scholarly journals Dynamic Pricing (and Assortment) Under a Static Calendar

2020 ◽  
Author(s):  
Will Ma ◽  
David Simchi-Levi ◽  
Jinglong Zhao
Keyword(s):  
Dynamic Pricing ◽  
Big Data Analytics ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Linear Programming Relaxation ◽  
Planning Problem ◽  
Packaged Goods ◽  
Demand Curves ◽  
Optimal Stopping Theory ◽  
Finite Time Horizon

This work is motivated by our collaboration with a large consumer packaged goods (CPG) company. We have found that whereas the company appreciates the advantages of dynamic pricing, they deem it operationally much easier to plan out a static price calendar in advance. We investigate the efficacy of static control policies for revenue management problems whose optimal solution is inherently dynamic. In these problems, a firm has limited inventory to sell over a finite time horizon, over which heterogeneous customers stochastically arrive. We consider both pricing and assortment controls, and derive simple static policies in the form of a price calendar or a planned sequence of assortments, respectively. In the assortment planning problem, we also differentiate between the static vs. dynamic substitution models of customer demand. We show that our policies are within 1-1/e (approximately 0.63) of the optimum under stationary demand, and 1/2 of the optimum under nonstationary demand, with both guarantees approaching 1 if the starting inventories are large. We adapt the technique of prophet inequalities from optimal stopping theory to pricing and assortment problems, and our results are relative to the linear programming relaxation. Under the special case of stationary demand single-item pricing, our results improve the understanding of irregular and discrete demand curves, by showing that a static calendar can be (1-1/e)-approximate if the prices are sorted high-to-low. Finally, we demonstrate on both data from the CPG company and synthetic data from the literature that our simple price and assortment calendars are effective. This paper was accepted by Hamid Nazerzadeh, big data analytics.

scholarly journals Optimum Distribution System Expansion Planning Incorporating DG Based on N-1 Criterion for Sustainable System

2021 ◽  
Vol 13 (12) ◽  
pp. 6708
Author(s):  
Hamza Mubarak ◽  
Nurulafiqah Nadzirah Mansor ◽  
Hazlie Mokhlis ◽  
Mahazani Mohamad ◽  
Hasmaini Mohamad ◽  
...  
Keyword(s):  
Power Systems ◽  
Distribution System ◽  
Industrial Revolution ◽  
Optimal Solution ◽  
Search Space ◽  
Planning Problem ◽  
System Expansion ◽  
Optimum Distribution ◽  
Optimal Sizing ◽  
Expansion Planning

Demand for continuous and reliable power supply has significantly increased, especially in this Industrial Revolution 4.0 era. In this regard, adequate planning of electrical power systems considering persistent load growth, increased integration of distributed generators (DGs), optimal system operation during N-1 contingencies, and compliance to the existing system constraints are paramount. However, these issues need to be parallelly addressed for optimum distribution system planning. Consequently, the planning optimization problem would become more complex due to the various technical and operational constraints as well as the enormous search space. To address these considerations, this paper proposes a strategy to obtain one optimal solution for the distribution system expansion planning by considering N-1 system contingencies for all branches and DG optimal sizing and placement as well as fluctuations in the load profiles. In this work, a hybrid firefly algorithm and particle swarm optimization (FA-PSO) was proposed to determine the optimal solution for the expansion planning problem. The validity of the proposed method was tested on IEEE 33- and 69-bus systems. The results show that incorporating DGs with optimal sizing and location minimizes the investment and power loss cost for the 33-bus system by 42.18% and 14.63%, respectively, and for the 69-system by 31.53% and 12%, respectively. In addition, comparative studies were done with a different model from the literature to verify the robustness of the proposed method.

