Saurabh Bansal

Immersive Analytics for Multi-objective Dynamic Integrated Climate-Economy (DICE) Models

We are creating an immersive analytics tool for exploring the output of a Dynamic Integrated Climate-Economy (DICE) model, and present early work on the prototype system. DICE models and other Integrated Assessment Models (IAMs) are critical for informing environmental decision making and policy analysis. They often produce complex and multi-layered output, but need to be understood by decision makers who are not experts. We discuss our current and targeted feature set in order to help address this challenge. Additionally, we look ahead to the potential for rigorous evaluation of the system to uncover whether or not it is an improvement over current visualization methods.

Managing production of high-tech products with high production quality variability

We consider production systems in technology industries where output quality of a single production run has a large variance. Firms operating such systems classify products into different quality bins and sell units in one bin at the same tagged quality level and the same price. Consumers have heterogeneous quality preferences and choose that quality that maximises their net utility. We examine firms’ assortment, production and pricing problem. We present a three-stage solution procedure that optimises the production quantity, quality specification and number of bins. In that regard, we show that for a manufacturing technology with known quality distribution and known distribution of customers’ quality preference, the optimal assortment and production quantity are set such that on average, the demand of each bin is exactly fulfilled. We examine the impact of an improved manufacturing technology, variation in consumer preferences and changing price premium on the optimal assortment, lot size, market share, yield loss and the overall profitability. We further show that when the quality distribution of the manufacturing process is unknown, downward substitution leads to product offering of higher quality and higher prices. Finally, we discuss practical considerations for pricing, technology and optimal product offerings, and explain the proliferation of bins witnessed in the last decade in the processor industry.

Product Portfolio Management with Production Flexibility in Agribusiness.

The acquisition of production flexibility is a well-documented strategy pursued by many firms to counteract certain operational constraints. However, these flexibilities can increase the complexity of a production system and the difficulties in managing increased complexity may hinder exploiting the full benefit of flexibility. In this paper, we consider one such flexibility paradox at an agribusiness firm for an annual

Using Experts’ Noisy Quantile Judgments to Quantify Risks: Theory and Application to Agribusiness

800 million production decision: The firm produces a number of products (hybrid seeds) using limited inventories of several raw materials (parent seeds) and a production process that is subject to random variations. To handle the raw material availability constraint and to partially mitigate the supply risk, the firm invests in a costly second production in South America that can be used if the yield in the first production in North America is low. We solve this joint problem of raw material allocation and sequential production by reformulating it as a tractable simultaneous optimization ...

Technical Note—Multivariate Partial-Expectation Results for Exact Solutions of Two-Stage Problems

Motivated by a unique agribusiness setting, this paper develops an optimization-based approach to estimate the mean and standard deviation of probability distributions from noisy quantile judgments provided by experts. The approach estimates the mean and standard deviations as weighted linear combinations of quantile judgments, where the weights are explicit functions of the expert’s judgmental errors. The approach is analytically tractable, and provides flexibility to elicit any set of quantiles from an expert. The approach also establishes that using an expert’s quantile judgments to deduce the distribution parameters is equivalent to collecting data with a specific sample size and enables combining the expert’s judgments with those of other experts. It also shows analytically that the weights for the mean add up to one and the weights for the standard deviation add up to zero—these properties have been observed numerically in the literature in the last 30 years, but without a systematic explanation. Th...

Solution to a Class of Two-stage Stochastic Programs with Multivariate Normal Uncertainty

We consider two-stage sequential decision-making problems where in Stage 1 an initial decision is made under a multivariate uncertainty, and in Stage 2 the uncertainty is resolved, a further decision is made based on the uncertainty realization, and the payoff is observed. We focus on problems where the payoff is a linear function of the multivariate uncertainty realization. Such problems can be written as single-stage nonlinear optimization problems composed of partial polyhedral expectations of the multivariate uncertainty. We identify the structural characteristics of multivariate probability density functions under which the integral expressions for the partial expectations can be directly evaluated for an exact value. We then focus on elliptical distributions, which are frequently used in operations management and do have these characteristics. We develop a sequence of three results to determine partial polyhedral expectations of elliptical probability distributions, with a special emphasis on the no...

