We study a class of discounted autonomous infinite horizon optimal control problems where the state dynamics may undergo discontinuous changes when the state crosses from one region of the state sp...
{"title":"Analysis of Optimal Control Problems for Hybrid Systems with One State Variable","authors":"P. V. Reddy, J. Schumacher, J. Engwerda","doi":"10.2139/ssrn.3424771","DOIUrl":"https://doi.org/10.2139/ssrn.3424771","url":null,"abstract":"We study a class of discounted autonomous infinite horizon optimal control problems where the state dynamics may undergo discontinuous changes when the state crosses from one region of the state sp...","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132918126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Discrete convexity, in particular, L-natural-convexity and M-natural-convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike-sharing. As a powerful framework, discrete convex analysis is becoming increasingly popular in the literature. This review will survey the landscape of the approach. We start by introducing several key concepts, namely, L-natural-convexity and M-natural-convexity and their variants, followed by a discussion of some fundamental properties that are most useful for studying operations models. We then illustrate various applications of these concepts and properties. Examples include network flow problem, stochastic inventory control, appointment scheduling, game theory, portfolio contract, discrete choice model, and bike-sharing. We focus our discussion on demonstrating how discrete convex analysis can shed new insights on existing problems, and/or bring about much simpler analyses and algorithm developments than previous methods in the literature. We also present several results and analyses that are new to the literature.
{"title":"Discrete Convex Analysis and Its Applications in Operations: A Survey","authors":"Xin Chen, Menglong Li","doi":"10.2139/ssrn.3549628","DOIUrl":"https://doi.org/10.2139/ssrn.3549628","url":null,"abstract":"Discrete convexity, in particular, L-natural-convexity and M-natural-convexity, provides a critical opening to attack several classical problems in inventory theory, as well as many other operations problems that arise from more recent practices, for instance, appointment scheduling and bike-sharing. As a powerful framework, discrete convex analysis is becoming increasingly popular in the literature. This review will survey the landscape of the approach. We start by introducing several key concepts, namely, L-natural-convexity and M-natural-convexity and their variants, followed by a discussion of some fundamental properties that are most useful for studying operations models. We then illustrate various applications of these concepts and properties. Examples include network flow problem, stochastic inventory control, appointment scheduling, game theory, portfolio contract, discrete choice model, and bike-sharing. We focus our discussion on demonstrating how discrete convex analysis can shed new insights on existing problems, and/or bring about much simpler analyses and algorithm developments than previous methods in the literature. We also present several results and analyses that are new to the literature.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"341 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132529303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the impact of pre-existing offline data on online learning in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that before the start of the selling horizon, the seller already has some pre-existing offline data. The offline data set contains n samples, each of which is an input-output pair consisting of a historical price and an associated demand observation. The seller wants to use both the pre-existing offline data and the sequentially revealed online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location, and dispersion of the offline data on the optimal regret of the online learning process. Specifically, the size, location, and dispersion of the offline data are measured by the number of historical samples, the distance between the average historical price and the optimal price, and the standard deviation of the historical prices, respectively. For both single-historical-price setting and multiple-historical-price setting, we design a learning algorithm based on the “Optimism in the Face of Uncertainty” principle, which strikes a balance between exploration and exploitation and achieves the optimal regret up to a logarithmic factor. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law. This paper was accepted by Omar Besbes, revenue management and market analytics.