Prophet Inequalities for Independent and Identically Distributed Random Variables from an Unknown Distribution

2021 ◽  
Author(s):  
José Correa ◽  
Paul Dütting ◽  
Felix Fischer ◽  
Kevin Schewior
Keyword(s):  
Stopping Time ◽  
Random Variables ◽  
Optimal Solution ◽  
Random Order ◽  
Secretary Problem ◽  
Maximum Value ◽  
Optimal Stopping Theory ◽  
Long Time ◽  
Object Of Study ◽  
Independent And Identically Distributed

A central object of study in optimal stopping theory is the single-choice prophet inequality for independent and identically distributed random variables: given a sequence of random variables [Formula: see text] drawn independently from the same distribution, the goal is to choose a stopping time τ such that for the maximum value of α and for all distributions, [Formula: see text]. What makes this problem challenging is that the decision whether [Formula: see text] may only depend on the values of the random variables [Formula: see text] and on the distribution F. For a long time, the best known bound for the problem had been [Formula: see text], but recently a tight bound of [Formula: see text] was obtained. The case where F is unknown, such that the decision whether [Formula: see text] may depend only on the values of the random variables [Formula: see text], is equally well motivated but has received much less attention. A straightforward guarantee for this case of [Formula: see text] can be derived from the well-known optimal solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F, and we show that, even with o(n) samples, [Formula: see text]. On the other hand, n samples allow for a significant improvement, whereas [Formula: see text] samples are equivalent to knowledge of the distribution: specifically, with n samples, [Formula: see text] and [Formula: see text], and with [Formula: see text] samples, [Formula: see text] for any [Formula: see text].

scholarly journals Decision Support Tool for Offshore Wind Farm Vessel Routing under Uncertainty

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2190 ◽  
Author(s):  
Rafael Dawid ◽  
David McMillan ◽  
Matthew Revie
Keyword(s):  
Wind Farm ◽  
Real Life ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Decision Support Tool ◽  
Offshore Wind ◽  
Offshore Wind Farm ◽  
Support Tool ◽  
Trade Offs ◽  
The Impact

This paper for the first time captures the impact of uncertain maintenance action times on vessel routing for realistic offshore wind farm problems. A novel methodology is presented to incorporate uncertainties, e.g., on the expected maintenance duration, into the decision-making process. Users specify the extent to which these unknown elements impact the suggested vessel routing strategy. If uncertainties are present, the tool outputs multiple vessel routing policies with varying likelihoods of success. To demonstrate the tool’s capabilities, two case studies were presented. Firstly, simulations based on synthetic data illustrate that in a scenario with uncertainties, the cost-optimal solution is not necessarily the best choice for operators. Including uncertainties when calculating the vessel routing policy led to a 14% increase in the number of wind turbines maintained at the end of the day. Secondly, the tool was applied to a real-life scenario based on an offshore wind farm in collaboration with a United Kingdom (UK) operator. The results showed that the assignment of vessels to turbines generated by the tool matched the policy chosen by wind farm operators. By producing a range of policies for consideration, this tool provided operators with a structured and transparent method to assess trade-offs and justify decisions.

scholarly journals RobOMP: Robust variants of Orthogonal Matching Pursuit for sparse representations

2019 ◽  
Author(s):  
Carlos A Loza
Keyword(s):  
Mean Squared Error ◽  
Matching Pursuit ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Parameter Tuning ◽  
Weight Vector ◽  
Orthogonal Matching Pursuit ◽  
Main Mode ◽  
Observation Matrix ◽  
And Performance

Sparse coding aims to find a parsimonious representation of an example given an observation matrix or dictionary. In this regard, Orthogonal Matching Pursuit (OMP) provides an intuitive, simple and fast approximation of the optimal solution. However, its main building block is anchored on the minimization of the Mean Squared Error cost function (MSE). This approach is only optimal if the errors are distributed according to a Gaussian distribution without samples that strongly deviate from the main mode, i.e. outliers. If such assumption is violated, the sparse code will likely be biased and performance will degrade accordingly. In this paper, we introduce five robust variants of OMP (RobOMP) fully based on the theory of M-Estimators under a linear model. The proposed framework exploits efficient Iteratively Reweighted Least Squares (IRLS) techniques to mitigate the effect of outliers and emphasize the samples corresponding to the main mode of the data. This is done adaptively via a learned weight vector that models the distribution of the data in a robust manner. Experiments on synthetic data under several noise distributions and image recognition under different combinations of occlusion and missing pixels thoroughly detail the superiority of RobOMP over MSE-based approaches and similar robust alternatives. We also introduce a denoising framework based on robust, sparse and redundant representations that open the door to potential further applications of the proposed techniques. The five different variants of RobOMP do not require parameter tuning from the user and, hence, constitute principled alternatives to OMP.

