An efficient method for joint product line selection and pricing with fixed costs. (English) Zbl 1422.91274
Summary: In this paper, we propose an exact solution approach to solve a joint product line selection and pricing problem with a fixed cost factor. We adopt the multinomial logit model to estimate the sales of each marketed product, and suppose that the introduction of each product to the market incurs some constant fixed costs. Utilizing an implicit function form of the optimal price, we transform the original problem into the one with the decision variables for the product introduction only. The efficiency of the proposed transformation approach is demonstrated through simulations. We further discuss its applicability to generalized problems.
Software:
KNITROReferences:
| [1] | Aydin, G., Ryan, J.K.: Product line selection and pricing under the multinomial logit choice model (2000) |
| [2] | Ben-Akiva, M.E., Lerman, S.R.: Discrete Choice Analysis: Theory and Application to Travel Demand, p. 9. MIT Press, Cambridge (1985) |
| [3] | Byrd, RH; Nocedal, J.; Waltz, RA; Pillo, G. (ed.); Roma, M. (ed.), Knitro: an integrated package for nonlinear optimization, 35-59 (2006), Berlin · Zbl 1108.90004 · doi:10.1007/0-387-30065-1_4 |
| [4] | Caro, F., Martínez-de Albéniz, V., Rusmevichientong, P.: The assortment packing problem: multiperiod assortment planning for short-lived products. Manag. Sci. 60(11), 2701-2721 (2014) · doi:10.1287/mnsc.2014.1991 |
| [5] | Chhajed, D., Raman, N.: An integrated approach to product design and process selection. BEBR Faculty Working Paper; No. 92-0178 (1992) |
| [6] | Davis, J., Gallego, G., Topaloglu, H.: Assortment planning under the multinomial logit model with totally unimodular constraint structures. Cornell (2013) |
| [7] | Davis, J.M., Gallego, G., Topaloglu, H.: Assortment optimization under variants of the nested logit model. Oper. Res. 62(2), 250-273 (2014) · Zbl 1295.90076 · doi:10.1287/opre.2014.1256 |
| [8] | Dence, T.P.: A brief look into the Lambert W function. Appl. Math. 4(6), 887 (2013) · doi:10.4236/am.2013.46122 |
| [9] | Dobson, G., Yano, C.A.: Product line and technology selection with shared manufacturing and engineering design resources. Simon School of Business Working Paper OP 95-01 (1995) |
| [10] | Gallego, G., Wang, R.: Multiproduct price optimization and competition under the nested logit model with product-differentiated price sensitivities. Oper. Res. 62(2), 450-461 (2014) · Zbl 1298.91087 · doi:10.1287/opre.2013.1249 |
| [11] | Kunnumkal, S., Martnez-de-Albniz, V.: Tractable Models and Algorithms for Assortment Planning with Product Costs. Project Report. Indian School of Business, Hyderabad (2016) |
| [12] | Li, H., Huh, W.T.: Pricing multiple products with the multinomial logit and nested logit models: concavity and implications. Manuf. Serv. Oper. Manag. 13(4), 549-563 (2011) · doi:10.1287/msom.1110.0344 |
| [13] | Li, H., Webster, S., Mason, N., Kempf, K.: Winner-2017 M&SOM practice-based research competition—product-line pricing under discrete mixed multinomial logit demand. Manuf. Serv. Oper, Manag (2018). https://doi.org/10.1287/msom.2017.0675 |
| [14] | Maddah, B., Bish, E.K.: Joint pricing, assortment, and inventory decisions for a retailer’s product line. Naval Res. Logist. (NRL) 54(3), 315-330 (2007) · Zbl 1149.90305 · doi:10.1002/nav.20209 |
| [15] | Méndez-Díaz, I., Miranda-Bront, J.J., Vulcano, G., Zabala, P.: A branch-and-cut algorithm for the latent-class logit assortment problem. Discrete Appl. Math. 164, 246-263 (2014) · Zbl 1326.90041 · doi:10.1016/j.dam.2012.03.003 |
| [16] | Moorthy, K.S.: Market segmentation, self-selection, and product line design. Mark. Sci. 3(4), 288-307 (1984) · doi:10.1287/mksc.3.4.288 |
| [17] | Rusmevichientong, P., Shen, Z.J.M., Shmoys, D.B.: Dynamic assortment optimization with a multinomial logit choice model and capacity constraint. Oper. Res. 58(6), 1666-1680 (2010) · Zbl 1228.90170 · doi:10.1287/opre.1100.0866 |
| [18] | Rusmevichientong, P., Shmoys, D., Tong, C., Topaloglu, H.: Assortment optimization under the multinomial logit model with random choice parameters. Prod. Oper. Manag. 23(11), 2023-2039 (2014) · doi:10.1111/poms.12191 |
| [19] | Rusmevichientong, P., Topaloglu, H.: Robust assortment optimization in revenue management under the multinomial logit choice model. Oper. Res. 60(4), 865-882 (2012) · Zbl 1262.90205 · doi:10.1287/opre.1120.1063 |
| [20] | Ryzin, G.V., Mahajan, S.: On the relationship between inventory costs and variety benefits in retail assortments. Manag. Sci. 45(11), 1496-1509 (1999) · Zbl 0953.90002 · doi:10.1287/mnsc.45.11.1496 |
| [21] | Schön, C.: On the product line selection problem under attraction choice models of consumer behavior. Eur. J. Oper. Res. 206(1), 260-264 (2010) · Zbl 1188.91106 · doi:10.1016/j.ejor.2010.01.012 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
