Publications
84 results found
Anderson E, Zachary S, 2023, Minimax decision rules for planning under uncertainty: drawbacks and remedies, European Journal of Operational Research, Vol: 311, Pages: 789-800, ISSN: 0377-2217
It is common to use minimax rules to make planning decisions when there is great uncertainty about what may happen in the future. Using minimax rules avoids the need to determine probabilities for each future scenario, which is an attractive feature in many public sector settings. However there are potential problems in the application of a minimax approach. In this paper our aim is to give guidance for planners considering a minimax approach, including minimax regret which is one popular version of this. We give an analysis of the behaviour of minimax rules in the case with a finite set of possible future scenarios. Minimax rules will have sensitivity to the choice of a small number of scenarios. When regret-based rules are used there are also problems arising since the independence of irrelevant alternatives property fails, which can lead to opportunities to game the process. We analyse these phenomena considering cases where the decision variables are chosen from a convex set in Rⁿ, as well as cases with a finite set of decision choices. We show that the drawbacks of minimax regret hold even when restrictions are placed on the problem setup, and we show how working with a structured set of scenarios can ameliorate the difficulty of having a final decision depend on the characteristics of just a handful of extreme scenarios.
Anderson E, Jiang H, Shao L, 2023, Competitive contract design in a retail supply chain under demand uncertainty, Naval Research Logistics, Vol: 70, Pages: 691-707, ISSN: 0894-069X
This article studies the design of contracts involving a single retailer and multiple competing manufacturers who supply substitutable products. We consider a retail context in which contracts with manufacturers are negotiated relatively infrequently and signed before the demand environment is known, and the retail prices are determined when the demand is known. We develop a Stackelberg model to study the retailer's product selection and pricing decisions and the manufacturers' contract design decisions. We show that it is optimal for each manufacturer to offer a contract with nonlinear prices so that total payments are the total production cost plus a fixed additional cost. In the case of two manufacturers this result allows us to characterize an equilibrium in which the retailer's choice maximizes the supply chain profit, each manufacturer makes a profit equal to its marginal contribution to the supply chain, and the retailer takes the remaining profit. We also find that while increasing demand correlation always benefits the retailer, it benefits the manufacturers only when the production costs are convex. In an extension it is found that our equilibrium continues to hold when the retailer's reservation profit is below a threshold, but the competition dynamics may change when the reservation profit is above the threshold. Finally, we show that the equilibrium results remain true for the case with more than two manufacturers under a submodularity property, which holds in the case of quadratic costs and linear demand.
Anderson E, Veldman J, Pulles N, et al., 2023, Developing a shared supplier with endogenous spillovers, Production and Operations Management, Vol: 32, Pages: 723-739, ISSN: 1059-1478
Firms who buy from suppliers often engage in supplier development to reduce the supplier's production cost. Being aware that their efforts may benefit a rival firm when there is a shared supplier, some buyers only invest in “specific supplier development,” that is, in those processes or technologies where spillover cannot occur. Other buyers willingly accept the spillover that arises from supplier development, and invest in “generic supplier development.” Our game-theoretic model captures a buyer's choice to invest in these distinct supplier development types as a way to endogenize spillovers. In contrast to the literature, this paper considers the benefits of investing in a combination (i.e., portfolio) of cost-reducing generic and specific supplier development. We demonstrate how supplier development affects a shared supplier's wholesale pricing decisions; whereas generic supplier development lowers wholesale prices equally across buyers, specific supplier development only lowers the wholesale price of the investing party. Our model shows that buyers should treat the spillovers from generic supplier development as an investment opportunity rather than a threat. In equilibrium, a buyer will always invest in a portfolio of both supplier development types, and having a better generic than specific investment capability may even make generic supplier development the most prevalent option for him, depending on the level of competition. Moreover, even if the buyers can commit to only investing in specific supplier investment, the resulting equilibrium gives lower buyer profits than a portfolio that includes generic investments. We also find that the presence of specific investments may raise generic supplier development, benefiting all supply chain actors. However, incorporating specific supplier development into a supplier development portfolio or a commitment to investment in only specific supplier development can lead to a prisoner's dilemma i