Pareto Optimal Solution Selection for a Multi-Site Supply Chain Planning Problem Using the VIKOR and TOPSIS Methods

2017 ◽  
Vol 8 (3) ◽  
pp. 21-39 ◽  
Author(s):  
Houssem Felfel ◽  
Omar Ayadi ◽  
Faouzi Masmoudi
Keyword(s):  
Supply Chain ◽  
Optimal Solution ◽  
Quality Level ◽  
Planning Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Compromise Solution ◽  
Optimal Solutions ◽  
Pareto Solution ◽  
Solution Approach

In this paper, a multi-objective, multi-product, multi-period production and transportation planning problem in the context of a multi-site supply chain is proposed. The developed model attempts simultaneously to maximize the profit and to maximize the product quality level. The objective of this paper is to provide the decision maker with a front of Pareto optimal solutions and to help him to select the best Pareto solution. To do so, the epsilon-constraint method is adopted to generate the set of Pareto optimal solutions. Then, the technique for order preference by similarity to ideal solution (TOSIS) is used to choose the best compromise solution. The multi-criteria optimization and compromise solution (VIKOR), a commonly used method in multiple criteria analysis, is applied in order to evaluate the selected solutions using TOPSIS method. This paper offers a numerical example to illustrate the solution approach and to compare the obtained results using TOSIS and VIKOR methods.

scholarly journals A Grey Wolf Optimization-based Track-Before-Detect Method for Maneuvering Extended Target Detection and Tracking

Sensors ◽  
2019 ◽  
Vol 19 (7) ◽  
pp. 1577 ◽  
Author(s):  
Bo Yan ◽  
Xu Yang Zhao ◽  
Na Xu ◽  
Yu Chen ◽  
Wen Bo Zhao
Keyword(s):  
Target Detection ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Real Data ◽  
Grey Wolf ◽  
Grey Wolf Optimization ◽  
Detection And Tracking ◽  
Extended Target ◽  
Air Surveillance ◽  
Track Before Detect

A grey wolf optimization-based track-before-detect (GWO-TBD) method is developed for extended target detection and tracking. The aim of the GWO-TBD is tracking weak and maneuvering extended targets in a cluttered environment using the measurement points of an air surveillance radar. The optimal solution is the trajectory constituted by the points of an extended target. At the beginning of the GWO-TBD, the measurements of each scan are clustered into alternative sets. Secondly, closely sets are associated for tracklets. Each tracklet equals a candidate solution. Thirdly, the tracklets are further associated iteratively to find a better solution. An improved GWO algorithm is developed in the iteration for removal of unappreciated solution and acceleration of convergence. After the iteration of several generations, the optimal solution can be achieved, i.e. trajectory of an extended target. Both the real data and synthetic data are performed with the GWO-TBD and several existing algorithms in this work. Result infers that the GWO-TBD is superior to the others in detecting and tracking maneuvering targets. Meanwhile, much less prior information is necessary in the GWO-TBD. It makes the approach is engineering friendly.

Study on the Improvement of Genetic Algorithm by Using Vehicle Routing Problem

2013 ◽  
Vol 365-366 ◽  
pp. 194-198 ◽  
Author(s):  
Mei Ni Guo
Keyword(s):  
Genetic Algorithm ◽  
Optimal Solution ◽  
Mathematic Model ◽  
Simulation Software ◽  
Initial Population ◽  
Planning Problem ◽  
Improved Genetic Algorithm ◽  
Routing Problem ◽  
Search Speed ◽  
Vehicle Path

mprove the existing genetic algorithm, make the vehicle path planning problem solving can be higher quality and faster solution. The mathematic model for study of VRP with genetic algorithms was established. An improved genetic algorithm was proposed, which consist of a new method of initial population and partheno genetic algorithm revolution operation.Exploited Computer Aided Platform and Validated VRP by simulation software. Compared this improved genetic algorithm with the existing genetic algorithm and approximation algorithms through an example, convergence rate Much faster and the Optimal results from 117.0km Reduced to 107.8km,proved that this article improved genetic algorithm can be faster to reach an optimal solution. The results showed that the improved GA can keep the variety of cross and accelerate the search speed.

