About

William L. Cooper is a Professor in the Department of Industrial and Systems Engineering at the University of Minnesota, where he has been a faculty member since 1999, progressing from Assistant Professor to Associate Professor and then to full Professor since Fall 2013. He holds a Ph.D. in Industrial Engineering from the Georgia Institute of Technology (1999) and a B.A. in Mathematics from the University of Pennsylvania (1993). His research interests focus primarily on revenue management and pricing, as well as applied probability. Throughout his career, Professor Cooper has contributed extensively to the field through numerous publications addressing topics such as pricing models with network effects, consumer behavior in revenue management, stochastic optimization, and dynamic pricing strategies. He has also been involved in funded research projects supported by the National Science Foundation, investigating areas like revenue management with network effects, model accuracy and learning in dynamic pricing, and stochastic optimization for revenue management. In addition to his research, Professor Cooper has played significant roles in academic service, including serving as Chair of the INFORMS Revenue Management and Pricing Section, Director of Graduate Studies at his department, and holding editorial positions for several leading journals in operations research and management science. He has also contributed to the academic community by advising numerous Ph.D. students who have gone on to successful careers in academia and industry.

Research topics

• Computer Science
• Mathematics
• Economics
• Mathematical optimization
• Microeconomics
• Econometrics
• Accounting
• Business
• Operations management
• Marketing

Selected publications

• Effect of Particle Size on the Compressive Behavior of Dry Sand under Confinement at High Strain Rates

  River Publishers eBooks · 2025-08-07

  book-chapter

  Dynamic compressive behavior of dry sand (Quikrete #1961 sand quarried in Pensacola, FL) under confinement was characterized using a split Hopkinson pressure bar (SHPB). The as-received dry Eglin sand was sieved into different grain sizes, following the ASTM D2487 standard. The sand were sorted into 0.60, 0.50, 0.42, 0.30, 0.212, 0.15, and 0.106 mm grains through a set of ASTM E11 sieves of #30, #35, #40, #50, #70, #100 and #140, respectively. Sand grains were confined inside a hollow cylinder of hardened steel and capped by cemented tungsten carbide cylindrical rods. This assembly was subjected to repeated manual shaking to consolidate sand to attain the desired bulk mass densities. It is then sandwiched between incident and transmission bars on SHPB for dynamic compression under high strain rate. Sand specimens of seven particle sizes (shaking into maximum mass density) were characterized to determine the volumetric and deviatoric behaviors at high strain rates, and the particle size effect was discussed. The stress-density relationship and the specific energy absorption were determined as a function of sand grain sizes. The void ratio-axial pressure relationships (e-log p curves) were obtained and the compressibility of sand was determined as a function of sand particle sizes.

  PublisherDOI

• Pricing a Product with Network Effects for Sale to a Fixed Population of Customers

  SSRN Electronic Journal · 2024

  Senior authorCorresponding
  • Business
  • Marketing
  • Economics
  PublisherDOI

• Pricing a product with network effects for sale to a fixed population of customers

  Naval Research Logistics (NRL) · 2024

  Senior authorCorresponding
  • Computer Science
  • Computer Science
  • Mathematical optimization

  Abstract We consider a deterministic dynamic pricing problem for a product that exhibits network effects and that is sold to a fixed heterogeneous population of customers. We begin by introducing a demand model wherein those customers are arrayed over two‐dimensional space according to a bivariate probability distribution. Each customer's location in space provides a description of that customer's intrinsic value for the product as well as the extent to which the customer is influenced by the network effect. In the pricing problem, as sales accumulate over time, the set of customers who have already purchased the product grows, while the set of customers who have not yet purchased the product shrinks. The total customer population remains fixed. Those who have not yet purchased constitute the remaining population of potential buyers of the product. As time moves forward, the mix of customers that remain as potential buyers evolves endogenously. The demand model yields a geometric interpretation of the remaining population of potential buyers, and gives rise to a dynamic program with states that are sets in two‐dimensional space. It is not practical to solve the dynamic pricing problem to optimality, so we present bounds and comparative statics results that help us identify tractable heuristics and obtain rigorous performance guarantees. In numerical experiments, we find that fixed‐price policies may perform poorly, especially when the network effect is strong or the time horizon is long. We also introduce a stochastic version of the problem that uses a spatial Poisson process to describe the customers, and we develop and analyze a heuristic approach for that formulation.

  PublisherDOI

• Performance degradation modeling of civil aviation engines based on component characteristic map optimization

  Journal of applied artificial intelligence. · 2024-10-18

  article1st authorCorresponding

  In order to provide a theoretical basis for the degradation of the air path performance of civil aviation engines at the unit level, the CFM56-3 engine was used as the research object. First, on the basis of using the characteristic map scaling method to obtain the component characteristic equation, the selection process of the scaling reference point of the fan general characteristic map was optimized, and a surface fitting method of the characteristic map was proposed to construct an engine component-level benchmark performance model that meets specific speed conditions under steady-state conditions. Then, by introducing the fault factor to generate the fault coefficient matrix, the deviation of the engine monitoring parameters as the component efficiency decreases was calculated, and compared with the fingerprint map data of the GE training manual, it was verified that the engine steady-state performance model that integrates the fan characteristic map scaling reference point optimization and the characteristic map surface fitting method has good accuracy and use in the analysis of air path performance degradation.

