A fuzzy goal programming approach for mid-term assortment planning in supermarkets. (English) Zbl 1215.90036

Summary: We develop a fuzzy mixed integer non-linear goal programming model for the mid-term assortment planning of supermarkets in which three conflicting objectives namely profitability, customer service, and space utilization are incorporated. The items and brands in a supermarket compete to obtain more space and better shelf level. This model offers different service levels to loyal and disloyal customers, applies joint replenishment policy, and accounts for the holding time limitation of perishable items. We propose a fuzzy approach due to the imprecise nature of the goals’ target levels and priorities as well as critical data. A heuristic method inspiring by the problem-specific rules is developed to solve this complex model approximately within a reasonable time. Finally, the proposed approach is validated through several numerical examples and results are reported.


90B60 Marketing, advertising
90C29 Multi-objective and goal programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Full Text: DOI


[1] Akoz, O.; Petrovic, D., A fuzzy goal programming method with imprecise goal hierarchy, European Journal of Operational Research, 181, 1427-1433 (2007) · Zbl 1123.90082
[2] Bellman, R. E.; Zadeh, L. A., Decision making in a fuzzy environment, Management Science, 17, 2, 141-164 (1970) · Zbl 0224.90032
[3] Borin, N.; Farris, P.; Freeland, J., A model for determining retail product category and shelf space allocation, Decision Science, 25, 3, 359-384 (1994)
[4] Chen, L. H.; Tsai, F. C., Fuzzy goal programming with different importance and priorities, European Journal of Operational Research, 133, 548-556 (2001) · Zbl 1053.90140
[5] Corstjens, M.; Doyle, P., A model for optimizing retail space allocations, Management Science, 27, 7, 822-833 (1981)
[6] Dreze, X.; Hoch, S. J.; Purk, M. E., Shelf management and space elasticity, Journal of Retailing, 70, 4, 301-326 (1994)
[8] Fadiloglu, M. M.; Karasan, O. E.A.; Pinar, M. C., Model and case study for efficient shelf usage and assortment analysis, Annals of Operational research (2008)
[9] Gass, S. I., The setting of weights in linear goal-programming problems, Computers and Operations Research, 14, 3, 227-229 (1987)
[10] Hansen, J. M.; Raut, S.; Swami, S., Retail shelf allocation: A comparative analysis of heuristic and Meta-heuristic approaches, Journal of Retailing, 86, 1, 94-105 (2010)
[11] Hariga, M. A.; Al-Ahmari, A.; Mohamed, A. A., A joint optimization model for inventory replenishment, product assortment, shelf space and display area allocation decisions, European Journal of Operational Research, 181, 239-251 (2007) · Zbl 1121.90303
[12] Hu, C. F.; Teng, C. J.; Li, S. Y., A fuzzy goal programming approach to multi-objective optimization problem with priorities, European Journal of Operational Research, 176, 1319-1333 (2007) · Zbl 1109.90070
[13] Hwang, H.; Choi, B.; Lee, M., A model for shelf space allocation and inventory control considering location and inventory level effects on demand, International Journal of Production Economics, 97, 185-195 (2005)
[14] Lai, Y. J.; Hwang, C. L., A new approach to some possibilistic linear programming problems, Fuzzy Sets and Systems, 49, 121-133 (1992)
[16] Liu, B.; Liu, Y.-K., Expected value of fuzzy variable and expected value models, IEEE Transactions on Fuzzy Systems, 10, 4, 445-450 (2002)
[17] Mandal, N. K.; Roy, T. K., A displayed inventory model with L-R fuzzy number, Fuzzy Optimization and Decision Making, 5, 227-243 (2006) · Zbl 1135.90447
[18] Narasimhan, R., Goal programming in a fuzzy environment, Decision Science, 11, 325-336 (1980)
[19] Pedrycz, W., Why triangular membership functions?, Fuzzy Sets and Systems, 64, 21-30 (1994)
[20] Reyes, P. M.; Fraizer, G. V., Goal programming model for grocery shelf space allocation, European Journal of Operational Research, 181, 634-644 (2007) · Zbl 1131.90420
[21] Romero, C., A general structure of achievement function for a goal programming model, European Journal of Operational Research, 153, 675-686 (2004) · Zbl 1099.90576
[22] Tiwari, R. N.; Dharmar, S.; Rao, J. R., Priority structure in fuzzy goal programming, Fuzzy Sets and Systems, 19, 251-259 (1986) · Zbl 0602.90078
[23] Tiwari, R. N.; Dharmar, S.; Rao, J. R., Fuzzy goal programming - An additive model, Fuzzy Sets and Systems, 24, 27-34 (1987) · Zbl 0627.90073
[24] Torabi, S. A.; Hassini, E., An interactive possibilistic programming approach for multiple objective supply chain master planning, Fuzzy Sets and Systems, 159, 193-214 (2008) · Zbl 1168.90352
[25] 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, International Journal of Production Research, 47, 19, 5475-5499 (2009) · Zbl 1198.90150
[26] Torabi, S. A.; Ebadian, M.; Tanha, R., Fuzzy hierarchical production planning (with a case study), Fuzzy Sets and Systems, 161, 1511-1529 (2010) · Zbl 1186.90046
[27] Urban, T. L., An inventory-theoretic approach to product assortment and shelf-space allocation, Journal of Retailing, 74, 1, 15-35 (1998)
[28] Van Donselaar, K.; Van Woensel, T.; Broekmeulen, R.; Fransoo, J., Inventory control of perishables in supermarkets, International Journal of Production Economics, 104, 462-472 (2006)
[29] Yang, M., An efficient algorithm to allocate shelf space, European Journal of Operational Research, 131, 107-118 (2001) · Zbl 0979.90083
[30] Yang, M.; Chen, W., A study of shelf space allocation and management, International Journal of Production Economics, 309-317 (1999)
[31] Zimmerman, H. J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 45-55 (1978) · Zbl 0364.90065
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