Integrated markdown pricing and aggregate production planning in a two echelon supply chain: a hybrid fuzzy multiple objective approach.

*(English)*Zbl 1349.90295Summary: Given high variability of demands for short life cycle products, a retailer has to decide about the products’ prices and order quantities from a manufacturer. In the meantime, the manufacturer has to determine an aggregate production plan involving for example, production, inventory and work force levels in a multi period, multi product environment. Due to imprecise and fuzzy nature of products’ parameters such as unit production and replenishment costs, a hybrid fuzzy multi-objective programming model including both quantative and qualitative constraints and objectives is proposed to determine the optimalprice markdown policy and aggregate production planning in a two echelon supply chain. The model aims to maximize the total profit of manufacturer, the total profit of retailer and improving service aspects of retailing simultaneously. After applying appropriate strategies to defuzzify the original model, the equivalent multi-objective crisp model is then solved by a fuzzy goal programming
method. An illustrative example is also provided to show the applicability and usefulness of the proposed model and solution method.

##### MSC:

90B30 | Production models |

90C29 | Multi-objective and goal programming |

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90B05 | Inventory, storage, reservoirs |

##### Keywords:

fuzzy mathematical programming; short life cycle products; markdown pricing; retailing; production planning
PDF
BibTeX
XML
Cite

\textit{R. G. Yaghin} et al., Appl. Math. Modelling 36, No. 12, 6011--6030 (2012; Zbl 1349.90295)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Chan, L.M.A.; Shen, Z.J.M.; Simchi-Levi, D.; Swann, J., Coordination of pricing and inventory decisions: a survey and classification, (), 335-392 · Zbl 1125.91322 |

[2] | Jamalnia, A.; Soukhakian, M.A., A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning, Comput. ind. eng., 56, 4, 1474-1486, (2009) |

[3] | 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 |

[4] | Wang, R.C.; Liang, T.F., Applying possibilistic linear programming to aggregate production planning, Int. J. prod. econ., 98, 328-341, (2005) |

[5] | Elmaghraby, W.; Keskinocak, P., Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions, Manage. sci., 49, 10, 1287-1309, (2003) · Zbl 1232.90042 |

[6] | Pashigian, P.B., Demand uncertainty and sales: a study of fashion and markdown pricing, Am. econ. rev., 78, 936-953, (1988) |

[7] | Rajan, A.; Rakesh, S.; Steinberg, R., Dynamic pricing and ordering decisions by a monopolist, Manage. sci., 38, 240-263, (1992) · Zbl 0763.90016 |

[8] | Bitran, G.; Caldentey, R.; Mondschein, S., Coordinating clearance markdown sales of seasonal products in retail chain, Oper. res., 46, 5, 609-624, (1998) · Zbl 0996.90006 |

[9] | Heching, A.; Gallego, G.; Van Ryzin, G., Markdown pricing: an empirical analysis of policies and revenue potential at one apparel retailer, J. revnue pricing manage., 1, 2, 139-160, (2002) |

[10] | Reiner, G.; Natter, M., An encompassing view on markdown pricing strategies: an analysis of the Austrian mobile phone market, OR spectrum, 29, 173-192, (2007) · Zbl 1144.90429 |

[11] | Elmaghraby, W.; Gülcü, A.; Keskinocak, P., Designing optimal preannounced markdowns in the presence of rational customers with multiunit demands, Manufact. service oper. manage., 10, 1, 126-148, (2008) |

[12] | Mantrala, M.; Rao, S., A decision-support system that helps retailers decide order quantities and markdowns for fashion goods, Interfaces, 31, 3, 146-165, (2001) |

[13] | Nair, A.; Closs, D.J., An examination of the impact of coordinating supply chain policies and price markdowns on short lifecycle product retail performance, Int. J. prod. econ., 102, 379-392, (2006) |

[14] | Bhattacharjee, S.; Ramesh, R., A multi-period profit maximizing model for retail supply chain management: an integration of demand and supply-side mechanisms, Eur. J. oper. res., 122, 584-601, (2000) · Zbl 0961.90004 |

[15] | Urban, T.L.; Baker, R.C., Optimal ordering and pricing policies in a single-period environment with multivariate demand and markdowns, Eur. J. oper. res., 103, 573-583, (1997) · Zbl 0921.90065 |

[16] | Nam, S.; Logendran, R., Aggregate production planning – a survey of models and methodologies, Eur. J. oper. res., 61, 255-272, (1992) |

[17] | Tang, J.; Wang, D.; Fang, R.Y.K., Fuzzy formulation for multi-product aggregate production planning, Prod. plan. control, 11, 7, 670-676, (2000) |

