Robust optimization approach for pricing and shelf space decisions with uncertain demand

Document Type : Article

Authors

1 Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez avenue, 1591634311, Tehran, Iran

2 Amirkabir University of Technology, Department of Industrial Engineering, 424, Hafez Avenue, Tehran, Iran

Abstract

Pricing and shelf space allocation are two main operational decisions in retailing industry. This study simultaneously optimizes these two decisions in a supply chain with two manufacturers and one retailer under uncertainty of demand and price sensitivity parameters. Two manufacturers have different conditions in terms of parameters affecting demand and production. A robust optimization model and an exact solution approach are developed to find the optimal solution. The results show that price sensitivity, market potential and production costs can have a synergistic effect on optimal values. Moreover, the market potential can be relied on in managerial decisions as it has significantly positive impact on profitability. This parameter is found to be the most important tool for securing profitability of supply chain members.

Keywords

References

References:
1. Anderson, E.E. and Amato, H.N., "A mathematical model for simultaneously determining the optimal brand-collection and display-area allocation", Operations Research, 22(1), pp. 13-21 (1974).
2. Corstjens, M. and Doyle, P. "A model for optimizing retail space allocation", Management Science, 27(7), pp. 822-833 (1981).
3. Corstjens, M. and Doyle, P. "A dynamic model for strategically allocating retail space", The Journal of 312 M.S. Sajadieh and M. Danaei/Scientia Iranica, Transactions E: Industrial Engineering 29 (2022) 303-319 the Operational Research Society, 34(10), pp. 943-951 (1983).
4. Bultez, A. and Naert, P. "Shelf allocation for retailers' profit", Marketing Science, 7(3), pp. 211-231 (1988).
5. Yang, M.H. "An efficient algorithm to allocate shelf space", European Journal of Operational Research, 131(1), pp. 107-118 (2001).
6. Hwang, H., Choi, B., and Lee, M.J. "A model for shelf space allocation and inventory control considering location and inventory level effects on demand", International Journal of Production Economics, 97, pp. 185-195 (2005).
7. Hansen, J.M., Raut, S., and Swami, S. "Retail shelf allocation: a comparative analysis of heuristic and metaheuristic approaches", Journal of Retailing, 86(1), pp. 94-105 (2010).
8. Castelli, M. and Vanneschi, L. "Genetic algorithm with variable neighborhood search for the optimal allocation of goods in shop shelves", Operations Research Letters, 42, pp. 355-360 (2014).
9. Zhou, W. and Piramuthu, S. "IoT and supply chain traceability", 1st International Conference on Future Network Systems and Security, FNSS, Paris, June, pp. 11-13 (2015).
10. Amit, R.K., Mehta, P., and Tripathi, R.P. "Optimal shelf-space stocking policy using stochastic dominance under supply-driven demand uncertainty", European Journal of Operational Research, 246(1), pp. 339-342 (2015).
11. Hubner, A. and Schaal, K. "An integrated assortment and shelf-space optimization model with demand substitution and space-elasticity effects", European Journal of Operational Research, 261(1), pp. 302-316 (2017).
12. Fatemi Ghomi, S.M.T. and Khalesi, S. "A hybrid approach for shelf space planning considering of stochastic demand and display facing area", 13th International Conference on Industrial Engineering (IIEC 2017) (2017).
13. Dusterhoft, T., Hubner, A., and Schaal, K. "A practical approach to the shelf-space allocation and replenishment
problem with heterogeneously sized shelves", European Journal of Operational Research, 282(1), pp. 252-266 (2020).
14. Gajjar, H.K. and Adil, G.K. "A dynamic programming heuristic for retail shelf space allocation problem", Asia-Pacific Journal of Operational Research, 28(2), pp. 183-199 (2011).
15. Gilland, W.G. and Heese, H.S. "Sequence matters: shelf-space allocation under dynamic customer-driven substitution", Production and Operations Management, 22(4), pp. 875-887 (2013).
16. Martin-Herran, G. and Taboubi, S. "Shelf-space allocation and advertising decisions in the marketing channel: a differential game approach", International Game Theory Review, 7(3), pp. 313-330 (2005).
17. Hariga, M.A. and Al-Ahmari, A. "An integrated retail space allocation and lot sizing models under vendor managed inventory and consignment stock arrangements", Computers & Industrial Engineering, 64(1), pp. 45-55 (2013).
18. Tsao, Y.C., Lu, J.C., A.n, N., et al. "Retailer shelfspace management with trade allowance: A Stackelberg game between retailer and manufacturers", International Journal of Production Economics, 148, pp. 133-144 (2014).
19. Urban, T.L. "An inventory-theoretic approach to product assortment and shelf-space allocation", Journal of Retailing, 74(1), pp. 15-35 (1998).
20. Maiti, M.K. and Maiti, M. "Multi-item shelf-space allocation of breakable items via genetic algorithm", Journal of Applied Mathematics & Computing, 20(1-2), pp. 327-343 (2006).
21. Hariga, M.A., Al-Ahmari, A., and Mohamed, A.A. "A joint optimisation model for inventory replenishment,product assortment, shelf space and display area allocation decisions", European Journal of Operational Research, 181(1), pp. 239-251 (2007).
