Efficient Real-time Policies for Revenue Management Problems

This dissertation studies the development of provably near-optimal real-time prescriptive analytics solutions that are easily implementable in a dynamic business environment. We consider several stochastic control problems that are motivated by different applications of the practice of pricing and revenue management. Due to high dimensionality and the need for real-time decision making, it is computationally prohibitive to characterize the optimal controls for these problems. Therefore, we develop heuristic controls with simple decision rules that can be deployed in real-time at large scale, and then show theirs good theoretical and empirical performances. In particular, the first chapter studies the joint dynamic pricing and order fulfillment problem in the context of online retail, where a retailer sells multiple products to customers from different locations and fulfills orders through multiple fulfillment centers. The objective is to maximize the total expected profits, defined as the revenue minus the shipping cost. We propose heuristics where the real-time computations of pricing and fulfillment decisions are partially decoupled, and show their good performances compared to reasonable benchmarks. The second chapter studies a dynamic pricing problem where a firm faces price-sensitive customers arriving stochastically over time. Each customer consumes one unit of resource for a deterministic amount of time, after which the resource can be immediately used to serve new customers. We develop two heuristic controls and show that both are asymptotically optimal in the regime with large demand and supply. We further generalize both of the heuristic controls to the settings with multiple service types requiring different service times and with advance reservation. Lastly, the third chapter considers a general class of single-product dynamic pricing problems with inventory constraints, where the price-dependent demand function is unknown to the firm. We develop nonparametric dynamic pricing algorithms that do not assume any functional form of the demand model and show that, for one of the algorithm, its revenue loss compared to a clairvoyant matches the theoretic lower bound in asymptotic regime. In particular, the proposed algorithms generalize the classic bisection search method to a constrained setting with noisy observations.PHDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145995/1/leiyz_1.pd

Dynamic Joint Pricing and Order Fulfillment for E-Commerce Retailers

We consider an e-commerce retailer (e-tailer) who sells a catalog of products to customers from different regions during a finite selling season and fulfills orders through multiple fulfillment centers. The e-tailer faces a Joint Pricing and Fulfillment (JPF) problem: At the beginning of each period, she needs to jointly decide the price for each product and how to fulfill an incoming order. The objective is to maximize the total expected profits defined as total expected revenues minus total expected shipping costs (all other costs are fixed in this problem). The exact optimal policy for JPF is difficult to solve; so, we propose two heuristics that have provably good performance compared to reasonable benchmarks. Our first heuristic directly uses the solution of a deterministic approximation of JPF as its control parameters whereas our second heuristic improves the first heuristic by adaptively adjusting the original control parameters at the beginning of every period. An important feature of the second heuristic is that it decouples the pricing and fulfillment decisions, making it easy to implement. We show theoretically and numerically that the second heuristic significantly outperforms the first heuristic and is very close to a benchmark that jointly re-optimizes the full deterministic problem at every period.http://deepblue.lib.umich.edu/bitstream/2027.42/117573/1/1310_Jasin.pd

Near-Optimal Bisection Search for Nonparametric Dynamic Pricing with Inventory Constraint

We consider a single-product revenue management problem with an inventory constraint and unknown, noisy, demand function. The objective of the fi rm is to dynamically adjust the prices to maximize total expected revenue. We restrict our scope to the nonparametric approach where we only assume some common regularity conditions on the demand function instead of a speci fic functional form. We propose a family of pricing heuristics that successfully balance the tradeo ff between exploration and exploitation. The idea is to generalize the classic bisection search method to a problem that is a ffected both by stochastic noise and an inventory constraint. Our algorithm extends the bisection method to produce a sequence of pricing intervals that converge to the optimal static price with high probability. Using regret (the revenue loss compared to the deterministic pricing problem for a clairvoyant) as the performance metric, we show that one of our heuristics exactly matches the theoretical asymptotic lower bound that has been previously shown to hold for any feasible pricing heuristic. Although the results are presented in the context of revenue management problems, our analysis of the bisection technique for stochastic optimization with learning can be potentially applied to other application areas.http://deepblue.lib.umich.edu/bitstream/2027.42/108717/1/1252_Sinha.pd

