Online Assortment Optimization with Reusable Resources

2021 ◽  
Author(s):  
Xiao-Yue Gong ◽  
Vineet Goyal ◽  
Garud N. Iyengar ◽  
David Simchi-Levi ◽  
Rajan Udwani ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Online Algorithm ◽  
Random Number ◽  
Optimal Algorithm ◽  
User Preference ◽  
Substitutable Products ◽  
Assortment Optimization ◽  
Myopic Policy ◽  
Expected Revenue ◽  
And Performance

We consider an online assortment optimization problem where we have n substitutable products with fixed reusable capacities [Formula: see text]. In each period t, a user with some preferences (potentially adversarially chosen) who offers a subset of products, St, from the set of available products arrives at the seller’s platform. The user selects product [Formula: see text] with probability given by the preference model and uses it for a random number of periods, [Formula: see text], that is distributed i.i.d. according to some distribution that depends only on j generating a revenue [Formula: see text] for the seller. The goal of the seller is to find a policy that maximizes the expected cumulative revenue over a finite horizon T. Our main contribution is to show that a simple myopic policy (where we offer the myopically optimal assortment from the available products to each user) provides a good approximation for the problem. In particular, we show that the myopic policy is 1/2-competitive, that is, the expected cumulative revenue of the myopic policy is at least half the expected revenue of the optimal policy with full information about the sequence of user preference models and the distribution of random usage times of all the products. In contrast, the myopic policy does not require any information about future arrivals or the distribution of random usage times. The analysis is based on a coupling argument that allows us to bound the expected revenue of the optimal algorithm in terms of the expected revenue of the myopic policy. We also consider the setting where usage time distributions can depend on the type of each user and show that in this more general case there is no online algorithm with a nontrivial competitive ratio guarantee. Finally, we perform numerical experiments to compare the robustness and performance of myopic policy with other natural policies. This paper was accepted by Gabriel Weintraub, revenue management and analytics.

Assortment Optimization Under the Multinomial Logit Model with Sequential Offerings

2020 ◽  
Vol 32 (3) ◽  
pp. 835-853 ◽  
Author(s):  
Nan Liu ◽  
Yuhang Ma ◽  
Huseyin Topaloglu
Keyword(s):  
Logit Model ◽  
Optimization Problem ◽  
Approximation Scheme ◽  
Optimization Problems ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Polynomial Time Approximation Scheme ◽  
Assortment Optimization ◽  
Last Stage ◽  
Expected Revenue

We consider assortment optimization problems, where the choice process of a customer takes place in multiple stages. There is a finite number of stages. In each stage, we offer an assortment of products that does not overlap with the assortments offered in the earlier stages. If the customer makes a purchase within the offered assortment, then the customer leaves the system with the purchase. Otherwise, the customer proceeds to the next stage, where we offer another assortment. If the customer reaches the end of the last stage without a purchase, then the customer leaves the system without a purchase. The choice of the customer in each stage is governed by a multinomial logit model. The goal is to find an assortment to offer in each stage to maximize the expected revenue obtained from a customer. For this assortment optimization problem, it turns out that the union of the optimal assortments to offer in each stage is nested by revenue in the sense that this union includes a certain number of products with the largest revenues. However, it is still difficult to figure out the stage in which a certain product should be offered. In particular, the problem of finding an assortment to offer in each stage to maximize the expected revenue obtained from a customer is NP hard. We give a fully polynomial time approximation scheme for the problem when the number of stages is fixed.

Revenue-Utility Tradeoff in Assortment Optimization Under the Multinomial Logit Model with Totally Unimodular Constraints

2020 ◽  
Author(s):  
Mika Sumida ◽  
Guillermo Gallego ◽  
Paat Rusmevichientong ◽  
Huseyin Topaloglu ◽  
James Davis
Keyword(s):  
Expected Utility ◽  
Logit Model ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Multinomial Logit Model ◽  
Multinomial Logit ◽  
Solution Quality ◽  
Assortment Optimization ◽  
Unimodular Matrix ◽  
Expected Revenue