{"title":"Online Pricing with Offline Data: Phase Transition and Inverse Square Law","authors":"Jinzhi Bu, D. Simchi-Levi, Yunzong Xu","doi":"10.2139/ssrn.3471501","DOIUrl":"https://doi.org/10.2139/ssrn.3471501","url":null,"abstract":"This paper investigates the impact of pre-existing offline data on online learning in the context of dynamic pricing. We study a single-product dynamic pricing problem over a selling horizon of T periods. The demand in each period is determined by the price of the product according to a linear demand model with unknown parameters. We assume that before the start of the selling horizon, the seller already has some pre-existing offline data. The offline data set contains n samples, each of which is an input-output pair consisting of a historical price and an associated demand observation. The seller wants to use both the pre-existing offline data and the sequentially revealed online data to minimize the regret of the online learning process. We characterize the joint effect of the size, location, and dispersion of the offline data on the optimal regret of the online learning process. Specifically, the size, location, and dispersion of the offline data are measured by the number of historical samples, the distance between the average historical price and the optimal price, and the standard deviation of the historical prices, respectively. For both single-historical-price setting and multiple-historical-price setting, we design a learning algorithm based on the “Optimism in the Face of Uncertainty” principle, which strikes a balance between exploration and exploitation and achieves the optimal regret up to a logarithmic factor. Our results reveal surprising transformations of the optimal regret rate with respect to the size of the offline data, which we refer to as phase transitions. In addition, our results demonstrate that the location and dispersion of the offline data also have an intrinsic effect on the optimal regret, and we quantify this effect via the inverse-square law. This paper was accepted by Omar Besbes, revenue management and market analytics.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134056974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider a periodic-review dual-sourcing inventory system, in which the expedited supplier is faster and more costly, while the regular supplier is slower and cheaper. Under full demand distributional information, it is well-known that the optimal policy is extremely complex but the celebrated Tailored Base-Surge (TBS) policy performs near optimally. Under such a policy, a constant order is placed at the regular source in each period, while the order placed at the expedited source follows a simple order-up-to rule. In this paper, we assume that the firm does not know the demand distribution a priori, and makes adaptive inventory ordering decisions in each period based only on the past sales (a.k.a. censored demand) data. The standard performance measure is regret, which is the cost difference between a feasible learning algorithm and the clairvoyant (full-information) benchmark. When the benchmark is chosen to be the (full-information) optimal Tailored Base-Surge policy, we develop the first nonparametric learning algorithm that admits a regret bound of O(T^{1/2} (log T)^{3} loglog T), which is provably tight up to a logarithmic factor. Leveraging the structure of this problem, our approach combines the power of bisection search and stochastic gradient descent and also involves a delicate high probability coupling argument between our and the clairvoyant optimal system dynamics. We also develop several technical results that are of independent interest.
{"title":"Tailored Base-Surge Policies in Dual-Sourcing Inventory Systems with Demand Learning","authors":"Boxiao Chen, Cong Shi","doi":"10.2139/ssrn.3456834","DOIUrl":"https://doi.org/10.2139/ssrn.3456834","url":null,"abstract":"We consider a periodic-review dual-sourcing inventory system, in which the expedited supplier is faster and more costly, while the regular supplier is slower and cheaper. Under full demand distributional information, it is well-known that the optimal policy is extremely complex but the celebrated Tailored Base-Surge (TBS) policy performs near optimally. Under such a policy, a constant order is placed at the regular source in each period, while the order placed at the expedited source follows a simple order-up-to rule. In this paper, we assume that the firm does not know the demand distribution a priori, and makes adaptive inventory ordering decisions in each period based only on the past sales (a.k.a. censored demand) data. The standard performance measure is regret, which is the cost difference between a feasible learning algorithm and the clairvoyant (full-information) benchmark. When the benchmark is chosen to be the (full-information) optimal Tailored Base-Surge policy, we develop the first nonparametric learning algorithm that admits a regret bound of O(T^{1/2} (log T)^{3} loglog T), which is provably tight up to a logarithmic factor. Leveraging the structure of this problem, our approach combines the power of bisection search and stochastic gradient descent and also involves a delicate high probability coupling argument between our and the clairvoyant optimal system dynamics. We also develop several technical results that are of independent interest.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129595653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The coupled task scheduling problem aims to schedule a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. We study the problem of scheduling a set of coupled jobs to be processed on a single machine with the objective of minimizing the makespan, which is known to be strongly NP-hard. We obtain competitive lower bounds for the problem through different procedures, including solving 0-1 knapsack problems. We obtain an upper bound by applying a heuristic algorithm. We then propose a binary search heuristic algorithm for the coupled task scheduling problem. We perform extensive computational experiments and show that the proposed method is able to obtain quality solutions. The results also indicate that the proposed solution method outperforms the standard exact solver Gurobi.
