An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation called SDCP that is based on segment-level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ESDCPκ, and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the benchmark data sets in the literature, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of constraints called product constraints, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product constraints and the ?SDCP method are very simple and easy to implement and are applicable to the case of overlapping segment consideration sets. In our computational testing on the benchmark data sets in the literature, SDCP with product constraints achieves the CDLP value at a fraction of the CPU time taken by column generation and we believe is a very promising approach for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.discrete-choice models, network revenue management, optimization

An Enhanced Concave Program Relaxation for Choice Network Revenue Management

The network choice revenue management problem models customers as choosing from an offerset, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of valid inequalities called product cuts, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called kSDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product cuts and the kSDCP method are very simple and easy to implement, work with general discrete choice models and are applicable to the case of overlapping segment consideration sets. In our computational testing SDCP with product cuts achieves the CDLP value at a fraction of the CPU time taken by column generation and hence has the potential to be scalable to industrial-size problems

An Enhanced Concave Program Relaxation for Choice Network Revenue Management

The network choice revenue management problem models customers as choosing from an offerset, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of valid inequalities called product cuts, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called kSDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product cuts and the kSDCP method are very simple and easy to implement, work with general discrete choice models and are applicable to the case of overlapping segment consideration sets. In our computational testing SDCP with product cuts achieves the CDLP value at a fraction of the CPU time taken by column generation and hence has the potential to be scalable to industrial-size problems.operations research, marketing, bid prices, yield management, heuristics, discrete-choice, network revenue management

Sensitive Commercial NASBA Assay for the Detection of Respiratory Syncytial Virus in Clinical Specimen

The aim of the study was to evaluate the usability of three diagnostic procedures for the detection of respiratory syncytial virus in clinical samples. Therefore, the FDA cleared CE marked NOW® RSV ELISA, the NucliSENS® EasyQ RSV A+B NASBA, and a literature based inhouse RT-PCR protocol were compared for their relative sensitivities. Thereby, NASBA turned out to be the most sensitive method with a total number of 80 RSV positive samples out of a cohort of 251 nasopharyngeal washings from patients suffering from clinical symptoms, followed by the inhouse RT-PCR (62/251) and ELISA (52/251). Thus, NASBA may serve as a rapid and highly sensitive alternative for RSV diagnostics

Crustal Azimuthal Anisotropy Beneath the Southeastern Tibetan Plateau and its Geodynamic Implications

The fast orientation and magnitude of crustal azimuthal anisotropy beneath the southeastern Tibetan Plateau and adjacent areas are measured by analyzing the sinusoidal moveout of the P to S converted phase from the Moho. Beneath the tectonically active plateau, the mean magnitude is 0.48 ±Â 0.13 s, which is about twice as large as that observed in the stable Sichuan Basin (0.23 ±Â 0.10 s). The two areas are separated by the Longmenshan fault zone, a zone of devastating earthquakes including the 12 May 2008 MW 7.9 Wenchuan earthquake. Fault orthogonal fast orientations observed in the southern Longmenshan fault zone, where previous studies have revealed high crustal Vp/Vs and suggested the presence of mid-lower crustal flow, may reflect flow-induced lattice preferred orientation of anisotropic minerals. Fault parallel anisotropy in the central segment of the fault zone is most likely related to fluid filled fractures, and fault perpendicular extensional cracks are probably responsible for the observed anisotropy in the northern segment. The crustal anisotropy measurements, when combined with results from previous studies, suggest the existence of mid-lower crustal flow beneath the southeastern margin of the plateau. Comparison of crustal anisotropy obtained before and after the Wenchuan earthquake suggests that the earthquake has limited influence on whole crustal anisotropy, although temporal changes of anisotropy associated with the earthquake have been reported using splitting of shear waves from local earthquakes occurred in the upper crust

A Synthesis of Marine Monitoring Methods With the Potential to Enhance the Status Assessment of the Baltic Sea