We examine the revenue–utility assortment optimization problem with the goal of finding an assortment that maximizes a linear combination of the expected revenue of the firm and the expected utility of the customer. This criterion captures the trade-off between the firm-centric objective of maximizing the expected revenue and the customer-centric objective of maximizing the expected utility. The customers choose according to the multinomial logit model, and there is a constraint on the offered assortments characterized by a totally unimodular matrix. We show that we can solve the revenue–utility assortment optimization problem by finding the assortment that maximizes only the expected revenue after adjusting the revenue of each product by the same constant. Finding the appropriate revenue adjustment requires solving a nonconvex optimization problem. We give a parametric linear program to generate a collection of candidate assortments that is guaranteed to include an optimal solution to the revenue–utility assortment optimization problem. This collection of candidate assortments also allows us to construct an efficient frontier that shows the optimal expected revenue–utility pairs as we vary the weights in the objective function. Moreover, we develop an approximation scheme that limits the number of candidate assortments while ensuring a prespecified solution quality. Finally, we discuss practical assortment optimization problems that involve totally unimodular constraints. In our computational experiments, we demonstrate that we can obtain significant improvements in the expected utility without incurring a significant loss in the expected revenue. This paper was accepted by Omar Besbes, revenue management and market analytics.

Adaptive Grouping Brain Storm Optimization for Multimodal Optimization Problems

2021 ◽  
Vol 12 (4) ◽  
pp. 81-100
Author(s):  
Yao Peng ◽  
Zepeng Shen ◽  
Shiqi Wang
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Algorithm ◽  
Peak Detection ◽  
Multimodal Optimization ◽  
Optimal Solutions ◽  
Grouping Strategy ◽  
Different Dimensions ◽  
Global Optimal ◽  
Localization Ability

Multimodal optimization problem exists in multiple global and many local optimal solutions. The difficulty of solving these problems is finding as many local optimal peaks as possible on the premise of ensuring global optimal precision. This article presents adaptive grouping brainstorm optimization (AGBSO) for solving these problems. In this article, adaptive grouping strategy is proposed for achieving adaptive grouping without providing any prior knowledge by users. For enhancing the diversity and accuracy of the optimal algorithm, elite reservation strategy is proposed to put central particles into an elite pool, and peak detection strategy is proposed to delete particles far from optimal peaks in the elite pool. Finally, this article uses testing functions with different dimensions to compare the convergence, accuracy, and diversity of AGBSO with BSO. Experiments verify that AGBSO has great localization ability for local optimal solutions while ensuring the accuracy of the global optimal solutions.

scholarly journals Location histogram privacy by Sensitive Location Hiding and Target Histogram Avoidance/Resemblance

2019 ◽  
Vol 62 (7) ◽  
pp. 2613-2651
Author(s):  
Grigorios Loukides ◽  
George Theodorakopoulos
Keyword(s):  
Price Discrimination ◽  
Optimization Problem ◽  
Optimal Algorithm ◽  
Search Space ◽  
Greedy Heuristic ◽  
Optimal Solutions ◽  
Area Of Interest ◽  
Minority Member ◽  
Specific Search

AbstractA location histogram is comprised of the number of times a user has visited locations as they move in an area of interest, and it is often obtained from the user in the context of applications such as recommendation and advertising. However, a location histogram that leaves a user’s computer or device may threaten privacy when it contains visits to locations that the user does not want to disclose (sensitive locations), or when it can be used to profile the user in a way that leads to price discrimination and unsolicited advertising (e.g., as “wealthy” or “minority member”). Our work introduces two privacy notions to protect a location histogram from these threats: Sensitive Location Hiding, which aims at concealing all visits to sensitive locations, and Target Avoidance/Resemblance, which aims at concealing the similarity/dissimilarity of the user’s histogram to a target histogram that corresponds to an undesired/desired profile. We formulate an optimization problem around each notion: Sensitive Location Hiding ($${ SLH}$$SLH), which seeks to construct a histogram that is as similar as possible to the user’s histogram but associates all visits with nonsensitive locations, and Target Avoidance/Resemblance ($${ TA}$$TA/$${ TR}$$TR), which seeks to construct a histogram that is as dissimilar/similar as possible to a given target histogram but remains useful for getting a good response from the application that analyzes the histogram. We develop an optimal algorithm for each notion, which operates on a notion-specific search space graph and finds a shortest or longest path in the graph that corresponds to a solution histogram. In addition, we develop a greedy heuristic for the $${ TA}$$TA/$${ TR}$$TR problem, which operates directly on a user’s histogram. Our experiments demonstrate that all algorithms are effective at preserving the distribution of locations in a histogram and the quality of location recommendation. They also demonstrate that the heuristic produces near-optimal solutions while being orders of magnitude faster than the optimal algorithm for $${ TA}$$TA/$${ TR}$$TR.

