Browsing by Subject "Assortment optimization"

Now showing 1 - 5 of 5

Open Access
Assortment planning under non-linear cost structures
(2019-04) Shams, Farzad
We first consider the assortment optimization problem with fixed product costs under the Mixtures of Multinomials (MMNL) Model. The problem is NP-hard even under the Multinomial Logit Model and the existing literature focuses on developing heuristics and bounds. We develop a conic integer programming formulation for the problem and valid inequalities to strengthen the formulation. We show that this approach can be used to solve instances that are very large { sizes beyond which it would be very difficult to accurately estimate parameters of the choice model { in a short amount of time, eliminating the need to develop and implement specialized algorithms for the problem. We also study the assortment planning problem where the inventory and replenishment costs are considered using the Economic Order Quantity model and the customers' choice is governed by the MMNL model. We show that the problem is NP-hard and propose a conic integer program for this problem. Our numerical experiments show that moderately sized instances can be solved in reasonable times and McCormick inequalities are effective in tightening the formulation.
Open Access
Capacitated assortment optimization and pricing problems under mixed multinomial logit model
(2016-08) Ghaniabadi, Mehdi
We study capacitated assortment optimization problem under mixed multinomial logit model where a retailer wants to choose the set of products to offer to various customer segments with the goal of maximizing revenue while satisfying different capacity constraints. Each customer segment is identiffed with a unique purchase behaviour modelled by multinomial logit demand. We consider three general cases of capacity constraints: single resource constraint, multiple resource constraints and multiple cardinality constraints. This problem is NP-hard and there exist two approaches to find exact solutions: formulating the problem as a mixed integer linear program (MILP) or a mixed integer conic quadratic program (CONIC). For each constraint structure, we develop new efficient procedures to derive McCormick valid inequalities. We provide extensive numerical studies the results of which demonstrate that when the CONIC model is accompanied with the McCormick inequalities, the problem can be solved effectively even for large sized instances using a commercial optimization software. We also study joint pricing and assortment optimization problem with a single cardinality constraint and establish a new procedure to construct McCormick inequalities. We then present the related numerical studies which indicate that the CONIC formulation accomplishes the best outcome in the presence of the McCormick inequalities.
Open Access
A Conic Integer Programming Approach to Constrained Assortment Optimization under the Mixed Multinomial Logit Model
(Institute for Operations Research and the Management Sciences (INFORMS), 2017-08-12) Şen, Alper; Atamtürk, Alper; Kaminsky, P.
We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations. This has motivated recent research exploring customized optimization strategies and approximation techniques. In contrast, we develop a novel conic quadratic mixed-integer formulation. This new formulation, together with McCormick inequalities exploiting the capacity constraints, enables the solution of large instances using commercial optimization software.
Open Access
A model and case study for efficient shelf usage and assortment analysis
(Springer, 2010) Fadıloğlu, M. M.; Karaşan, O. E.; Pinar, M. C.
In the rapidly changing environment of Fast Moving Consumer Goods sector where new product launches are frequent, retail channels need to reallocate their shelf spaces intelligently while keeping up their total profit margins, and to simultaneously avoid product pollution. In this paper we propose an optimization model which yields the optimal product mix on the shelf in terms of profitability, and thus helps the retailers to use their shelves more effectively. The model is applied to the shampoo product class at two regional supermarket chains. The results reveal not only a computationally viable model, but also substantial potential increases in the profitability after the reorganization of the product list.
Open Access
Technical note-a conic integer optimization approach to the constrained assortment problem under the mixed multinomial logit model
(INFORMS The Institute for Operations Research and the Management Sciences, 2018) Şen, A.; Atamtürk, A.; Kaminsky, P.
We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations. This has motivated recent research exploring customized optimization strategies and approximation techniques. In contrast, we develop a novel conic quadratic mixed-integer formulation. This new formulation, together with McCormick inequalities exploiting the capacity constraints, enables the solution of large instances using commercial optimization software.