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arxiv: 2604.07312 · v1 · submitted 2026-04-08 · 💻 cs.MA

Intertemporal Demand Allocation for Inventory Control in Online Marketplaces

Rene Caldentey , Tong Xie This is my paper

Pith reviewed 2026-05-10 16:55 UTC · model grok-4.3

classification 💻 cs.MA
keywords demand allocationinventory controlonline marketplacesforecast uncertaintyfulfillment servicesbase-stock policiesplatform operations
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The pith

Platforms can steer sellers' inventory levels by controlling the predictability of each seller's demand stream through nondiscriminatory allocation rules.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper models a platform that observes total demand and routes orders across sellers over time while sellers choose between merchant and platform fulfillment and manage inventory with base-stock policies. It shows that nondiscriminatory rules, which keep each seller's average demand share fixed, can still vary the forecast uncertainty each seller faces. Uniform splitting of demand produces the lowest uncertainty and thus the smallest safety stocks; any higher uncertainty level can be achieved with simple low-memory routing rules, but only if those rules stop sellers from backing out the aggregate demand pattern from their own histories. This reduces the platform's design choice to selecting an uncertainty level that balances greater adoption of platform fulfillment against the extra inventory held by adopters.

Core claim

Within the class of nondiscriminatory intertemporal allocation policies that assign identical demand shares and forecast risk to all sellers, uniform splitting minimizes forecast uncertainty, while any higher uncertainty level can be realized by low-memory allocation rules; achieving such higher uncertainty further requires that the rules prevent sellers from inferring aggregate demand from their private sales histories.

What carries the argument

Nondiscriminatory intertemporal demand allocation policies that fix each seller's long-run demand share but vary the serial correlation and predictability of the realized sales process for that seller.

If this is right

  • Uniform allocation produces the lowest safety stock among all nondiscriminatory rules with the same average shares.
  • Any desired uncertainty above that minimum can be implemented with finite-memory routing that depends only on recent aggregate demand.
  • Rules that raise uncertainty must block sellers' ability to reconstruct total demand from their own observations.
  • The platform's operational problem collapses to choosing one uncertainty level that trades off fulfillment adoption against inventory holdings.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same informational lever could be used to influence other seller decisions such as pricing or capacity expansion if those decisions also depend on demand predictability.
  • In settings where sellers employ more sophisticated forecasting models, the platform may need stronger masking of aggregate signals to sustain the intended uncertainty levels.
  • Empirical tests could compare inventory and fulfillment choices across matched seller cohorts exposed to different allocation uncertainty levels while holding average shares constant.

Load-bearing premise

Sellers follow state-dependent base-stock policies and cannot fully reverse-engineer the platform's aggregate demand process from the histories they observe under the chosen allocation rule.

What would settle it

Observe whether sellers' safety-stock levels remain unchanged when the platform switches from uniform splitting to a higher-uncertainty low-memory rule while keeping average shares fixed, or whether sellers can accurately forecast total demand despite the rule.

read the original abstract

Online marketplaces increasingly do more than simply match buyers and sellers: they route orders across competing sellers and, in many categories, offer ancillary fulfillment services that make seller inventory a source of platform revenue. We investigate how a platform can use intertemporal demand allocation to influence sellers' inventory choices without directly controlling stock. We develop a model in which the platform observes aggregate demand, allocates orders across sellers over time, and sellers choose between two fulfillment options, fulfill-by-merchant (FBM) and fulfill-by-platform (FBP), while replenishing inventory under state-dependent base-stock policies. The key mechanism we study is informational: by changing the predictability of each seller's sales stream, the platform changes sellers' safety-stock needs even when average demand shares remain unchanged. We focus on nondiscriminatory allocation policies that give sellers the same demand share and forecast risk. Within this class, uniform splitting minimizes forecast uncertainty, whereas any higher level of uncertainty can be implemented using simple low-memory allocation rules. Moreover, increasing uncertainty above the uniform benchmark requires routing rules that prevent sellers from inferring aggregate demand from their own sales histories. These results reduce the platform's problem to choosing a level of forecast uncertainty that trades off adoption of platform fulfillment against the inventory held by adopters. Our analysis identifies demand allocation as a powerful operational and informational design lever in digital marketplaces.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper develops a model in which an online marketplace platform observes aggregate demand and allocates orders intertemporally across sellers using nondiscriminatory policies. Sellers choose between fulfill-by-merchant and fulfill-by-platform options while managing inventory via state-dependent base-stock policies. The central mechanism is informational: by modulating the predictability of each seller's sales stream without changing average demand shares, the platform alters sellers' safety-stock requirements. Within the class of nondiscriminatory policies, uniform splitting minimizes forecast uncertainty, while higher uncertainty levels are achievable via simple low-memory allocation rules that prevent sellers from recovering the aggregate demand process from their private histories. The platform's problem thereby reduces to selecting a target uncertainty level that trades off fulfillment adoption against inventory costs.

Significance. If the modeling framework and the claimed properties of the low-memory rules hold, the work identifies demand allocation as a distinct operational and informational design lever that extends classical inventory theory to platform settings. This could enable platforms to influence seller behavior and fulfillment choices indirectly, with potential efficiency gains in e-commerce inventory and ancillary services. The reduction of the design space to uncertainty selection is a clean conceptual contribution when the assumptions on seller policies and rule credibility are satisfied.

major comments (1)
  1. [Abstract] Abstract: The claim that 'simple low-memory allocation rules' can implement any higher level of uncertainty while preventing sellers from inferring aggregate demand from their sales histories is load-bearing for the separation between average share and forecast risk. No explicit construction of such a rule or proof that the induced filtration is strictly coarser than the aggregate filtration (for the demand processes under which base-stock policies are optimal) is supplied; without this, it is unclear whether the informational lever remains effective under the state-dependent policies assumed.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback. The comment highlights an important point about the rigor of our informational mechanism, and we address it directly below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that 'simple low-memory allocation rules' can implement any higher level of uncertainty while preventing sellers from inferring aggregate demand from their sales histories is load-bearing for the separation between average share and forecast risk. No explicit construction of such a rule or proof that the induced filtration is strictly coarser than the aggregate filtration (for the demand processes under which base-stock policies are optimal) is supplied; without this, it is unclear whether the informational lever remains effective under the state-dependent policies assumed.

    Authors: We agree that an explicit construction and proof would strengthen the paper and make the separation between average share and forecast risk fully rigorous. In the revision we will add a dedicated subsection (new Section 4.3) providing a parametric family of low-memory rules. For target uncertainty level sigma > sigma_uniform, the rule first draws a zero-mean noise term from a calibrated distribution (e.g., scaled Gaussian or discrete uniform) and adds it to each seller's allocation before normalizing to preserve the fixed long-run share; the noise is drawn independently of the aggregate demand realization and is not recoverable from any seller's private history. We will prove that, for the i.i.d. demand processes under which state-dependent base-stock policies are optimal, the seller filtration is strictly coarser than the aggregate filtration: the conditional variance of next-period demand given a seller's history is strictly larger than under uniform splitting, and the seller cannot reconstruct the aggregate path. This construction satisfies nondiscriminatory constraints and keeps the informational lever effective. revision: yes

Circularity Check

0 steps flagged

Theoretical derivation of allocation rules is self-contained

full rationale

The paper constructs a model of platform demand allocation under nondiscriminatory policies and state-dependent base-stock inventory rules. The central claims—that uniform splitting minimizes forecast uncertainty and that higher uncertainty is achievable via simple low-memory rules that also block inference—are presented as consequences of the model's informational structure and policy class. No equations reduce a target quantity to a fitted parameter defined by that same quantity, no load-bearing uniqueness theorems are imported via self-citation, and no ansatz is smuggled in. The reduction of the platform's problem to selecting an uncertainty level follows directly from the stated assumptions without circular redefinition of inputs as outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only the abstract is available, so the full ledger cannot be audited. The model relies on standard inventory-management assumptions whose precise statements and any fitted parameters are not visible.

axioms (2)
  • domain assumption Sellers replenish inventory under state-dependent base-stock policies
    Explicitly stated as part of the model setup in the abstract.
  • domain assumption Platform observes aggregate demand and allocates orders nondiscriminatorily
    Core modeling premise stated in the abstract.

pith-pipeline@v0.9.0 · 5533 in / 1241 out tokens · 39316 ms · 2026-05-10T16:55:59.300557+00:00 · methodology

discussion (0)

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Reference graph

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