scholarly journals Nonlinear Inertia Weighted Teaching-Learning-Based Optimization for Solving Global Optimization Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Zong-Sheng Wu ◽  
Wei-Ping Fu ◽  
Ru Xue
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Random Number ◽  
Nonlinear Problems ◽  
Tlbo Algorithm ◽  
Teaching Learning Based Optimization ◽  
Linear And Nonlinear ◽  
Weighted Factor ◽  
Teaching Learning ◽  
Dynamic Inertia

Teaching-learning-based optimization (TLBO) algorithm is proposed in recent years that simulates the teaching-learning phenomenon of a classroom to effectively solve global optimization of multidimensional, linear, and nonlinear problems over continuous spaces. In this paper, an improved teaching-learning-based optimization algorithm is presented, which is called nonlinear inertia weighted teaching-learning-based optimization (NIWTLBO) algorithm. This algorithm introduces a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and uses a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is tested on a number of benchmark functions, and its performance comparisons are provided against the basic TLBO and some other well-known optimization algorithms. The experiment results show that the proposed algorithm has a faster convergence rate and better performance than the basic TLBO and some other algorithms as well.

scholarly journals A PARALLEL SOLVER FOR THE DESIGN OF OIL FILTERS

2011 ◽  
Vol 16 (1) ◽  
pp. 326-341 ◽  
Author(s):  
Vadimas Starikovičius ◽  
Raimondas Čiegis ◽  
Oleg Iliev
Keyword(s):  
Automotive Industry ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Geometry Optimization ◽  
Parallel Optimization ◽  
Parallel Solvers ◽  
Flow Through ◽  
And Performance ◽  
Easy Integration ◽  
Computational Resources

Nowadays, it is widely recognized that computer simulation plays a crucial role in designing oil filters used in the automotive industry. However, even a single direct simulation of the flow usually requires significant computational resources. Thus, it is obvious that solution of optimization problems is only feasible using parallel computers and algorithms.In this paper, we present a general master-slave parallel template, which was specially designed for the easy integration of direct parallel solvers into a parallel optimization tool. We show how an already existing direct solver for the 3D simulation of flow through the oil filter is integrated into our template to obtain a parallel optimization solver. Some capabilities and performance of this solver are demonstrated by solving geometry optimization problem of a filter element.

Parameter Optimization of Decentralized OS-CFAR System Based Modified PSO Method

2012 ◽  
Vol 532-533 ◽  
pp. 881-886
Author(s):  
Pan Zhi Liu ◽  
Ruo Yu Pan ◽  
Guo Fang Guo
Keyword(s):  
Optimization Problem ◽  
Detection System ◽  
Pso Algorithm ◽  
Optimization Method ◽  
Fusion Center ◽  
Threshold Values ◽  
Cfar Detection ◽  
Computation Technique ◽  
And Performance ◽  
Ordered Statistics

For decentralized ordered statistics (OS) constant false alarm ration (CFAR) detection system, the parameter estimation and performance analysis in complicated detection condition is a typical nonlinear optimization problem. Owing to the nonlinear property of distributed OS-CFAR detection system, it is seriously difficult to obtain optimal threshold values using some optimization method at the fusion center. This paper provides a novel solution based on an effective and flexible particle swarm optimization (PSO) algorithm. As a novel evolutionary computation technique, PSO has attracted much attention and wide applications, owing to its simple concept, easy implementation and quick convergence. Using this approach, all system parameters can be optimized simultaneously. The simulation results show that the proposed approach can achieve effective performances with the above method.

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