{"title":"A Binary Search Method for the General Coupled Task Scheduling Problem","authors":"M. Khatami, A. Salehipour","doi":"10.2139/ssrn.3451871","DOIUrl":"https://doi.org/10.2139/ssrn.3451871","url":null,"abstract":"The coupled task scheduling problem aims to schedule a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. We study the problem of scheduling a set of coupled jobs to be processed on a single machine with the objective of minimizing the makespan, which is known to be strongly NP-hard. We obtain competitive lower bounds for the problem through different procedures, including solving 0-1 knapsack problems. We obtain an upper bound by applying a heuristic algorithm. We then propose a binary search heuristic algorithm for the coupled task scheduling problem. We perform extensive computational experiments and show that the proposed method is able to obtain quality solutions. The results also indicate that the proposed solution method outperforms the standard exact solver Gurobi.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122912167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study offers an empirical investigation of inventory and sales dynamics in a large-scale retail network setting. We infer the impact of product shortages on sales in neighboring outlets using unique data from a large fast fashion retailing chain. Since the product shortages do not occur at the same time, we conduct a novel Difference-in-Differences (DiD) methodology to align the stock-out periods across the stores in the network. In addition, we stratify data based on the periods in which stock-out is observed and apply pairwise DiD analyses to validate the robustness of our results. Our analysis reveals that sales for a particular item at a focal store increases when that same item experiences stock-outs in neighboring stores, especially so for neighboring stores that are physically closer to the focal store. These findings suggest that there is substitutability across stores, and that this substitutability is the strongest in the period when the stock-out is observed for the first time, and decreases in the time since the stock-out and dissipates with physical distance. In order to assess the value of considering the impact of stock-outs on inventory allocation, we develop an optimization model and calibrate it by using parameters estimated via DiD analysis. The simulation analysis confirms that revenues markedly improve on average by 2.2% when neighboring stock-out information is taken into account for sales forecasting when optimizing inventory allocations. Finally, we conduct sensitivity analysis to evaluate how this effect changes with problem parameters such as product price, and inventory.
{"title":"An Empirical Analysis of Intra-Firm Product Substitutability in Fashion Retailing","authors":"Elcin Ergin, M. Gumus, N. Yang","doi":"10.2139/ssrn.3444467","DOIUrl":"https://doi.org/10.2139/ssrn.3444467","url":null,"abstract":"This study offers an empirical investigation of inventory and sales dynamics in a large-scale retail network setting. We infer the impact of product shortages on sales in neighboring outlets using unique data from a large fast fashion retailing chain. Since the product shortages do not occur at the same time, we conduct a novel Difference-in-Differences (DiD) methodology to align the stock-out periods across the stores in the network. In addition, we stratify data based on the periods in which stock-out is observed and apply pairwise DiD analyses to validate the robustness of our results. Our analysis reveals that sales for a particular item at a focal store increases when that same item experiences stock-outs in neighboring stores, especially so for neighboring stores that are physically closer to the focal store. These findings suggest that there is substitutability across stores, and that this substitutability is the strongest in the period when the stock-out is observed for the first time, and decreases in the time since the stock-out and dissipates with physical distance. In order to assess the value of considering the impact of stock-outs on inventory allocation, we develop an optimization model and calibrate it by using parameters estimated via DiD analysis. The simulation analysis confirms that revenues markedly improve on average by 2.2% when neighboring stock-out information is taken into account for sales forecasting when optimizing inventory allocations. Finally, we conduct sensitivity analysis to evaluate how this effect changes with problem parameters such as product price, and inventory.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123248853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Large-scale railway network revenue management models with customer choice behavior are not only a challenge from an optimization perspective, it is also complex and time-consuming to collect and set up test data for large networks. To promote research in this field, we present an algorithm that generates test data based on the schedules of railway companies, e.g., the set of itineraries and corresponding data, such as the resource consumption or product attribute values like travel time, number of transfers, etc. The generated data are also useful for other fields of research, such as crew scheduling or delay management. We show that the algorithm generates realistic test data for large-scale networks in only a few seconds. To promote research in the field of large-scale railway revenue management, we make the programming code (incl. a small schedule dataset) publicly available.
{"title":"An Algorithm to Create Test Data for Large-Scale Railway Network Revenue Management Models with Customer Choice","authors":"Simon Hohberger, C. Schoen","doi":"10.2139/ssrn.3439270","DOIUrl":"https://doi.org/10.2139/ssrn.3439270","url":null,"abstract":"Large-scale railway network revenue management models with customer choice behavior are not only a challenge from an optimization perspective, it is also complex and time-consuming to collect and set up test data for large networks. To promote research in this field, we present an algorithm that generates test data based on the schedules of railway companies, e.g., the set of itineraries and corresponding data, such as the resource consumption or product attribute values like travel time, number of transfers, etc. The generated data are also useful for other fields of research, such as crew scheduling or delay management. We show that the algorithm generates realistic test data for large-scale networks in only a few seconds. To promote research in the field of large-scale railway revenue management, we make the programming code (incl. a small schedule dataset) publicly available.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121867068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper develops a tractable methodology for designing an optimal priority system for assigning agents to heterogeneous items while accounting for agents’ choice behavior. The space of mechanisms being optimized includes deferred acceptance and top trading cycles as special cases. In contrast to previous literature, I treat the inputs to these mechanisms, namely the priority distribution of agents and quotas of items, as parameters to be optimized. The methodology is based on analyzing large market models of one-sided matching using techniques from revenue management and solving a certain assortment planning problem whose objective is social welfare. I apply the methodology to school choice and show that restricting choices may be beneficial to student welfare. Moreover, I compute optimized choice sets and priorities for elementary school choice in Boston. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.