Real-Time Dynamic Pricing for Revenue Management with Reusable Resources and Deterministic Service Time Requirements

We consider the setting of a firm that sells a finite amount of resources to price-sensitive customers who arrive randomly over time according to a specified non-stationary rate. Each customer requires a service that consumes one unit of resource for a deterministic amount of time, and the resource is reusable in the sense that it can be immediately used to serve a new customer upon the completion of the previous service. The firm’s objective is to set the price dynamically to maximize its expected total revenues. This is a fundamental problem faced by many firms in many industries. We formulate this as an optimal stochastic control problem and develop two heuristic controls based on the solution of the deterministic relaxation of the original stochastic problem. The first heuristic control is static since the corresponding price sequence is determined before the selling horizon starts; the second heuristic control is dynamic, it uses the first heuristic control as its baseline control and adaptively adjusts the price based on previous demand realizations. We show that both heuristic controls are asymptotically optimal in the regime with large demand and large number of resources. Finally, we consider two important generalizations of the basic model to the setting with multiple service types requiring different service times and the setting with advance service bookings.http://deepblue.lib.umich.edu/bitstream/2027.42/122970/1/1327_Lei.pd

Ursolic Acid Ameliorates Inflammation in Cerebral Ischemia and Reperfusion Injury Possibly via High Mobility Group Box 1/Toll-Like Receptor 4/NFκB Pathway

Toll-like receptors (TLRs) play key roles in cerebral ischemia and reperfusion injury by inducing the production of inflammatory mediators, such as interleukins (ILs) and tumor necrosis factor-alpha (TNF-α). According to recent studies, ursolic acid (UA) regulates TLR signaling and exhibits notable anti-inflammatory properties. In the present study, we explored the mechanism by which UA regulates inflammation in the rat middle cerebral artery occlusion and reperfusion (MCAO/R) model. The MCAO/R model was induced in male Sprague–Dawley rats (MCAO for 2 h, followed by reperfusion for 48 h). UA was administered intragastrically at 0.5, 24, and 47 h after reperfusion. The direct high mobility group box 1 (HMGB1) inhibitor glycyrrhizin (GL) was injected intravenously after 0.5 h of ischemia as a positive control. The degree of brain damage was estimated using the neurological deficit score, infarct volume, histopathological changes, and neuronal apoptosis. We assessed IL-1β, TNF-α, and IL-6 levels to evaluate post-ischemic inflammation. HMGB1 and TLR4 expression and phosphorylation of nuclear factor kappa-light-chain-enhancer of activated B cell (NFκB) were also examined to explore the underlying mechanism. UA (10 and 20 mg/kg) treatment significantly decreased the neurological deficit scores, infarct volume, apoptotic cells, and IL-1β, TNF-α, and IL-6 concentrations. The infarct area ratio was reduced by (33.07 ± 1.74), (27.05 ± 1.13), (27.49 ± 1.87), and (39.74 ± 2.14)% in the 10 and 20 mg/kg UA, GL, and control groups, respectively. Furthermore, UA (10 and 20 mg/kg) treatment significantly decreased HMGB1 release and the TLR4 level and inactivated NFκB signaling. Thus, the effects of intragastric administration of 20 mg/kg of UA and 10 mg/kg of GL were similar. We provide novel evidence that UA reduces inflammatory cytokine production to protect the brain from cerebral ischemia and reperfusion injury possibly through the HMGB1/TLR4/NFκB signaling pathway

Association of Apolipoprotein C3 Genetic Polymorphisms with the Risk of Ischemic Stroke in the Northern Chinese Han Population