22. Ramaseshan, B., Achuthan, N.R., and Collinson, R. "Decision support tool for retail shelf space optimization", International Journal of Information Technology & Decision Making, 7(3), pp. 547-565 (2008).
23. Bai, R. and Kendall, G. "A model for fresh produce shelf-space allocation and inventory management with freshness-condition-dependent demand", Journal of Computing, 20(1), pp. 78-85 (2008).
24. Gao, J.J. and Yu, L.R. "Joint decision model of variants selection, shelf-space allocation and inventory control", Xitong Gongcheng Xuebao, 24(5), pp. 614- 620 (2009).
25. Baron, O., Berman, O., and Perry, D. "Shelf space management when demand depends on the inventory level", Production and Operations Management, 20(5), pp. 714-726 (2011).
26. Hwang, H., Choi, B., and Lee, G. "A genetic algorithm approach to an integrated 12 problem of shelf space design and item allocation", Computers & Industrial Engineering, 56, pp. 809-820 (2009).
27. Ghazavi, E. and Lotfi, M.M. "Formulation of customers' shopping path in shelf space planning: A simulation-optimization approach", Expert Systems with Applications, 55, pp. 243-254 (2016).
28. Flamand, T., Ghoniem, A., Haouari, M., and Maddah, B. "Integrated assortment planning and storewide shelf space allocation: An optimization-based approach", Omega, 81, pp. 134-149 (2018).
29. Schaal, K. and Hubner, A. "When does cross-space elasticity matter in shelf-space planning? A decision analytics approach", Omega, 80, pp. 135-152 (2018).
30. Shafiee-Gole, S., Nasiri, M., and Taleizadeh, A. "Pricing and production decisions in multi-product single machine manufacturing system with discrete delivery and rework", OPSEARCH (2016).
31. Sadjadi, S.J., Asadi, H., Sadeghian, R., et al. "Retailer Stackelberg game in a supply chain with pricing and service decisions and simple price discount contract", PLOS ONE, 13(4), e0195109 (2018). https://doi.org/10.1371/journal.pone.0195109.
32. Reyes, P.M. and Frazier, G.V. "Goal programming model for grocery shelf space allocation", European Journal of Operational Research, 181(2), pp. 634-644 (2007).
33. Murray, C.C., Talukdar, D., and Gosavi, A. "Joint optimization of product price, display orientation and shelf-space allocation in retail category management, Journal of Retailing, 86(2), pp. 125-136 (2010).
34. Tan, M. and Wang, H. "Retailer's shelf-space and pricing decisions under revenue sharing contracts", International Conference on Management and Service Science (2011).
35. Kurtulus, M. and Toktay, L.B. "Category captainship vs. retailer category management under limited retail shelf space", Production and Operations Management Society, 20, pp. 47-56 (2011).
36. Leng, M., Parlar, M., and Zhang, D., Retail Space-Exchange Problem with Pricing and Space Allocation Decisions, Production and Operations Management Society, pp. 1|14 (2011).
37. Li, X. Nukal, S., and Moheb, S. "Game theory methodology for optimizing retailers' pricing and shelf-space allocation decisions on competing substitutable products", International Journal of Advanced Design and Manufacturing Technology, 68, pp. 375-389 (2013).
38. Eisend, M. "Shelf space elasticity: A meta-analysis", Journal of Retailing, 90(2), pp. 168-181 (2014).
39. Wang, S.Y., Sheen, G.J., and Yeh, Y. "Pricing and shelf space decisions with non-symmetric market demand", International Journal of Production Economics, 169, pp. 233-239 (2015).
40. Hubner, A. and Schaal, K. "A shelf-space optimization model when demand is stochastic and space-elastic", Omega, 68, pp. 139-154 (2017).
41. Moon, I., Park, K.S, Hao, J., and Kim, D. "Joint decisions on product line selection, purchasing, and pricing", European Journal of Operational Research, 262(1), pp. 207-216 (2017).
42. Li, H.L. "An efficient method for solving linear goal programming problems", Journal of Optimization Theory and Applications, 90, pp. 465-469 (1996).
43. Mirzapour, Al-e-hashem, S.M.J., Malekly, H., and Aryanezhad, M.B. "A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty", International Journal of Production Economics, 134, pp. 28-42 (2011).
44. Mulvey, J.M., Vanderbei, R.J., and Zenios, S.A. "Robust optimization of large-scale systems", Operations Research, 43(2), pp. 264-281 (1995).
45. Feng, P. and Rakesh, N. "Robust supply chain design under uncertain demand in agile manufacturing", Computers & Operations Research, 37(4), pp. 668-683 (2010).
46. Leung, S.C.H., Tsang, S.O.S., Ng., W.L., et al. "A robust optimization model for multi-site production planning problem in an uncertain environment, European Journal of Operational Research, 181(1), pp. 224-238 (2007).
47. Wagner, H.M., Principles of Operations Research, Second Ed., Prentice Hall, New Jersey (1975).
48. Yu, C.S. and Li, H.L. "A robust optimization model for stochastic logistic problem", International Journal of Production Economics, 64(1-3), pp. 385-397 (2000).
49. Shubik, M. and Levitan, R., Market Structure and Behavior, Harvard University Press, Cambridge (1980).
Scientia Iranica
Volume 29, Issue 1
Transactions on Industrial Engineering (E)
January and February 2022
Pages 303-319

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History

  • Receive Date: 01 April 2019
  • Revise Date: 18 March 2020
  • Accept Date: 11 May 2020

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