Paper summary by Leo Gomes Vakharia, A., Wang, L., 2014, Uniform vs. Retailer-Specific Pricing: Incentive Alignment to Enhance Supply Chain Efficiency, POM 23(7), pp. 1176-1182

1. June, 2015
Paper’s summary
Uniform vs. Retailer-Specific Pricing:
Incentive Alignment to Enhance Supply
Chain Efficiency
Based on the paper “Vakharia, A., Wang, L., 2014, Uniform vs. Retailer-Specific Pricing: Incentive Alignment to Enhance Supply Chain
Efficiency, POM 23(7), pp. 1176-1182
Leonardo Laranjeira Gomes
PhD Student
MIT-Zaragoza International Logistics Program
Zaragoza Logistics Center

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Overview: comparison of UWP and RSWP and proposition of a coord.
contract combining UWP and slotting allowance and/or side payment
Overview
•The setting: one supplier selling to multiple, cost-asymmetric, retailers.
•Two wholesale pricing strategies:
• Uniform wholesale price (UWP); and
• Retailer-specific wholesale price (RSWP).
•In a myopic and uncoordinated setting:
• The less efficient retailer and the supplier prefers RSWP; while
• The more efficient retailer prefers UWP.
•However, as UWP leads to superior profits for the whole system:
• The authors proposed a coordinating contract using a combination of UWP and slotting
allowance and/or side payment.
• Through the specification of its parameters, the contract scheme proposed allows the supplier
to exert some control of the profit splitting among the retailers
Source: Vakharia and Wang 2014

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Contents
1. Introduction
2. The model
3. RSWP vs. UWP and Total Supply Chain Profits
4. Conclusions
5. Extension

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Contents
1. Introduction
2. The model
3. RSWP vs. UWP and Total Supply Chain Profits
4. Conclusions
5. Extension

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The setting: pricing scheme decision for a supplier selling a single product
to non-competing retailers, which are equally sized and cost-asymmetric
•The supplier: single product.
•The retailers:
• Non-competing;
• Equally sized; and
• Asymmetric regarding cost-efficiency.
•The retailer decides whether to sell under a UWP or a RSWP pricing scheme.
•Retailers have their own preferences regarding the pricing scheme.
•Retailers are allowed to set their market prices
•Research question: “how the choice of the wholesale pricing scheme impacts not only the supplier
and individual retailer profits but also the profits of the entire supply chain?”
Source: Vakharia and Wang 2014
Note on cost asymmetries: different levels of operating economies are due to several factors, such as
transportation costs and business processes.
Note on RSWP’s legality in some countries: by assuming that retailers are not in direct competition
with one another, no anti-competitive impact is present in the model.

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Previous literature consider uniform market prices and prioritizes
consumer welfare. It has been showed that RSWP can achieve coord’n.
Source: Vakharia and Wang 2014
Literature review on RSWP and UWP
Author(s) Year(s) Field General Idea
Katz
DeGrapa
Yoshida
1987
1990
2000
Economics
Compares RSWP and UWP; however:
• DeGrapa and Katz consider identical market
prices at the retailers.
• Consumer welfare as a major concern (the
quantity available to the final consumer).
Berenstein and
Federgruen
2004
and
2005
SC coordination
RSWP can achieve coordination under demand
uncertainty, with or without competition, if each
retailer adopts a baseline stock policy and/or by
contractual arrangements
Vakharia and Wang allow retailers to determine market prices, and are concerned about
total supply chain profits. They show that UWP leads to greater supply chain efficiency

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Yet, as the supplier would prefer UWP, the authors propose a contract
scheme combining UWP with a slotting allowance and/or side payment
Source: Vakharia and Wang 2014
Slotting allowances and fees
• Represent a significant cost to grocery manufacturers and two schools of though dominate its
controversial debate (Bloom et al., 2000):
• One views them as a tool for improving channel efficiency through cost and risk sharing; and
• The other considers them as a tool for enhancing market power and damaging competition.
A slotting allowance is a payment from the supplier to the retailer. On the other hand, a side
payment, is a payment collected by the supplier from the retailer
“Slotting allowances and slotting fees describe a family of marketing practices that
involve payments by manufacturers to persuade downstream channel members to
stock, display, and support new products” (Bloom et al., 2000)

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Contents
1. Introduction
2. The model
3. RSWP vs. UWP and Total Supply Chain Profits
4. Conclusions
5. Extension

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The model approach involves a supplier and two retailers
Source: Vakharia and Wang 2014
• One supplier offering a single product, with
marginal cost z.
• Two retailers i, i=1,2
- Asymmetric, w/ cost efficiencies ci
• Order quantities, qi, depend on the wholesale
price vi, which is determined by the supplier.
• Demand qi(pi) is a strictly non-decreasing
function of the consumer price pi, which is
stated by the retailer.
- qi(pi)=A-Bpi, where A is the market
potential and B is the price elasticity of
demand.
- The parameters related to market size are
constant across retailers.
The processThe model setup
1. The supplier offers a wholesale price
vi to each retailer;
2. Each retailer makes its own decision
on the order quantity qi,
simultaneously defining the market
price pi; and
3. The final profits of each party in the
supply chain are determined.