scholarly journals Network Completion for Static Gene Expression Data

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Natsu Nakajima ◽  
Tatsuya Akutsu
Keyword(s):  
Gene Expression ◽  
Gene Expression Data ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Genetic Networks ◽  
Expression Data ◽  
Initial Network ◽  
Static Data ◽  
Normal Gene ◽  
Stationary Conditions

We tackle the problem of completing and inferring genetic networks under stationary conditions from static data, where network completion is to make the minimum amount of modifications to an initial network so that the completed network is most consistent with the expression data in which addition of edges and deletion of edges are basic modification operations. For this problem, we present a new method for network completion using dynamic programming and least-squares fitting. This method can find an optimal solution in polynomial time if the maximum indegree of the network is bounded by a constant. We evaluate the effectiveness of our method through computational experiments using synthetic data. Furthermore, we demonstrate that our proposed method can distinguish the differences between two types of genetic networks under stationary conditions from lung cancer and normal gene expression data.

scholarly journals AI-Based Early Change Detection in Smart Living Environments

Sensors ◽  
2019 ◽  
Vol 19 (16) ◽  
pp. 3549
Author(s):  
Giovanni Diraco ◽  
Alessandro Leone ◽  
Pietro Siciliano
Keyword(s):  
Deep Learning ◽  
Vital Signs ◽  
Big Data Analytics ◽  
Synthetic Data ◽  
Value Added ◽  
Care Recipient ◽  
Sensor Data ◽  
Detection Accuracy ◽  
Learning Techniques ◽  
Unsupervised Deep Learning

In the smart environments we live today, a great variety of heterogeneous sensors are being increasingly deployed with the aim of providing more and more value-added services. This huge availability of sensor data, together with emerging Artificial Intelligence (AI) methods for Big Data analytics, can yield a wide array of actionable insights to help older adults continue to live independently with minimal support of caregivers. In this regard, there is a growing demand for technological solutions able to monitor human activities and vital signs in order to early detect abnormal conditions, avoiding the caregivers’ daily check of the care recipient. The aim of this study is to compare state-of-the-art machine and deep learning techniques suitable for detecting early changes in human behavior. At this purpose, specific synthetic data are generated, including activities of daily living, home locations in which such activities take place, and vital signs. The achieved results demonstrate the superiority of unsupervised deep-learning techniques over traditional supervised/semi-supervised ones in terms of detection accuracy and lead-time of prediction.

INTEGRATED DYNAMIC PRICING FOR SEASONAL PRODUCTS WITH PRICE AND TIME DEPENDENT DEMAND

2010 ◽  
Vol 27 (03) ◽  
pp. 393-410 ◽  
Author(s):  
SUBRATA SAHA ◽  
MANJUSRI BASU
Keyword(s):  
Dynamic Pricing ◽  
Price Change ◽  
Planning Horizon ◽  
Solution Procedure ◽  
Fixed Number ◽  
Optimal Number ◽  
Inventory Model ◽  
Lot Size ◽  
Decision Variables ◽  
Finite Time Horizon

In this paper, an inventory model for deteriorating items with ramp-type time and price dependent consumption rate over a finite planning horizon is considered. In contrast to the traditional deterministic inventory model with static price over the entire planning horizon or fixed number of price changes over the finite time horizon, an alternative model is derived in which prices and the number of price change are to be decision variables. We show that the total profit function is concave. With the concavity, a solution procedure is presented to determine optimal prices, optimal number of pricing cycles and optimal lot size and optimal profit. We illustrate the model with numerical examples. Sensitivity analysis of the model is also carried out.

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