Attended home delivery (AHD) lets online customers book narrow delivery time slots and requires the retailer to manage scarce delivery capacity under uncertain demand. Lang, Cleophas and Ehmke (2021) proposed anticipative dynamic slotting: an offline preparation phase that anticipates delivery schedules and approximates the opportunity cost of accepting an order, followed by fast accept/decline and offer-set decisions during booking. Their model assumes a fixed fleet and driver staff and treats the variable cost per delivery as negligible, whereas the rival dynamic pricing stream for AHD explicitly models delivery-dependent costs such as fuel and per-delivery fees to external carriers. The open problem they pose at the end of their paper is to benchmark dynamic slotting against dynamic pricing approaches in a variety of settings where variable cost significantly affects earnings, in order to match demand-management model assumptions to real operational circumstances.

Background

Attended home delivery (AHD) is the e-commerce fulfillment mode, typical for grocery and bulky-goods retailing, in which the customer must be present to receive the order; retailers therefore offer narrow delivery time slots (e.g., one- or two-hour windows) for online booking. Because delivery capacity is scarce relative to uncertain demand, retailers apply revenue management ideas originally developed for airlines: rather than accepting every request, they steer demand during the booking horizon. A standard taxonomy (Agatz, Campbell, Fleischmann, van Nunen and Savelsbergh, 2013) distinguishes slotting decisions — which time slots to offer or keep available, i.e., availability control — from pricing decisions — what fee or discount to attach to each slot; each can be static (designed offline from forecasts) or dynamic (revised in real time as requests arrive). The early AHD literature is reviewed by Agatz, Campbell, Fleischmann and Savelsbergh (2011).

The pricing stream explicitly models delivery-dependent costs. Campbell and Savelsbergh (2006) steered demand with incentives and estimated the marginal delivery cost of an order by inserting it into planned routes; Klein, Mackert, Neugebauer and Steinhardt (2018) approximated opportunity cost for dynamic time slot pricing using model-based routing cost estimates; Yang and Strauss (2017) and Koch and Klein (2020) developed approximate dynamic programming (a technique from reinforcement learning that approximates the value of future states instead of solving the full stochastic dynamic program) for dynamic pricing in AHD; Vinsensius, Wang, Chew and Lee (2020) introduced the notion of marginal fulfillment cost of an order; and Strauss, Gülpınar and Zheng (2021) priced flexible time slots.

The slotting stream culminates in the source paper. Dynamic slotting decides, for each arriving order request, which delivery time slots to offer, comparing the reward of accepting the order against the opportunity cost of not reserving the required delivery capacity for potentially more valuable later orders. Computing this opportunity cost exactly would require solving a complex vehicle routing and scheduling problem, so Lang, Cleophas and Ehmke (2021) proposed anticipative dynamic slotting: a simulation-based preparation phase before the order horizon solves the Team Orienteering Problem with Multiple Time Windows (TOP-MTW) — a routing problem in which a fleet of vehicles each selects a profit-maximizing subset of customers, every customer having several allowed visit time windows, under travel-time limits — on sampled demand to build anticipatory Boolean schedule patterns; learning-based value function approximation estimates the delivery effort of accepting a request; and during the booking horizon an assortment optimization problem (selecting which options to offer under a discrete choice model, in their case a multinomial logit model, MNL, in which each option's choice probability is its exponential utility normalized over the offered set) determines the offer set per request. Their computational study shows strongly scenario-dependent performance — the pattern variant combined with theft-based mechanisms (flexible mechanisms that let an arriving request “steal” delivery capacity reserved for a neighboring area or time slot of the anticipatory pattern) earns the highest basket value in the majority of scenarios but risks accepting orders that later prove infeasible to deliver — and a companion paper extends slotting to multiple business criteria such as truck visibility and customer social influence (Lang, Cleophas and Ehmke, Omega 2021).

The gap the source identifies sits on the cost side. Its model assumes a fixed fleet and a fixed staff of drivers and hence regards the variable cost per delivery as negligible — appropriate when labor costs dominate, but not when fuel consumption or per-delivery fees paid to external carriers significantly affect earnings. The pricing stream already accounts for such delivery-dependent costs; the slotting stream does not. Applying a method that ignores delivery-dependent costs where they matter can be expected to perform poorly, just as applying a cost-aware method where variable costs are irrelevant can. Later work unified both settings conceptually: Fleckenstein, Klein, Klein and Steinhardt (published online December 2024) formalize integrated demand management and vehicle routing problems (i-DMVRPs) and prove that opportunity cost in them decomposes into expected displacement cost (lost future revenue from using capacity now) plus marginal cost-to-serve (expected additional fulfillment cost), a decomposition the traditional revenue-management concept lacks. What remains unresolved is the empirical comparison between the two demand-management paradigms in variable-cost settings that the source poses directly; a cost-aware algorithmic extension of anticipative dynamic slotting is an adjacent direction for which this decomposition supplies the theoretical basis.

Problem Statement

How do dynamic slotting and dynamic pricing approaches for attended home delivery compare in settings in which delivery-dependent variable costs (fuel consumption, per-delivery fees paid to external carriers) significantly affect earnings, and under which demand and cost regimes is each approach preferable?

Specifically, as posed at the end of Lang, Cleophas and Ehmke (2021): their dynamic slotting model assumes a fixed fleet of delivery vehicles and a fixed staff of drivers and therefore regards the variable cost per delivery as negligible, while existing dynamic pricing approaches for attended home delivery do model delivery-dependent costs; because applying a cost-negligent method in a setting where variable costs matter 'can be expected to perform poorly' — and vice versa — the open problem is to compare the performance of dynamic slotting and dynamic pricing approaches in a variety of settings where variable cost does significantly affect earnings, characterizing the demand and cost regimes under which each approach is preferable. The comparison is between dynamic slotting as proposed and cost-aware dynamic pricing approaches for attended home delivery, with performance measured as earnings — the expected basket value of accepted orders net of delivery-dependent costs; the two arms differ in both the decision lever (availability control versus slot pricing) and the cost accounting (cost-negligent slotting versus cost-aware pricing), so a difference in earnings reflects the compared approaches as instantiated rather than either difference alone. The comparison is posed over a stated range of variable-cost levels and stated demand conditions, and concerns which approach yields higher earnings across that range — whether the range spans at least one variable-cost level and one demand condition at which each approach is preferable, or whether no such reversal occurs within the studied range. The overarching objective is to match demand-management model assumptions on the cost side to real operational circumstances.

Scope: this problem concerns the slotting-versus-pricing comparison only; the source's conclusion additionally lists several independent improvement directions (a TOP-MTW preparation formulation with customer choice, alternative dissimilarity measures, alternative choice models, routing heuristics for problem variants, spatial pre-clustering, an infeasibility-risk mechanism for the pattern-based variant, and a benchmarking tool for AHD research) that are separate open directions, not components of this comparison.

References

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