[18] | 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 |

[19] | Liang, T.F., Integrating production – transportation planning decision with fuzzy multiple goals in supply chains, Int. J. prod. res., 46, 1477-1494, (2008) · Zbl 1160.90714 |

[20] | Torabi, S.A.; Hassini, E., Multi-site production planning integrating procurement and distribution plans in multi-echelon supply chains: an interactive fuzzy goal programming approach, Int. J. prod. res., 47, 19, 5475-5499, (2009) · Zbl 1198.90150 |

[21] | Aliev, R.A.; Fazlollahi, B.; Guirimov, B.G.; Aliev, R.R., Fuzzy-genetic approach to aggregate production-distribution planning in supply chain management, Inform. sci., 177, 4241-4255, (2007) · Zbl 1142.90416 |

[22] | Ertek, G.; Griffin, P.M., Supplier- and buyer-driven channels in a two-stage supply chain, IIE trans., 34, 691-700, (2002) |

[23] | Raju, J.; Zhang, Z.J., Channel coordination in the presence of a dominant retailer, Market. sci., 24, 254-262, (2005) |

[24] | Luo, W., An integrated inventory system for perishable goods with backordering, Comput. ind. eng., 34, 685-693, (1998) |

[25] | 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) |

[26] | Haugen, K.K.; Olstad, A.; Pettersen, B.I., The profit maximizing capacitated lot-size (PCLSP) problem, Eur. J. oper. res., 176, 165-176, (2007) · Zbl 1137.90619 |

[27] | Erenguc, S.S.; Simpson, N.C.; Vakharia, A.J., Integrated production/distribution planning in supply chains: an invited review, Eur. J. oper. res., 115, 219-236, (1999) · Zbl 0949.90658 |

[28] | Abad, P.L., Supplier pricing and lot-sizing when demand is price sensitive, Eur. J. oper. res., 78, 334-354, (1994) · Zbl 0816.90045 |

[29] | Abad, P.L., Optimal pricing and lot-sizing under conditions of perishability and partial back-ordering, Manage. sci., 42, 1093-1104, (1996) · Zbl 0879.90069 |

[30] | Mondal, B.; Bhunia, A.K.; Maiti, M., Inventory models for defective items incorporating marketing decisions with variable production cost, Appl. math. model., 33, 2845-2852, (2009) · Zbl 1205.90039 |

[31] | Philips, R.L., Pricing and revenue optimization, (2005), Stanford University Press California |

[32] | Berry, L.L., Retail businesses are service businesses, J. retail., 62, 1, 3-6, (1986) |

[33] | Mulhern, F.J., Retail marketing: from distribution to integration, Int. J. res. mark., 14, 2, 103-124, (1997) |

[34] | Roy, T.K.; Maiti, M., Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment, Comput. oper. res., 25, 1085-1095, (1998) · Zbl 1042.90511 |

[35] | Tiwari, R.N.; Harmar, S.; Rao, J.R., Fuzzy goal programming—an additive model, Fuzzy sets syst., 24, 27-34, (1987) · Zbl 0627.90073 |

[36] | Parra, M.A.; Terol, A.B.; Gladish, B.P.; Rodriguez, M.V., Solving a multiobjective possibilistic problem through compromise programming, Eur. J. oper. res., 164, 748-759, (2005) · Zbl 1057.90056 |

[37] | Jimenez, M.; Arenas, M.; Bilbao, A.; Rodriguez, M.V., Linear programming with fuzzy parameters: an interactive method resolution, Eur. J. oper. res., 177, 1599-1609, (2007) · Zbl 1102.90345 |

[38] | Lai, Y.J.; Hwang, C.L., A new approach to some possibilistic linear programming problems, Fuzzy sets syst., 49, 121-133, (1992) |

[39] | L.A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning. Parts 1, 2 and 3, Inform. Sci. 8 (1975) 199-249, 301-357; 9 (1976) 43-80. · Zbl 0397.68071 |

[40] | Li, L.; Lai, K.K., Fuzzy dynamic programming approach to hybrid multi objective multi stage decision making problems, Fuzzy sets syst., 117, 13-25, (2001) · Zbl 1002.90108 |

[41] | 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 |

[42] | Narasimhan, R., Goal programming in a fuzzy environment, Decision sci., 11, 325-336, (1980) |

[43] | Tiwari, R.N.; Dharmar, S.; Rao, J.R., Priority structure in fuzzy goal programming, Fuzzy sets syst., 19, 251-259, (1986) · Zbl 0602.90078 |

[44] | Chen, L.H.; Tsai, F.C., Fuzzy goal programming with different importance and priorities, Eur. J. oper. res., 133, 548-556, (2001) · Zbl 1053.90140 |

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.