Anderson E, Chen B, Shao L, 2022, Capacity games with supply function competition, Operations Research, Vol: 70, Pages: 1969-1983, ISSN: 0030-364X
We introduce a general model for suppliers competing for a buyer’s procurement business. The buyer faces uncertain demand, and there is a requirement to reserve capacity in advance of knowing the demand. Each supplier has costs that are two-dimensional, with some capacity costs incurred prior to production and some production costs incurred at the time of delivery. These costs are general functions of quantity, and this naturally leads us to a supply function competition framework in which each supplier offers a schedule of prices and quantities. We show that there is an equilibrium of a particular form: the buyer makes a reservation choice that maximizes the overall supply chain profit, each supplier makes a profit equal to their marginal contribution to the supply chain, and the buyer takes the remaining profit. This is a natural equilibrium for the suppliers to coordinate on, since no supplier can do better in any other equilibrium. These results make use of a submodularity property for the supply chain optimal profits as a function of the suppliers available and build on the assumption that the buyer breaks a tie in favor of the solutions that give the largest supply chain profit. We demonstrate the applications of our model in three operations management problems: a newsvendor problem with unreliable suppliers, a portfolio procurement problem with supply options and a spot market, and a bundling problem with nonsubstitutable products.
Anderson E, Philpott A, 2021, Improving sample average approximation using distributional robustness, INFORMS Journal on Optimization, Vol: 4, Pages: 90-124, ISSN: 2575-1484
We consider stochastic optimization problems in which we aim to minimize the expected value of an objective function with respect to an unknown distribution of random parameters. We analyse the out-of-sampleperformance of solutions obtained by solving a distributionally robust version of the sample average approximation problem for unconstrained quadratic problems, and derive conditions under which these solutionsare improved in comparison with those of the sample average approximation. We compare different mechanisms for constructing a robust solution: phi-divergence using both total variation and standard smooth φfunctions; a CVaR-based risk measure; and a Wasserstein metric.
Shao L, Anderson E, Chen B, 2020, Achieving efficiency in capacity procurement, Foundations and Trends® in Technology, Information and Operations Management, Vol: 14, Pages: 138-154, ISSN: 1571-9545
This chapter studies a capacity procurement problem in which a buyer meets an uncertain demand using a combination of spot purchases and supply options that are offered by a number of competing suppliers. The specific setting we consider involves the suppliers each owning a block of capacity and the buyer restricted to reserving the entire block or none. For this setting, we are interested in understanding the buyer’s optimal procurement strategy and the suppliers’ competitive bidding behavior in the supply option market. To this end, we first examine the buyer’s optimal decision given a set of supply options, and then study the suppliers’ optimal bidding strategies in equilibrium. We find that it is optimal for suppliers to set execution price at cost and hence make a profit only through the reservation payment. We also prove that when all the blocks have the same size the buyer’s optimal profit as a function of supplier set is submodular. This property allows us to characterize an equilibrium in which the supply chain optimum is achieved, each supplier makes a profit equal to their marginal contribution to the supply chain and the buyer takes the remaining profit. When the blocks have different sizes, we develop a recursive procedure to characterize a class of equilibria in which the supply chain efficiency is achieved.
Anderson E, Nguyen H, 2020, When can we improve on sample average approximation for stochastic optimization?, Operations Research Letters, Vol: 48, Pages: 566-572, ISSN: 0167-6377
We explore the performance of sample average approximation in comparison with several other methods for stochastic optimization. The methods we evaluate are (a) bagging; (b) kernel density estimation; (c) maximum likelihood estimation; and (d) a Bayesian approach. We use two test sets: first a set of quadratic objective functions allowing different types of interaction between the random component and the univariate decision variable; and second a set of portfolio optimization problems. We make recommendations for effective approaches.
