-->PONE-D-26-16015-->-->Retailer’s Inventory-Based Financing with Bounded Advance Rates: Interplay between Wholesale Price Contract and Loan Menu-->-->PLOS One

Dear Dr. Tian,

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Additional Editor Comments:

This paper studies a three-party supply chain consisting of a capital-constrained retailer, a supplier, and a bank. The retailer uses inventory-based financing (IBF) to procure products from the supplier, using purchased inventory as collateral. The central contribution is the derivation of upper and lower bounds for the inventory advance rate—defining what the authors call IBF with bounded advance rates (IBF-B)—and an analysis of the interplay between the bank's loan menu (interest rate and advance rate) and the supplier's wholesale price contract. The paper is set up as a Stackelberg game and solved using a newsvendor framework and KKT conditions.

Given the comments of two knowledgeable reviewers, I invite the authors to submit a revised manuscript. Please address the issues raised by the two reviewers and my additional comments below.

The topic is relevant and the general research design is sound. However, the manuscript has significant issues across mathematical consistency, notational clarity, presentation, and certain gaps in the analysis that must be addressed before publication. These are detailed below.

1. Critical Inconsistency in Liquidation Value

The model states in Section 3.1 that "the bank has a legal right to liquidate the retailer's inventory at salvage value s in the event of default," and the entire bankruptcy analysis in Sections 4 and 6 uses s as the recovery value. However, Section 8.2 (Limitations) states: "We assume that the liquidation value of inventory equals the wholesale price." This is a direct contradiction. The collateral valuation is central to the model (the loan limit is βwq, which is based on wholesale price w, while recovery is based on s), so the authors must clearly state and justify the liquidation value assumption in Section 3, not only as an afterthought limitation. If the liquidation value truly equals the wholesale price, the entire bankruptcy threshold structure would need revisiting.

2. Fix the Numbering Mismatch Between Main Text and Appendix in the lemma proofs

3. Some of the figures can be enhanced with high-definition images.

4. Implicit Fixed-Point Equation for q₃ Is Not Justified

Lemma 3 defines q₃(w, R, k) as the solution to:

q₃ = F̄⁻¹( [(w·e^R − s)/(p − s)] · F̄(ξ̂(q₃)) )

This is an implicit fixed-point equation. The existence and uniqueness of a solution are never established. Given that the IFR assumption is used throughout, the authors should either (a) prove existence and uniqueness explicitly, or (b) cite a supporting result. Without this, the upper bound β̂ is not well-defined, which undermines the entire IBF-B framework.

5. Ambiguity in the Stackelberg Game Structure

The game structure is described inconsistently. Section 1.1 says "the supplier acts as the leader and the capital-constrained retailer functions as the follower," yet Assumption 3 states "the bank can act as a Stackelberg game leader, the supplier is a sub-leader and the capital-constrained retailer is a follower." Figure 1 shows the bank and supplier both acting at the beginning of the selling season, making it unclear whether the bank or the supplier moves first. The sequential structure needs to be specified precisely: Does the bank announce (R, β) before or after the supplier announces w? The current analysis in Section 6 treats w as given when the bank optimizes, which is inconsistent with the bank being the overall leader. This needs to be clarified both in the text and in Figure 1.

6. Contract Efficiency Values Are Very Low and Require Discussion

Table 6 shows contract efficiency (E[Π*]/E[Πcn*]) as low as 6.46%–26.96% for BU-retailers who do not use IBF-B. These values are extremely low by the standards of supply chain coordination literature. Even for retailers who do use IBF-B, efficiency is 77–81%. The authors are largely silent on why such severe inefficiency persists even with IBF-B, and whether these magnitudes are realistic or are artifacts of the specific parameter choices. A more substantive discussion—potentially with sensitivity analysis over key parameters—is required.

7. No Sensitivity Analysis

The paper uses a single numerical example throughout (p=3, c=0.5, s=0.4, r_f=0.02, U(0,10)). There is no sensitivity analysis with respect to key parameters: monitoring cost r_c, salvage value s, demand spread (b−a), or retail price p. Given that the paper positions the bounded advance rate as an operational tool for banks, it is important to understand how the optimal bounds and loan menu change with the economic environment.

8. Reference Formatting Issues

Several references are inconsistently formatted:

Reference [2] lists a DOI that appears to belong to a different paper (doi:10.1111/poms.13323 is listed for a 2022 IEEE Trans paper, but the same DOI is also used for Reference [35], the Fu et al. (2021) paper).

Reference [11] is a working paper from 2007 and is not published in a peer-reviewed venue. The paper relies on this work repeatedly; if it remains unpublished, the authors should verify that the results are not superseded by subsequent published work.

Reference [19] (Hu and Sobel 2005) is also an unpublished working paper. The authors should either cite the published version or clarify the current status.