Using Imperfectly Elicited Fractiles for the Estimation of Probability Distribution Parameters

We provide results for an efficient analytical valuation of partial moments of the multivariate Gaussian distribution over convex polyhedrons to aid the solution, sensitivity analysis and structural analysis of a large number of two-stage resource acquisition and allocation problems. These results decompose a partial multivariate moment into a function of multivariate probabilities that can be easily determined using the existing efficient numerical routines. The results are most useful in practice when (i) the structure of the Stage 2 allocation problem is known a-priori, for example when a greedy allocation algorithm is known to be optimal as is commonly the case for many resource sharing problems, or (ii) when the performances of various a-priori policies need to be evaluated, or (iii) when the number of uncertainties is small. We illustrate the use and benefit of the results over traditional simulation based approaches using a multi-resource newsvendor problem of practical size.

Impact of Compound and Reduced Specification on Valuation of Projects with Multiple Risks

We develop direct and indirect analytical approaches to determine the parameters of a distribution using elicited fractile values in the presence of elicitation errors. Both approaches seek to minimize the variance on the errors in the estimation of the parameters of the distribution. In the indirect approach we obtainweights for the elicited fractile values to estimate the moments of the distribution; estimates for the probability distribution parameters can then be obtained indirectly from the moment estimates. The direct approach provides weights to estimate the parameters directly from the elicited fractile values. For both approaches, we show that the weights are independent of the actual parameter values and depend only on the fractile probabilities being elicited when the distribution is a location-scale distribution. We show numerically that both these approaches should be preferred over approaches that ignore elicitation error or elicit only a specific set of fractiles. The parameter invariant weights for an arbitrary set of fractile probabilities provide for a flexible elicitation of probability distributions. Subsequently, we extend the results to other non location-scale distributions including the Johnson family of distributions.

Estimating Substitution and Basket Effects in Retail Stores: Implications for Assortment Planning

Several firms make business decisions based on risk specifications or estimates provided by domain-experts. But research on whether the format of risk specifications systematically affects decision making in multi-dimensional environments is scarce. We show using laboratory experiments that subjective valuations of multi-dimensional projects are highly sensitive to the format of risk specifications. We considered a technology project that has two dimensions each with an associated risk, and would be considered a success when favorable outcomes occur on both dimensions. Participants were provided with the probabilities of success for each dimension, in two different specifications. In the simple risk specification, each probability was specified as a point estimate. In the compound risk specification, each probability was specified as a two-point distribution. The data show that decision-making under compound specifications is subject to two biases in processing conjunctive events and compound risk specifications; these biases act in opposite directions, and as outcome, judgmental valuations for the technology are closer to the true value with compound risk specification versus with simple risk specification. These results have an important implication for communicating risk: when compound risk specifications are available for multiple risks, substituting them with simple risk specifications leads to an overly optimistic outlook during decision-making.

Managing Demand Uncertainty through Core Acquisition in Remanufacturing

Many retailers are reducing store footprint and downsizing their assortments accordingly to improve store productivity. Some of the revenue for items removed from the assortment may be recouped by substitution, but also some of the revenue for items kept in the assortment may be lost due to basket abandonment. For a practical setting where baskets may contain any subset of items from thousands of products, estimating both substitution and basket effects is a challenge. To address this we develop a demand model that incorporates a multinomial logit (MNL) model to estimate substitution within a subcategory and a parsimonious model to estimate basket retention. Using transaction and product availability data from 8 stores of an office supplies retail chain that were dramatically downsized from large- to small-format stores, we show that inclusion of the basket retention effect in assortment selection for the small stores can significantly improve profits at these stores.