Qian C, Anderson E, 2020, Buyer's optimal information revelation strategy in procurement auctions, European Journal of Operational Research, Vol: 283, Pages: 1011-1025, ISSN: 0377-2217
We consider a procurement auction where the buying firm can manipulate the distribution of the uncertainty facing competing suppliers via reducing subjectivity in the scoring rule announced before the auction, and we examine the optimal choice of information revelation for the buyer. Specifically, we model a multi-attribute scoring auction in which the suppliers submit bids involving both price and non-price attributes and the buyer selects one supplier according to a weighted scoring system. Although the scoring rule is preannounced and the buyer commits to it during the bid evaluation, it contains elements that are subjective in nature and not precisely defined, so the suppliers still do not have full information about the exact score that will be awarded. It may be possible for the buyer to reduce the subjective component in the scoring rule by giving unusually detailed descriptions of what corresponds to specific scores. We demonstrate that it is beneficial for the buyer to limit the information revealed by retaining some subjective or imprecisely defined components in the announced scoring rule, so that the suppliers continue to be uncertain about their final scores. It is also shown that the buyer can gain more from this type of imprecision (i.e., releasing less information) if the suppliers are more different in terms of their costs to achieve a given quality level or other aspects of utility for the buyer. We consider both sealed bid and open auction formats.
Anderson E, Prokhorov A, Zhu Y, 2020, A simple estimator of two-dimensional copulas, with applications, Oxford Bulletin of Economics and Statistics, Vol: 82, Pages: 1375-1412, ISSN: 0305-9049
Copulas are distributions with uniform marginals. Non‐parametric copula estimates may violate the uniformity condition in finite samples. We look at whether it is possible to obtain valid piecewise linear copula densities by triangulation. The copula property imposes strict constraints on design points, making an equi‐spaced grid a natural starting point. However, the mixed‐integer nature of the problem makes a pure triangulation approach impractical on fine grids. As an alternative, we study the ways of approximating copula densities with triangular functions which guarantees that the estimator is a valid copula density. The family of resulting estimators can be viewed as a non‐parametric MLE of B‐spline coefficients on possibly non‐equally spaced grids under simple linear constraints. As such, it can be easily solved using standard convex optimization tools and allows for a degree of localization. A simulation study shows an attractive performance of the estimator in small samples and compares it with some of the leading alternatives. We demonstrate empirical relevance of our approach using three applications. In the first application, we investigate how the body mass index of children depends on that of parents. In the second application, we construct a bivariate copula underlying the Gibson paradox from macroeconomics. In the third application, we show the benefit of using our approach in testing the null of independence against the alternative of an arbitrary dependence pattern.
Anderson E, Xu H, Zhang D, 2020, Varying confidence levels for CVaR risk measures and minimax limits, Mathematical Programming, Vol: 180, Pages: 327-370, ISSN: 0025-5610
Conditional value at risk (CVaR) has been widely studied as a risk measure. In this paper we add to this work by focusing on the choice of confidence level and its impact on optimization problems with CVaR appearing in the objective and also the constraints. We start by considering a problem in which CVaR is minimized and investigate the way in which it approximates the minimax robust optimization problem as the confidence level is driven to one. We make use of a consistent tail condition which ensures that the CVaR of a random function will converge uniformly to its supremum as the confidence level increases, and establish an error bound for the CVaR optimal solution under second order growth conditions. The results are extended to a minimization problem with a constraint on the CVaR value which in the limit as the confidence level approaches one coincides with a problem having semi-infinite constraints. We study the sample average approximation scheme for the CVaR constraints and establish an exponential rate of convergence for the sample averaged optimal solution. We propose a procedure to explore the possibility of varying the confidence level to a lower value which can give an advantage when there is a need to find good solutions to CVaR-constrained problems out of sample. Our numerical results demonstrate that using the optimal solution to an adjusted problem with lower confidence level can lead to better overall performance.
Anderson E, Monjardino M, 2019, Contract design in agriculture supply chains with random yield, European Journal of Operational Research, Vol: 277, Pages: 1072-1082, ISSN: 0377-2217
In an agricultural setting it is natural to consider yield risk in the context of a three level supply chain: with a small number of suppliers, large numbers of growers, and a small number of buyers. In the cereal growing case that is our focus, there is a supplier of fertiliser, a potentially large number of growers of cereal crops and a buyer, who purchases grain from the growers. The yield depends both on the input level of fertiliser and also on random weather-related factors. We study the impact of a new type of contract structure in which the grower purchases inputs at a discount, but agrees to a reduced price for the crop. The buyer makes a payment to the supplier to compensate for the discount offered. We show how this can coordinate the supply chain and demonstrate the potential advantages of this contract form when producers are risk averse. We look in detail at the implications of the use of these contracts by Australian wheat growers using data generated by APSIM, a growth simulation tool, to understand the connection between yields, fertiliser use and the weather. By using APSIM we can estimate the distribution of yields implied by the grower’s decision on fertiliser application and hence estimate optimal fertiliser use for risk averse growers.
Anderson EJ, Philpott AB, 2019, Forward commodity trading with private information, Operations Research, Vol: 67, Pages: 58-71, ISSN: 0030-364X
We consider the use of forward contracts to reduce risk for firms operating in a spot market. Firms have private information on the distribution of prices in the spot market. We discuss different ways in which firms may agree on a bilateral forward contract: either through direct negotiation or through a broker. We introduce a form of supply-function equilibrium in which two firms each offer a supply function, and the clearing price and quantity for the forward contracts are determined from the intersection. In this context, a firm can use the offer of the other player to augment its own information about the future price.
Anderson E, Holmberg P, 2018, Price instability in multi-unit auctions, Journal of Economic Theory, Vol: 175, Pages: 318-341, ISSN: 0022-0531
We consider a uniform-price procurement auction with indivisible units and private independent costs. We find an explicit solution for a Bayesian Nash equilibrium, which is unique if demand shocks are sufficiently evenly distributed. The equilibrium has a price instability in the sense that a minor change in a supplier's realized cost can result in a drastic change in the market price. We quantify the resulting volatility and show that it is reduced as the size of indivisible units decreases. In the limit, the equilibrium converges to the Supply Function Equilibrium (SFE) for divisible goods if costs are common knowledge.
Anderson E, Chen B, Shao L, 2017, Supplier competition with option contracts for discrete blocks of capacity, Operations Research, Vol: 65, Pages: 952-967, ISSN: 0030-364X
When a firm faces an uncertain demand, it is common to procure supply using some type of option in addition to spot purchases. A typical version of this problem involves capacity being purchased in advance, with a separate payment made that applies only to the part of the capacity that is needed. We consider a discrete version of this problem in which competing suppliers choose a reservation price and an execution price for blocks of capacity, and the buyer, facing known distributions of demand and spot price, needs to decide which blocks to reserve. We show how to solve the buyer’s (combinatorial) problem efficiently and also show that suppliers can do no better than offer blocks at execution prices that match their costs, making profits only from the reservation part of their bids. Finally we show that in an equilibrium the buyer selects the welfare maximizing set of blocks.
Anderson EJ, Yang S-JS, 2015, The Timing of Capacity Investment with Lead Times: When Do Firms Act in Unison?, PRODUCTION AND OPERATIONS MANAGEMENT, Vol: 24, Pages: 21-41, ISSN: 1059-1478
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- Citations: 17
Yang S-JS, Anderson EJ, 2014, Competition through capacity investment under asymmetric existing capacities and costs, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 237, Pages: 217-230, ISSN: 0377-2217
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- Citations: 10
Anderson EJ, 2013, Business Risk Management: Models and Analysis, ISBN: 9781118349465
A comprehensive and accessible introduction to modern quantitative risk management. The business world is rife with risk and uncertainty, and risk management is a vitally important topic for managers. The best way to achieve a clear understanding of risk is to use quantitative tools and probability models. Written for students, this book has a quantitative emphasis but is accessible to those without a strong mathematical background. Business Risk Management: Models and Analysis. Discusses novel modern approaches to risk management: Introduces advanced topics in an accessible manner; Includes motivating worked examples and exercises (including selected solutions); Is written with the student in mind, and does not assume advanced mathematics; Is suitable for self-study by the manager who wishes to better understand this important field. Aimed at postgraduate students, this book is also suitable for senior undergraduates, MBA students, and all those who have a general interest in business risk.
Anderson EJ, 2013, On the existence of supply function equilibria, MATHEMATICAL PROGRAMMING, Vol: 140, Pages: 323-349, ISSN: 0025-5610
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- Citations: 14
Anderson EJ, Holmberg P, Philpott AB, 2013, Mixed strategies in discriminatory divisible-good auctions, RAND JOURNAL OF ECONOMICS, Vol: 44, Pages: 1-32, ISSN: 0741-6261
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- Citations: 13
Anderson E, 2012, Ranking Games and Gambling: When to Quit When You're Ahead, OPERATIONS RESEARCH, Vol: 60, Pages: 1229-1244, ISSN: 0030-364X
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- Citations: 2
Anderson EJ, Hu X, 2012, Asymmetric Supply Function Equilibria with Forward Contracts, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol: 152, Pages: 198-224, ISSN: 0022-3239
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- Citations: 3
Anderson EJ, Cau TDH, 2011, Implicit collusion and individual market power in electricity markets, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 211, Pages: 403-414, ISSN: 0377-2217
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- Citations: 33
Anderson E, 2011, A new model for cycles in retail petrol prices, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 210, Pages: 436-447, ISSN: 0377-2217
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- Citations: 6
Anderson EJ, Coltman T, Devinney TM, et al., 2011, WHAT DRIVES THE CHOICE OF A THIRD-PARTY LOGISTICS PROVIDER?, JOURNAL OF SUPPLY CHAIN MANAGEMENT, Vol: 47, Pages: 97-115, ISSN: 1523-2409
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- Citations: 62
Anderson EJ, Bao Y, 2010, Price competition with integrated and decentralized supply chains, EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, Vol: 200, Pages: 227-234, ISSN: 0377-2217
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- Citations: 130
Anderson EJ, Cau TDH, 2009, Modeling Implicit Collusion Using Coevolution, OPERATIONS RESEARCH, Vol: 57, Pages: 439-455, ISSN: 0030-364X
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- Citations: 22
Anderson EJ, Hu X, 2008, Finding supply function equilibria with asymmetric firms, OPERATIONS RESEARCH, Vol: 56, Pages: 697-711, ISSN: 0030-364X
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- Citations: 41
Anderson EJ, Hu X, 2008, Forward contracts and market power in an electricity market, INTERNATIONAL JOURNAL OF INDUSTRIAL ORGANIZATION, Vol: 26, Pages: 679-694, ISSN: 0167-7187
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- Citations: 37
Anderson E, Kelly F, Steinberg R, et al., 2007, A contract and balancing mechanism for sharing capacity in a communication network (vol 53, pg 1029, 2007), MANAGEMENT SCIENCE, Vol: 53, Pages: 1029-1031, ISSN: 0025-1909
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- Citations: 2
Anderson EJ, Hu X, Winchester D, 2007, Forward contracts in electricity markets: The Australian experience, International Research Conference on Social Acceptance of Renewable Energy Innovation, Publisher: ELSEVIER SCI LTD, Pages: 3089-3103, ISSN: 0301-4215
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- Citations: 51
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