9. The Role of the Supplier for NB-Retailer is Trivial

Section 5.2.1 (NB-retailer: retailer who orders using all working capital) does not use IBF-B and reduces to a standard "selling to the newsvendor" problem already studied by Lariviere and Porteus (2001). The results in Proposition 4 add little novelty. The authors should either (a) clearly position this case as a benchmark, or (b) reduce the space devoted to it and focus the analysis on the IBF-B-relevant cases (Sections 5.2.2–5.2.3).

10. Comparison with Jiang and Liu (2018) [34] Needs Strengthening

The paper [34] also studies inventory advance rates with wholesale price contracts. While Table 1 notes that [34] does not consider interest rates, the verbal distinction in the main text is insufficient. Section 2 should explicitly explain what analytical results this paper obtains that [34] does not, and why the simultaneous optimization of (R, β) yields qualitatively different insights.

11. Definition of "Moderate" Advance Rate Is Circular

The paper defines IBF-B as the medium range (γ, β̂], and states the bank should set a "moderate advance rate" when the shadow price is non-positive. The term "moderate" is used to simultaneously describe the full feasible range (γ, β̂] and a specific point β̄ within that range. This circular language creates confusion. The authors should use distinct terminology for the feasible range versus the specific optimal rate within it.

12. Table 3 Is Difficult to Read

Table 3 (Optimal Order Quantity Corresponding to Wholesale Price) is cluttered and requires cross-referencing multiple earlier definitions to interpret. A brief verbal summary of each row's economic meaning would substantially improve accessibility.

13. Typographical Errors

The following typographical errors should be corrected:

Section 1.1, line 132: "enhancment ofsupply chain performance" → "enhancement of supply chain performance"

Appendix, Proof of Lemma 3: "the retailer's loan amount is constrained by the loam limit" → "loan limit"

Section 3.2, line 293: "We first analyze the retailer's optimal order quantity qr*" — the asterisk renders poorly; use consistent mathematical typesetting

Section 3.1, line 72: "Since the decisions cannot made independently" → "cannot be made independently"

Section 5.2, line 493: the comma placement in "called NB-retailer; the retailer who intends to borrow below the loan limit, i.e., k≤k≤k̄, called BB-retailer" omits the subject in the second clause

14. Lemma EC.1 in the Appendix Is Not Labeled in the Main Text

Lemma EC.1 (Appendix B) is referenced in the main text (Section 7.1) but is not stated there. At minimum, the result should be summarized in the main text, since it is used to derive Proposition 8. Alternatively, a clear forward reference with an inline statement would help readers follow the argument.

15. The Bank's "Bargaining Advantage" Is Not Formally Modeled

The paper repeatedly asserts that the bank has a "bargaining advantage" over the retailer (Abstract, Sections 1, 3, Assumption 3). However, no formal bargaining model (e.g., Nash bargaining, take-it-or-leave-it offer) is specified. The bank is simply modeled as a Stackelberg leader. The term "bargaining advantage" is misleading and should either be formalized or replaced with "market power" or "first-mover advantage."

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Reviewers' comments:

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: N/A

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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-->5. Review Comments to the Author

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Reviewer #1: After reviewing this paper, I have following comments:

Comment 1: The demand distribution is assumed to be uniform. It's useful to consider general distribution in the extension.

Comment 2: It's better the compare supplier financing and bank financing in this study.

Comment 3: The bounded rate should be added some evidence in the introduction.

Reviewer #2: The research paper “Retailer’s Inventory-Based Financing with Bounded Advance Rates: Interplay between Wholesale Price Contract and Loan Menu” investigated a supply chain model comprises a capital constrained retailer, a bank, and a supplier. Specifically, a capital constrained retailer utilizing inventory-based financing to purchase products from the supplier by choosing from bank loan menu and wholesale price contracts by the supplier. The authors aim to help financial institutions to balance profit goals with the necessity of reducing credit risk. To this end, a mathematical framework was developed to assist in leveraging their physical assets to overcome common funding obstacles.

Please see the attached file for review comments.

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Reviewer #1: No

Reviewer #2: No

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Retailer’s Inventory-Based Financing with Bounded Advance Rates: Interplay between Wholesale Price Contract and Loan Menu

PONE-D-26-16015R1

Dear Dr. Tian,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Bo Li, Ph.D.

Academic Editor

PLOS One

Additional Editor Comments (optional):

In Section 1.1, the authors state that a sizable loan "in turn lead to a remarkable enhancement in supply chain performance". This contains a subject-verb agreement error and should be corrected to "leads to a remarkable enhancement."

In Section 1.2, the phrase "other typical literature" is used when introducing Table 1. This would read much more professionally as "closely related literature" or "prior seminal literature."

Reviewers' comments: