Source-linked AI summary
Why Customer Choice Models Matter
Berry Gerrits, Fabian Akkerman
TL;DR
The paper asks whether customer choice-model assumptions materially affect attended-home-delivery revenue management, where such models underpin slotting and pricing decisions. It examines model mismatch, parameter uncertainty, and customer heterogeneity within a common framework, finding that policies can look substantially better when judged under their own assumed model or a single parameter estimate.
Problem
AHD revenue-management studies often assume a known customer choice model and fixed parameters, despite noisy behavior and limited sensitivity analysis.
Method
The paper evaluates AHD pricing and slotting through a common four-component framework and experiments with alternative choice models, uncertain parameters, and customer segmentation.
Results
Policies evaluated under mismatched choice models can lose up to 22%, while logit and attraction models retain only 45–48% when rank-based choices generate demand.
Takeaways & Limitations
Customer choice models are decision-relevant rather than innocent modeling details, so policies should be tested against multiple plausible models and uncertainty.
Abstract
from arXiv · showhide
Customer choice models are central to revenue management in attended home delivery, yet the field usually picks one without much thought. Does the choice model matter? We believe it does, and this paper shows that revenue management policies judged by their own assumed model, or trusted under a single set of parameters, can be worse than they look.
1 Introduction
Customer choice models are foundational inputs to attended-home-delivery revenue management, but assumed models and parameters can materially distort policy evaluation. The paper frames AHD methods through four shared components and argues that the choice-model component deserves explicit scrutiny.
- 1 Introduction: Customer choice models determine how customers select delivery slots and can heavily determine revenue-management outcomes.AHD policies offer time slots and prices, while the choice model and cost approximation provide the foundation for those decisions.
- 1 Introduction: The paper argues that evaluating policies under the same assumed choice model can make pricing or slotting claims appear overconfident.The true customer choice model is unknown, may differ substantially from the assumed model, and is rarely tested through sensitivity analysis.
- 1.1 A Unified View of Attended Home Delivery: AHD revenue management comprises slotting, pricing, customer choice, and cost-approximation components within a common profit-maximization framework.Slotting determines offered availability, pricing determines delivery fees, customer choice models responses, and cost models estimate fulfillment costs.
- 1.1 A Unified View of Attended Home Delivery: Slotting and pricing may be static or dynamic, with dynamic decisions adapting offered slots or prices to the current booking state.Static decisions are fixed before bookings, whereas dynamic policies use the current system state z.
- 1.1 A Unified View of Attended Home Delivery: The paper positions customer choice models as an underexamined input to AHD policies and uses a unified framework to disentangle their role.The framework remains unchanged across virtually all AHD revenue-management models, while different methods choose different component specifications.
2 Literature Overview
The literature review presents AHD choice models as variants of a shared random-utility framework, while showing how their assumptions produce different substitution and heterogeneity patterns. It introduces the model families and illustrates their behavioral distinctions through a common delivery-slot example.
- 2 Literature Overview: AHD choice models differ mainly in their deterministic utility structure, residual distribution, and resulting choice rule.The reviewed families include rank-based, conditional logit, MNL, nested MNL, mixed logit, BAM, and GAM.
- 2 Literature Overview: The running example maps offered slots and prices into slot-choice and no-purchase probabilities, with a discount on slot B motivating comparison across models.The retailer prefers slot B because it is cheap to insert into the route.
- 2 Literature Overview: MNL provides closed-form probabilities but imposes IIA, redistributing a withdrawn slot’s demand across remaining alternatives in fixed proportion.This can over-capture demand, especially when the assortment is narrow; lowering pB proportionally shrinks the probabilities of A, C, and no purchase.
- 2 Literature Overview: Nested logit allows correlated options within nests, so withdrawing one slot shifts probability mainly toward alternatives in the same nest rather than uniformly.In the example, removing A shifts probability mainly toward C rather than B and no purchase.
- 2 Literature Overview: Mixed logit represents customer heterogeneity through random coefficients, capturing differentiated responses while requiring simulation when choice probabilities lack a closed form.Customers with different timing preferences respond differently to a lower price for slot B.
- 2 Literature Overview: Attraction models assign alternatives nonnegative attraction values, with BAM reducing to the logit softmax under exponential attractions.The resulting formulation includes the always-available no-purchase alternative and links attraction values to utilities through ws = exp(vs).
3 Experiments
The experiments isolate how customer-choice-model assumptions affect attended-home-delivery pricing, examining model misspecification, parameter uncertainty, and customer-segment aggregation. Results show that policies can appear optimal under their assumed model while performing substantially worse under alternative plausible populations or parameter distributions.
- Experimental design: The pricing design compares seven customer choice models sharing one utility specification while varying active terms and error structures.Models include conditional logit, MNL, hybrid, attraction, nested logit, mixed logit, and rank-based variants; fees are optimised analytically when possible and numerically otherwise within [−15, 15].
- Experimental design: The experiments compute assumed-model profit-maximising fees, evaluate resulting choices under the true model, and use expected profit to isolate choice-model effects.Using realised profit would additionally confound the choice model with customer arrival sequence and routing costs.
- Misspecification of the customer choice model: 45 to 48% of correctly specified expected profit remains when a rank-based model determines choices but one of five logit or attraction models sets prices.When mixed logit determines choices, the corresponding models retain 65 to 78%; reverse-direction comparisons retain 65 to 74% under mixed logit and 63 to 69% under rank-based pricing.
- Misspecification of the customer choice model: At most 4% is lost among the conditional, MNL, hybrid, and nested logit models, while GAM mismatches lose up to 22%.Figure 1 reports expected profit relative to the correctly specified model, averaged over customer segments and offer sets.
- Lack of sensitivity analysis: Expected profit can differ when prices use the mean price coefficient instead of integrating over its distribution, because profit is nonlinear in uncertain choice-model parameters.The MNL sensitivity experiment perturbs price sensitivity by ε ∼ N(0, σ^2) and compares mean-based pricing with full-distribution integration as σ grows.
- Too few customer segments: Single-segment approximations are near-optimal for nearly homogeneous customers, whereas more segments improve performance as price-sensitivity heterogeneity increases.The study approximates a continuous population with K discrete segments and varies heterogeneity from ε = 0.25 to ε = 2.0; practical segment requirements depend on the acceptable approximation error.
4 Conclusion
Customer choice models matter beyond attended home delivery: they can change reported profit and even the direction of an effect, motivating uncertainty-aware revenue management.
- 4 Conclusion: Customer choice models can change reported profit and even reverse the direction of an effect in revenue management experiments.The paper identifies three fallacies involving model misspecification, point estimates, and insufficient customer segmentation.
- 4 Conclusion: The remedies are to test policies against plausible models, parameters, and customer segments and develop revenue management models that hedge against uncertainty.The paper calls for richer heterogeneous choice models that relax independence of irrelevant alternatives and disaggregate data to estimate them reliably.
- 4 Conclusion: The same four-component revenue management structure and three fallacies extend to last-mile logistics beyond attended home delivery.Examples include out-of-home delivery, where choice models select pickup locations and policies are derived and evaluated under assumed models.