
[42] Maity, K.; Maiti, M., Possibility and necessity constraints and their defuzzification—a multi-item production-inventory scenario via optimal control theory, Eur. J. Oper. Res., 177, 882-896, (2007) · Zbl 1109.90035
[43] Maity, K., Possibility and necessity representations of fuzzy inequality and its application to two warehouse production-inventory problem, Appl. Math. Model., 35, 1252-1263, (2011) · Zbl 1211.90022
[44] Yager, R., A procedure for ordering fuzzy subsets of the unit interval, Inform. Sci., 24, 143-161, (1981) · Zbl 0459.04004
[45] Yaghoobi, M. A.; Tamiz, M., A method for solving fuzzy goal programming problems based on MINMAX approach, Eur. J. Oper. Res., 177, 1580-1590, (2007) · Zbl 1102.90061
[46] R.C. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, pp. 39-43.
[47] Poli, R.; Kennedy, J.; Blackwell, T., Particle swarm optimizationan overview, Swarm Intell., 1, 33-57, (2007)
[48] Tsou, C. S., Multi-objective inventory planning using MOPSO and TOPSIS, Expert Syst. Appl., 35, 136-142, (2008)
[49] Zhao, L.; Qian, F.; Yang, Y.; Zeng, Y.; Su, H., Automatically extracting T-S fuzzy models using cooperative random learning particle swarm optimization, Appl. Soft Comput., 10, 938-944, (2010)
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.