Assortment Optimization under the Multi-Purchase Multinomial Logit Choice Model

2021 ◽  
Author(s):  
Jacob Feldman ◽  
Danny Segev ◽  
Huseyin Topaloglu ◽  
Laura Wagner ◽  
Yicheng Bai
Keyword(s):  
Choice Model ◽  
Multinomial Logit ◽  
Assortment Optimization

Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection

2021 ◽  
Author(s):  
Pin Gao ◽  
Yuhang Ma ◽  
Ningyuan Chen ◽  
Guillermo Gallego ◽  
Anran Li ◽  
...  
Keyword(s):  
Logit Model ◽  
Choice Model ◽  
Multinomial Logit Model ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Multinomial Logit ◽  
Impatient Customers ◽  
Purchasing Decisions ◽  
Assortment Optimization ◽  
Decision Variables

Sequential Recommendation Under the Multinomial Logit Model with Impatient Customers In many applications, customers incrementally view a subset of offered products and make purchasing decisions before observing all the offered products. In this case, the decision faced by a firm is not only what assortment of products to offer, but also in what sequence to offer the products. In “Assortment Optimization and Pricing Under the Multinomial Logit Model with Impatient Customers: Sequential Recommendation and Selection”, Gao, Ma, Chen, Gallego, Li, Rusmevichientong, and Topaloglu propose a choice model where each customer incrementally view the assortment of products in multiple stages, and their patience level determines the maximum number of stages. Under this choice model, the authors develop a polynomial-time algorithm that finds a revenue-maximizing sequence of assortments. If the sequence of assortments is fixed, the problem of finding revenue-maximizing prices can be transformed to a convex program. They combine these results to develop an effective approximation algorithm when both the sequence of assortments and prices are decision variables.

scholarly journals A regret lower bound for assortment optimization under the capacitated MNL model with arbitrary revenue parameters

2021 ◽  
pp. 1-9
Author(s):  
Yannik Peeters ◽  
Arnoud V. den Boer
Keyword(s):  
Lower Bound ◽  
Incomplete Information ◽  
Positive Constant ◽  
Time Horizon ◽  
Choice Model ◽  
Multinomial Logit ◽  
Asymptotically Optimal ◽  
Assortment Optimization ◽  
Mnl Model ◽  
Expected Revenue

Abstract In this note, we consider dynamic assortment optimization with incomplete information under the capacitated multinomial logit choice model. Recently, it has been shown that the regret (the cumulative expected revenue loss caused by offering suboptimal assortments) that any decision policy endures is bounded from below by a constant times $\sqrt {NT}$ , where $N$ denotes the number of products and $T$ denotes the time horizon. This result is shown under the assumption that the product revenues are constant, and thus leaves the question open whether a lower regret rate can be achieved for nonconstant revenue parameters. In this note, we show that this is not the case: we show that, for any vector of product revenues there is a positive constant such that the regret of any policy is bounded from below by this constant times $\sqrt {N T}$ . Our result implies that policies that achieve ${{\mathcal {O}}}(\sqrt {NT})$ regret are asymptotically optimal for all product revenue parameters.

Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint

2010 ◽  
Vol 58 (6) ◽  
pp. 1666-1680 ◽  
Author(s):  
Paat Rusmevichientong ◽  
Zuo-Jun Max Shen ◽  
David B. Shmoys
Keyword(s):  
Choice Model ◽  
Multinomial Logit ◽  
Capacity Constraint ◽  
Assortment Optimization

Assortment Optimization under the Multinomial Logit Model with Random Choice Parameters

2014 ◽  
Vol 23 (11) ◽  
pp. 2023-2039 ◽  
Author(s):  
Paat Rusmevichientong ◽  
David Shmoys ◽  
Chaoxu Tong ◽  
Huseyin Topaloglu
Keyword(s):  
Logit Model ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Random Choice ◽  
Assortment Optimization

scholarly journals Integrating Dynamic Pricing and Inventory Control for Fresh Agriproduct under Multinomial Logit Choice

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Xiong-zhi Wang ◽  
Wenliang Zhou
Keyword(s):  
Dynamic Pricing ◽  
Programming Model ◽  
Choice Model ◽  
Multinomial Logit ◽  
Linear Ordering ◽  
Stochastic Dynamic ◽  
Inventory Problem ◽  
Numerical Illustration ◽  
Dynamic Stochastic ◽  
Joint Pricing