{"title":"Optimal Priority-Based Allocation Mechanisms","authors":"Peng Shi","doi":"10.2139/ssrn.3425348","DOIUrl":"https://doi.org/10.2139/ssrn.3425348","url":null,"abstract":"This paper develops a tractable methodology for designing an optimal priority system for assigning agents to heterogeneous items while accounting for agents’ choice behavior. The space of mechanisms being optimized includes deferred acceptance and top trading cycles as special cases. In contrast to previous literature, I treat the inputs to these mechanisms, namely the priority distribution of agents and quotas of items, as parameters to be optimized. The methodology is based on analyzing large market models of one-sided matching using techniques from revenue management and solving a certain assortment planning problem whose objective is social welfare. I apply the methodology to school choice and show that restricting choices may be beneficial to student welfare. Moreover, I compute optimized choice sets and priorities for elementary school choice in Boston. This paper was accepted by Gabriel Weintraub, revenue management and market analytics.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"105 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116870018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop a novel mixed-integer programming (MIP) formulation for a traveling salesman problem with a truck-drone team, consisting of one truck and multiple drones, that carries out a set of deliveries. Our model takes an approach different from other MIP formulations in the literature. Benchmarks show that it can compete with those as well as with purpose-built exact solution methods but has the advantage of being easily implementable with an off-the-shelf solver. Additionally, we present an even tighter formulation for a special case where the drone range is non-binding. We conduct several numerical experiments to explore the performance of the model and to gain insights into the problem with multiple drones.
{"title":"The Traveling Salesman Problem With One Truck and Multiple Drones","authors":"K. Seifried","doi":"10.2139/ssrn.3389306","DOIUrl":"https://doi.org/10.2139/ssrn.3389306","url":null,"abstract":"We develop a novel mixed-integer programming (MIP) formulation for a traveling salesman problem with a truck-drone team, consisting of one truck and multiple drones, that carries out a set of deliveries. Our model takes an approach different from other MIP formulations in the literature. Benchmarks show that it can compete with those as well as with purpose-built exact solution methods but has the advantage of being easily implementable with an off-the-shelf solver. Additionally, we present an even tighter formulation for a special case where the drone range is non-binding. We conduct several numerical experiments to explore the performance of the model and to gain insights into the problem with multiple drones.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"61 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126664011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We analyze the question of whether the inf-convolution of law-invariant risk functionals (preferences) is still law-invariant. In other words, we try to understand whether the representative economic agent (after risk redistribution) only cares about the distribution of the total risk, assuming all individual agents do so. Although the answer to the above question seems to be affirmative for many examples of commonly used risk functionals in the literature, the situation becomes delicate without assuming specific forms and properties of the individual functionals. We illustrate with examples the surprising fact that the answer to the main question is generally negative, even in an atomless probability space. Furthermore, we establish a few very weak conditions under which the answer becomes positive. These conditions do not require any specific forms or convexity of the risk functionals, and they are the richness of the underlying probability space, and monotonicity or continuity of one of the risk functionals. We provide several examples and counter-examples to discuss the subtlety of the question on law-invariance.
{"title":"Is the Inf-convolution of Law-invariant Preferences Law-invariant?","authors":"Peng Liu, Ruodu Wang, Linxiao Wei","doi":"10.2139/ssrn.3371642","DOIUrl":"https://doi.org/10.2139/ssrn.3371642","url":null,"abstract":"Abstract We analyze the question of whether the inf-convolution of law-invariant risk functionals (preferences) is still law-invariant. In other words, we try to understand whether the representative economic agent (after risk redistribution) only cares about the distribution of the total risk, assuming all individual agents do so. Although the answer to the above question seems to be affirmative for many examples of commonly used risk functionals in the literature, the situation becomes delicate without assuming specific forms and properties of the individual functionals. We illustrate with examples the surprising fact that the answer to the main question is generally negative, even in an atomless probability space. Furthermore, we establish a few very weak conditions under which the answer becomes positive. These conditions do not require any specific forms or convexity of the risk functionals, and they are the richness of the underlying probability space, and monotonicity or continuity of one of the risk functionals. We provide several examples and counter-examples to discuss the subtlety of the question on law-invariance.","PeriodicalId":275253,"journal":{"name":"Operations Research eJournal","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116048984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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