<div><p>The apolipoprotein C3 (APOC3) gene, which is a member of the APOA1/C3/A4/A5 gene cluster, plays a crucial role in lipid metabolism. Dyslipidemia is an important risk factor for ischemic stroke. In the present study, we performed a hospital-based case—control study of 895 ischemic stroke patients and 883 control subjects to examine the effects of four APOC3 single nucleotide polymorphisms (SNPs) (rs2854116, rs2854117, rs4520 and rs5128) on the risk of ischemic stroke in a northern Chinese Han population. The SNaPshot Multiplex sequencing assay was used for SNP genotyping, and the potential association of genotype distributions and allele frequencies with ischemic stroke was analyzed statistically. Compared with the GG genotype, the CC+GC genotype of rs5128 was significantly associated with an increased risk in females (adjusted OR = 3.38, 95% CI = 1.82–6.28, P <0.01) after all of the risk factors were adjusted for with logistic regression analyses. A similar relationship was found between the rs4520 polymorphism and ischemic stroke risk in Han Chinese women. Under a recessive genetic model, the TT+TC genotypes of this variant increased ischemic stroke risk (adjusted OR = 2.05; 95% CI = 1.28–3.29; P <0.01). Haplotype analysis revealed that in males, the T-C-T-C haplotype of rs2854116-rs2854117-rs4520-rs5128 was significantly more frequent in the ischemic stroke group than in the control group (OR = 1.49, 95% CI = 1.18–1.87, P<0.01). The results of our study indicate that the APOC3 polymorphisms contribute to ischemic stroke susceptibility in females in the northern Chinese Han population.</p></div

Characteristics and risk factors for stroke.

<p>Characteristics and risk factors for stroke.</p

Prediction formulae of sagittal alignment in thoracolumbar kyphosis secondary to ankylosing spondylitis after osteotomy

Abstract To construct and validate prediction formulae of sagittal alignment in thoracolumbar kyphosis secondary to ankylosing spondylitis (AS) after osteotomy. A total of 115 AS patients who suffered from thoracolumbar kyphosis and underwent osteotomy were enrolled, with 85 patients in derivation group and 30 patients in validation group. Radiographic parameters were measured on lateral radiographs, including thoracic kyphosis, lumbar lordosis (LL), T1 pelvic angel (TPA), sagittal vertical axis (SVA), osteotomized vertebral angle, pelvic incidence (PI), pelvic tilt (PT), sacral slope (SS), and PI and LL mismatch (PI-LL). Prediction formulae of SS, PT, TPA and SVA were established; and their effectiveness was evaluated. There was no significant difference in baseline characteristics between the two groups (p > 0.05). In derivation group, LL and PI-LL were correlated with SS, and were then used to establish the prediction formula of SS[SS = − 12.791–0.765 × (LL) + 0.357 × (PI-LL), R2 = 68.3%]; PI and PI-LL were correlated with PT, and the prediction formula of PT were thus established[PT = 12.108 + 0.402 × (PI-LL) + 0.252 × (PI), R2 = 56.8%]; PT, PI-LL and LL were correlated with TPA, and were used to establish the prediction formula of TPA[TPA = 0.225 + 0.597 × (PT) + 0.464 × (PI-LL)-0.161 × (LL), R2 = 87.4%]; PT, PI-LL and age were correlated with SVA, and were used to establish the prediction formula of SVA[SVA = 36.157 + 2.790 × (PI-LL) + 1.657 × (Age)-1.813 × (PT), R2 = 41.5%]. In validation group, the predictive SS, PT, TPA and SVA were basically consistent with corresponding real values; and the mean error between predictive values and real values was of 1.3° in SS, 1.2° in PT, 1.1° in TPA and 8.6 mm in SVA. Postoperative SS, PT, TPA and SVA could be predicted with PI and the planned LL and PI-LL using prediction formulae, providing a method for AS kyphosis to plan postoperative sagittal alignment. Change of pelvic posture after osteotomy was quantitatively evaluated using the formulae

Plasma lipid levels among different individuals with various rs5128 genotypes and rs4520 genotypes.

<p>Plasma lipid levels among different individuals with various rs5128 genotypes and rs4520 genotypes.</p