In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh agriproducts (FAPs) with two-period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period the retailer makes ordering decision for new FAP and sets regular and discount price for new and old inventories, respectively. After demand realization, the expired leftover is disposed and unexpired inventory is carried to the next period, continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximize the total expected discount profit over the whole planning horizon. We present a price-dependent, stochastic dynamic programming model taking into account zero lead time, linear ordering costs, inventory holding, and backlogging costs, as well as disposal cost. Considering the influence of the perishability, we integrate a Multinomial Logit (MNL) choice model to describe the consumer behavior on purchasing fresh or nonfresh product. By way of the inverse of the price vector, the original formulation can be transferred to be jointly concave and tractable. Finally we characterize the optimal policy and develop effective methods to solve the problem and conduct a simple numerical illustration.

Optimal Policy for Dynamic Assortment Planning Under Multinomial Logit Models

2021 ◽  
Author(s):  
Xi Chen ◽  
Yining Wang ◽  
Yuan Zhou
Keyword(s):  
Choice Model ◽  
Current Knowledge ◽  
Search Algorithm ◽  
Multinomial Logit ◽  
Planning Problem ◽  
Assortment Planning ◽  
Substitutable Products ◽  
Dynamic Decisions ◽  
Mnl Model ◽  
Regret Bound

We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and the customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Because all the utility parameters of the MNL model are unknown, the seller needs to simultaneously learn customers’ choice behavior and make dynamic decisions on assortments based on the current knowledge. The goal of the seller is to maximize the expected revenue, or, equivalently, to minimize the expected regret. Although dynamic assortment planning problem has received an increasing attention in revenue management, most existing policies require the estimation of mean utility for each product and the final regret usually involves the number of products [Formula: see text]. The optimal regret of the dynamic assortment planning problem under the most basic and popular choice model—the MNL model—is still open. By carefully analyzing a revenue potential function, we develop a trisection-based policy combined with adaptive confidence bound construction, which achieves an item-independent regret bound of [Formula: see text], where [Formula: see text] is the length of selling horizon. We further establish the matching lower bound result to show the optimality of our policy. There are two major advantages of the proposed policy. First, the regret of all our policies has no dependence on [Formula: see text]. Second, our policies are almost assumption-free: there is no assumption on mean utility nor any “separability” condition on the expected revenues for different assortments. We also extend our trisection search algorithm to capacitated MNL models and obtain the optimal regret [Formula: see text] (up to logrithmic factors) without any assumption on the mean utility parameters of items.

scholarly journals Multi-route choice modelling in a metropolitan context: A comparative analysis using Multinomial Logit and Fuzzy Logic based approaches

2020 ◽  
Vol 79 (ET.2020) ◽  
pp. 1-17
Author(s):  
Sowjanya Dhulipala
Keyword(s):  
Decision Making ◽  
Fuzzy Logic ◽  
Choice Model ◽  
Route Choice ◽  
Fuzzy Rule ◽  
Multinomial Logit ◽  
Choice Modelling ◽  
Choice Behaviour ◽  
Linguistic Rules ◽  
Mnl Model

Route choice plays a vital role in the traffic assignment and network building, as it involves decision making on part of riders. The vagueness in travellers’ perceptions of attributes of the available routes between any two locations adds to the complexities in modelling the route choice behaviour. Conventional Logit models fail to address the uncertainty in travellers’ perceptions of route characteristics (especially qualitative attributes, such as environmental effects), which can be better addressed through the theory of fuzzy sets and linguistic variables. This study thus attempts to model travellers’ route choice behaviour, using a fuzzy logic approach that is based on simple and logical ‘if-then’ linguistic rules. This approach takes into consideration the uncertainty in travellers’ perceptions of route characteristics, resembling humans’ decision-making process. Three attributes – travel time, traffic congestion, and road-side environment are adopted as factors driving people’s choice of routes, and three alternative routes between two typical locations in an Indian metropolitan city, Surat, are considered in the study. The approach to deal with multiple routes is shown by analyzing two-wheeler riders’ (e.g. motorcyclists’ and scooter drivers’) route choice behaviour during the peak-traffic time. Further, a Multinomial Logit (MNL) model is estimated, to enable a comparison of the two modelling approaches. The estimated Fuzzy Rule-Based Route Choice Model outperformed the conventional MNL model, accounting for the uncertain behaviour of travellers.

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