  PublisherDOI

• Pricing for a product with network effects and mixed logit demand

  Naval Research Logistics (NRL) · 2020 · 22 citations

  • Computer Science
  • Computer Science
  • Mathematical optimization

  Abstract We consider a pricing problem for a single product that experiences network effects. Demand is described by a consumer choice model in which each individual chooses between purchasing the product and not purchasing the product. We assume that there are multiple segments in the population of potential buyers, and that individuals' intrinsic values for the product and sensitivities to the network effect (ie, the extent to which their values are affected by how many others buy the product) vary across segments. The demand model may be viewed as a version of the mixed multinomial logit model, modified to incorporate network effects. We formulate and analyze an optimization problem that aims to find the seller's revenue‐maximizing price. In settings with an arbitrary number of demand segments, we present a simple, effective heuristic solution approach. In settings with two segments, we obtain a solution method that outputs provably near‐optimal prices. We close with an extensive numerical study.

  PublisherDOI

• Information Provision and Pricing in the Presence of Consumer Search Costs

  Production and Operations Management · 2019-02-05 · 33 citations

  articleCorresponding

  Should a seller make information about its products readily accessible to customers, so that customers do not have to incur any substantive cost—in terms of time and effort—to learn about those products? To help answer this question, we consider a monopolist selling two substitute products to a population of customers, who have differing tastes about the products. Each customer a priori has uncertainty about whether or not he will like each of the products. The seller may choose to make product information easily accessible, thereby allowing customers to resolve their uncertainties for free. Otherwise, customers may conduct research to resolve their uncertainties by incurring a search cost before making purchase decisions. We consider three “information structures” differing in whether the seller makes information about the products freely accessible or not. Our primary objective is to determine which structure gives the seller the highest revenue, while accounting for the seller’s pricing decisions as well as the induced customer responses to both the information structure and prices. We find that if each customer’s uncertainties are small in magnitude but highly positively correlated, then withholding both products’ information is the best for the seller. If the uncertainties are small in magnitude and negatively correlated, then providing one product’s information but not the other’s is the best. If the uncertainties are large in magnitude and positively correlated, then providing both products’ information is the best. We also show that when the correlation is negative, withholding both products’ information cannot be optimal. In addition, we also analyze various extensions of the model. These include a variant in which customers’ research is imperfect and may yield incorrect information to the customers, and a variant in which each customer’s uncertainty about a product can be decomposed into multiple uncertainties associated with individual attributes of the product.

  PublisherDOI

• Optimal worst-case pricing for a logit demand model with network effects

  Operations Research Letters · 2018-03-28 · 18 citations

  articleOpen accessCorresponding

  We consider optimal pricing problems for a product that experiences network effects. Given a price, the sales quantity of the product arises as an equilibrium, which may not be unique. In contrast to previous studies that take a best-case view when there are multiple equilibrium sales quantities, we maximize the seller’s revenue assuming that the worst-case equilibrium quantity will arise in response to a chosen price. We compare the best- and worst-case solutions, and provide asymptotic analysis of revenues.

  PublisherDOI

• Information Provision and Revenue Management in the Presence of Consumer Search Costs

  SSRN Electronic Journal · 2017-01-01 · 3 citations

  articleOpen access
  PublisherDOI

• Dancing on a Volcano

  Minerva Access (University of Melbourne) · 2016-12-17

  article

  Dancing on a Volcano, presented by Forest Collective. “The whole town and all its inhabitants are quite drowned in carnival din, masks and confetti. And on top of that the news of the Reichstag fire. Dancing on a volcano” -- Alban Berg. Dancing on a Volcano features rarely heard works created during the time of the Nazi regime. The performance focuses mainly on German and Jewish composers who were either supported or banned during this time, including works by Isla Webber, Kurt Weill, Franz Schreker, Frederich Hollander, Mischa Spoliansky, Henri Dutilleux and Olivier Messiaen.

  Publisher

• Optimal Pricing for a Multinomial Logit Choice Model with Network Effects

  Operations Research · 2016-03-25 · 120 citations

  article

  We consider a seller’s problem of determining revenue-maximizing prices for an assortment of products that exhibit network effects. Customers make purchase decisions according to a multinomial logit choice model, modified—to incorporate network effects—so that the utility each individual customer gains from purchasing a particular product depends on the market’s total consumption of that product. In the setting of homogeneous products, we show that if the network effect is comparatively weak, then the optimal pricing decision of the seller is to set identical prices for all products. However, if the network effect is strong, then the optimal pricing decision is to set the price of one product low and to set the prices of all other products to a single high value. This boosts the sales of the single low-price product in comparison to the sales of all other products. We also obtain comparative statics results that describe how optimal prices and sales levels vary with a parameter that determines the strength of the network effects. We extend our analysis to settings with heterogeneous products and establish that optimal solutions have a structure similar to that found in the homogeneous case: either maintain a semblance of balance among all products or boost the sales of just one product. Based on this structure, we propose an effective computational algorithm for such general heterogeneous settings.

  PublisherDOI

Recent grants

• Revenue Management with Network Effects

  NSF · $270k · 2015–2020

Frequent coauthors

• Zizhuo Wang

  9 shared

• Hongbing Lu

  The University of Texas at Dallas

  7 shared

• Patrick Tong

  Vanderbilt University

  4 shared

• Diwakar Gupta

  The University of Texas at Austin

  4 shared

• Hua Liu

  Renmin Hospital of Wuhan University

  4 shared

• Jian-Guo Ren

  4 shared

• Chenhao Du

  University of Minnesota

  4 shared

• Charles E. Hawkins

  Johns Hopkins Medicine

  4 shared

Labs

• William L. Cooper LabPI

Awards & honors

• Russell J. Penrose Excellence in Teaching Award (2019)
• Harold W. Kuhn Award for exceptional paper published in Nava…
• INFORMS M&SOM Best Paper Award Finalist (2009)
• INFORMS Revenue Management and Pricing Section (Best Publica…