Manel Baucells

In “Search in the Dark: The Case with Recall and Gaussian Learning,” Manel Baucells and Saša Zorc address the classic sequential search problem where decision makers sample from a distribution to maximize rewards minus sampling costs. They focus on search with recall, where the reward is the highest sampled value. They solve the long-standing problem of determining optimal stopping rules when the sampling distribution is normal but both its mean and variance are unknown, and hence, they are progressively learned via sampling. The solution reveals that traditional methods, which rely on single reservation prices, are inadequate. The proposed approach offers a practical and efficient way to determine the optimal stopping rule. Relevant applications include job search, the sale of an asset, or technology adoption.

In this case, students explore decision-making under uncertainty and apply dynamic programming (DP), a powerful tool for optimizing sequential decisions. Set in the context of the ore mining industry, the case revolves around a strategic auction for a 10-year lease of the Silver Crest Mine (Silver Crest), recently reopened due to a rise in silver prices. Two firms—TerraGold and MineralCorp—are the sole qualified bidders. The auction winner secures exclusive rights to operate the mine for the next decade and can make annual decisions on whether to keep the mine open or close it down. Silver produced during any operational year is sold at that year's prevailing market price, which is highly volatile and follows a stochastic process.The central challenge lies in valuing the lease. To do so, each firm must account not only for the expected future trajectory of silver prices but also for the irreversible fixed costs of opening and closing the mine. Further, MineralCorp benefits from access to a high-efficiency continuous miner, which reduces its per-ounce operating cost, while TerraGold possesses advanced analytical expertise and leverages DP to construct an operating policy adaptable to evolving market conditions. Working from TerraGold's perspective, students develop a bidding strategy informed by dynamic optimization.At the University of Virginia Darden School of Business, this case is used in the Executive MBA core Decision Analysis course as part of a three-session module on DP. It can be taught in a core course in Decision Analysis or Business Analytics, or as part of an elective on Optimization or Quantitative Methods for Management. In all settings, we strongly recommend using this case with the companion technical note, “Introduction to Dynamic Programming” (UVA-QA-0955).ExcerptThe Silver Crest MineIn 2023, eight years after closing operations in the Silver Crest Mine (Silver Crest), the current owners of Silver Crest decided to lease out the mine in reaction to the recent uptick in silver prices. A stringent bidding process was put in place to decide the next mine operator, and MineralCorp and TerraGold were the only two companies that met the requirements to participate in the bidding. The highest bidder in a sealed-price auction would win the rights to operate the mine for the next 10 years. At the end of the 10 years, the mine would revert to the lessor “as is,” with no obligation by the lessee to have the mine in operation or idle prior to the expiration of the lease. The minimum bidding price was $1 million.Silver Crest dated back to the silver rush of the late 1800s, when the mine was discovered in a remote region known for its rich and abundant mineral deposits. A combination of economic challenges, environmental concerns, and operational difficulties led to its closure in 2015. The prevailing factor behind the mine's closure was a protracted period of low silver prices that rendered operations economically unviable.With a track record of employing state-of-the-art mining equipment, MineralCorp possessed an idle continuous miner that it could conveniently put to use if the company were to win the lease, allowing it to streamline operations. On the other hand, TerraGold, a rising star in the industry, had developed a reputation for its expertise in optimizing manual drilling and blasting.. . .

Project leaders are responsible for planning, controlling, and revising projects. As a project unfolds, the leader evaluates the project’s progress by comparing ongoing costs and scope to a baseline plan and considers potential revisions. We offer a general model of managerial mental accounting, which includes loss aversion, reference point updating, and narrow framing, and examine how it impacts downstream decisions. Our model predicts insufficient adjustments of project scope and cost at revision, resulting in reduced financial profit. We show that the choice of measure to quantify the project progress—planned, actual, or earned—affects the updating of reference points, and hence the downstream decisions. Thus, progress measures could be wisely employed to mitigate insufficient adjustments. It turns out that measuring progress via planned scope is often advantageous, whereas utilizing earned value for cost is never advisable. This paper was accepted by David Simchi-Levi, behavioral economics and decision analysis. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2021.02929 .

Problem definition: Sequencing of consumption has significant implications for enjoyment of experiential goods and derived ex-post utility due to psychological and physiological effects, such as satiation, habituation, or memory decay. In this paper, we examine the effect of consumption sequencing on ex-ante valuations of bundles, with the goal of increasing consumer surplus and revenue. Methodology/results: We conduct a lab experiment to elicit preferences and willingness to pay for three bundles of goods consisting of two high (H) type products and one low (L) type product that vary only in the position of low type product. We find that consistent with the satiation model, 53% of subjects prefer the HLH sequence, placing an approximately 2.7% greater ex-ante valuation over the second-best LHH sequence. The LHH sequence is optimal under the acclimation, and memory decay model and preferred by 31% of subjects. The front-loaded HHL sequence, optimal under the discounted expected utility model, is preferred by 16% of subjects. We estimate the parameters of the satiation model and find that satiation effects are significant with a half-life of 17 hours. Managerial implications: Using the calibrated satiation model, we optimize consumption for each period and find that, compared to a bundle with equal consumption in each period, the optimal bundle has a greater selling probability and achieves a revenue lift in excess of 4.5%.