Highlights - We rated novel methods regarding their ability to improve the Baltic Sea monitoring. - Methods were assessed with respect to their costs and applicability. - All methods can potentially increase data resolution or monitor novel ecosystem elements. - We recommend several novel methods for the Baltic status assessment.A multitude of anthropogenic pressures deteriorate the Baltic Sea, resulting in the need to protect and restore its marine ecosystem. For an efficient conservation, comprehensive monitoring and assessment of all ecosystem elements is of fundamental importance. The Baltic Marine Environment Protection Commission HELCOM coordinates conservation measures regulated by several European directives. However, this holistic assessment is hindered by gaps within the current monitoring schemes. Here, twenty-two novel methods with the potential to fill some of these gaps and improve the monitoring of the Baltic marine environment are examined. We asked key stakeholders to point out methods likely to improve current Baltic Sea monitoring. We then described these methods in a comparable way and evaluated them based on their costs and applicability potential (i.e., possibility to make them operational). Twelve methods require low to very low costs, while five require moderate and two high costs. Seventeen methods were rated with a high to very high applicability, whereas four methods had moderate and one low applicability for Baltic Sea monitoring. Methods with both low costs and a high applicability include the Manta Trawl, Rocket Sediment Corer, Argo Float, Artificial Substrates, Citizen Observation, Earth Observation, the HydroFIA®pH system, DNA Metabarcoding and Stable Isotope Analysis

Choice-Based Network Revenue Management under Weak Market Segmentation

We present improved network revenue management methods that assume customers to choose according to the multinomial logit choice model with the specific feature that the sets of considered products of the different customer segments are allowed to overlap. This approach can be used to model markets with weak segmentation: For example, high-yield customer segments can be modelled to also consider low yield products intended for low-yield customers, introducing implicit buy-down behavior into the model. The arising linear programs are solved using column generation and involves NP-hard mixed integer sub problems. However, we propose efficient polynomial-time heuristics that considerably speed-up the solution process. We numerically investigate the effect of varying the intensity of overlap on the respective policies and find that improvements are most pronounced in the case of high overlap, rendering the method highly interesting for weakly segmented market applications.revenue management, dynamic programming, optimal control, applications, approximate

Improved Bid Prices for Choice-Based Network Revenue Management

In many implemented network revenue management systems, a bid price control is being used. In this form of control bid, prices are attached to resources, and a product is offered if the revenue derived from it exceeds the sum of the bid prices of its consumed resources. This approach is appealing because once bid prices have been determined, it is fairly simple to derive the products that should be offered. Yet it is still unknown how well a bid price control actually performs. Recently, considerable progress has been made with network revenue management by incorporating customer purchase behavior via discrete choice models. However, the majority of authors have presented control policies for the booking process that are expressed in terms of which combination of products to offer at a given point in time and given resource inventories. The recommended combination of products as identified by these policies might not be representable through bid price control. If demand were independent from available product alternatives, an optimal choice of bid prices is to use the marginal value of capacity for each resource in the network. But under dependent demand, this is not necessarily the case. In fact, it seems that these bid prices are typically not restrictive enough and result in buy-down effects. We propose (1) a simple and fast heuristic that iteratively improves on an initial guess for the bid price vector; this first guess could be, for example, dynamic estimates of the marginal value of capacity. Moreover

Network Revenue Management with Inventory-Sensitive Bid Prices and Customer Choice

We develop a new approximate dynamic programming approach to network revenue management models with customer choice that approximates the value function of the Markov decision process with a concave function which is separable across resource inventory levels. This approach reflects the intuitive interpretation of diminishing marginal utility of inventory levels and allows for significantly improved accuracy compared to currently available methods. The model allows for arbitrary aggregation of inventory units and thereby reduction of computational workload, yields upper bounds on the optimal expected revenue that are provably at least as tight as those obtained from previous approaches, and is asymptotically optimal under fluid scaling. Computational experiments for the multinomial logit choice model with distinct consideration sets show that policies derived from our approach outperform available alternatives, and we demonstrate how aggregation can be used to balance solution quality and runtime.revenue management, dynamic programming, optimal control, applications, approximate