Trend indicators aim to visualize the effect of input assumptions and parameters into model output. Their use is increasingly important, especially when the output is generated by a black box algorithm. We investigate the properties of several trend indicators used in simulation and machine learning, and discover that not all give consistent results when applied to well understood problems. We show that some indicators (individual conditional expectations (ICE), gradients, and partial dependence functions) are convexity and monotonicity consistent even when inputs are not independent; while some others (ALE plots, regression lines, correlation coefficients) may not be. We advocate the combined use of ICE and partial dependence plots, discuss their connection with Tornado Diagrams and Spiderplots, and propose two discrepancy indices to ease their interpretation.

This note discusses a variety of methods to assist intuition in complex situations with multiple objectives and a potentially large set of alternatives. It begins with heuristic rules, which are relatively simple ways to sort out alternatives without thinking too much about trade-offs. After discussing the reliability of such rules, it moves to multicriteria analysis, which is a more rational method of balancing conflicting objectives. Excerpt UVA-QA-0914 Rev. Jun. 7, 2021 Resolving Trade-Offs: From Simple Heuristics to Multicriteria Analysis Imagine you need to buy a new toaster for your morning breakfast. A quick online search reveals two options: a cheap, simple toaster with a manual timer for $99 (option A), and an electronic toaster with an automatic timer for $179 (option B). You decide that, for the price difference, a simple toaster would do. After driving to the home products store, you are relieved to find the two toasters on display at the online price. There is a third toaster on display, with pretty much the same features as the $179 one, but priced at $199 (option C). Who is going to buy a toaster that matches the quality but costs more than the $179 toaster? We say that the $179 toaster dominates the $199 one, because it is better or equal in all attributes. After giving it some more thought, however, you change your mind, and you leave the store with the $179 one. Saving $20 makes you feel good, doesn't it? In reality, you have fallen prey to the decoy effect! The decoy effect is the instinctive attraction toward dominant alternatives, and is felt when dominated alternatives are added to the mix. This effect has even been observed in frogs! It is as if all the alternatives are seen as equally likely to be correct from the outset, but if alternative B dominates alternative C, then B absorbs the probability from C of being correct. This logic may be appropriate in environments where alternatives are presented by nature at random, but it is vulnerable to manipulation when the menu of offerings is designed by marketeers. Indeed, alternative C was artificially included so you would choose the expensive toaster! Thus even with only two attributes—price and quality as in the toaster case—intuition may fail to make consistent trade-offs. Things can only get worse if more than two attributes and many alternatives are in play. Such complex choices are routine in business, say when a company executive must acquire hundreds of personal computers or a large fleet of cars for the firm, or select a location for a new factory. In such cases, we recognize that “you can't have everything,” which is an intuitive statement reflecting that trade-offs need to be made. Making trade-offs, however, creates internal conflicts in the decision-maker. As individuals, do we have the capacity to integrate correctly all the information required to make a good decision? . . .

Models in which current utility depends solely on current consumption (a.k.a. time-separable preferences) are widely acknowledged to be unrealistic, especially when attempting to describe preferences over consumption rates. Alternatively, one may stipulate that instant utility also depends on a state, for example, some stock of past consumption. Escaping the gravitational pull of time separability, however, is difficult because (1) the behavioral axioms that characterize the state and the instant utility are not known, (2) how to elicit the preference parameters—most notably the initial level of the state and the decay rate—is not known, and (3) managerial applications where state-dependent preferences produce interesting insights and solutions are scarce. This paper makes advances on these three fronts by proposing a novel set of axioms that characterize the satiation model, a proof of concept on how to elicit all preference parameters using consumption rates, and a mixed-integer linear formulation to solve the optimal design of experiential services under satiation. Our preferences introduce a de-satiation motive, absent in separable preferences, and we explore how to optimally manage this motive. This paper was accepted by David Simchi-Levi, decision analysis.

Present equivalents of future payouts elicited from individuals exhibit a high variability in the underlying discount rate, suggesting that multiple factors influence discounting. One such factor --- shown to be robust --- is the magnitude effect, whereby small future payouts are discounted more than larger ones. When individuals are confronted with more than one future payout, it is unknown whether the magnitude effect is driven by the sum of cash flows, or the highest cash flow, or the first, or the last, or the lowest. In this paper, we elicit the discount rate of diverse cash flows following a ceteris paribus design. The best predictive model has the discount rate decreasing with the sum and the highest cash flow, with noticeable effects kicking in for sums below 600 euros and/or the maximum cash flow below 18 euros. We also take decreasing impatience into account, and distill a prescriptive base discount rate after removing the effects of magnitude and decreasing impatience. We illustrate the approach with applications to energy conserving decisions.