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Notation summary
Source: Vakharia and Wang 2014

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Supplier’s incentive-compatible profit maximization under RSWP:
Supplier’s incentive-compatible profit maximization under UWP:
For each retailer i, given a wholesale price vi, the optimization problem is
to maximize the profit function
Source: Vakharia and Wang 2014

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Letting retailer 2 be the most efficient (i.e. c1>c2), the first analysis was
conducted by comparing prices, quantities, and profits
Source: Vakharia and Wang 2014

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Under RSWP, the more efficient retailer is penalized
Source: Vakharia and Wang 2014
Under RSWP, the more efficient retailer is charged a higher wholesale price (i.e. v2>v1). Therefore,
the supplier is in a position to extract a higher “rent” from the more efficient retailer, as compared to
the less efficient.
Additionally, the optimal wholesale price under UWP is bounded such that v2>v ̃>v1.

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RSWP is a preferred scheme if the retailers differ in their efficiencies
Source: Vakharia and Wang 2014
The supplier profits are larger when it adopts the RSWP scheme as compared to the UWP (i.e. ϕ>ϕ˜ ).
However, if c1=c2, UWP is preferred

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The less efficient retailer prefers RSWP, while the more efficient retailer
prefers UWP
Source: Vakharia and Wang 2014
The comparative impact in the retailers profits and order quantities are: under RSWP, the less (more)
efficient retailer makes larger (smaller) profits and orders more (less) as compared to UWP
RSWP penalizes the more efficient and rewards the less efficient. The UWP scheme would
alleviate this risk by sending a signal of “fairness”, but the retailer would make less profits.

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Contents
1. Introduction
2. The model
3. RSWP vs. UWP and Total Supply Chain Profits
4. Conclusions
5. Extension

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Authors also included Integrated Supply Chain (ISP) profits, which are independent of the wholesale pricing scheme.
Next step: examining total supply chain profits for each pricing scheme.
Integrated Supply Chain (ISP) were also included, as a reference
Source: Vakharia and Wang 2014
Intuition: the more efficient retailer tends to charge lower market prices under the UWP and
this tends to increase the market coverage for this retailer, compen
• The difference between UWP and RSWP
demonstrates that the former dominates the
latter from a total SC profits perspective.
• As the retailer asymmetry, c2-c1, increases:
- The difference between the pricing schemes
also increases and UWP becomes even more
preferable over RSWP; and
- The difference between ISP and UWP
decreases, thus it increases the degree of
coordination of UWP.
•
FindingsSupply Chain Profits

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These results lead to a contract that could be used by the supplier to
ensure that his profits are greater under UWP than under RSWP
Source: Vakharia and Wang 2014
Contract optimal parameters:
• Offer a UWP for both retailers of:
• For the less efficient retailer (retailer 1), provide a slotting allowance of:
• For the more efficient retailer (retailer 2), collect a side payment of:
Net effect for the supplier: profits are at least as large as under RSWP

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In addition, the parameters δ and ϵ allow the supplier to exert some
control over the profit splits
Source: Vakharia and Wang 2014
Retailers’ profit functions under the proposed contract
• Profits for retailer 1 (the less efficient) are in the range [π ̃1 ,π1].
• By defining δ, the supplier controls the profits for retailer 1. However, δ also influences the profits
for retailer 2.
• If the supplier wants to ensure that the profits for retailer 2 are at least those obtained under the
RSWP strategy, then the following must hold:
• If the supplier wants to simultaneously ensure that the minimum profits for retailer 1 is similar to
UWP and for retailer 2 is similar to RSWP, then:

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Finally, the authors discuss whether it is possible to design a UWP
contract that leads to all the parties obtaining the maximum profit
Source: Vakharia and Wang 2014
• This is not possible as the loss for the supplier adopting the UWP scheme is larger than the total
gain in supply chain profits when using the UWP scheme as compared to the RSWP strategy:
• Therefore, if the supplier offers the UWP scheme, it requires the collection of a minimum side
payment this would result in at least one of the retailers not realizing the maximum possible
profits.

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Contents
1. Introduction
2. The model
3. RSWP vs. UWP and Total Supply Chain Profits
4. Conclusions
5. Extension

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Conclusions
• The authors have investigated the impact of alternative wholesale pricing schemes on
the supply chain profits.
• They were able to structurally characterize the respective impacts of UWP and RSWP.
• The key findings are that if retailers are asymmetric with respect to cost-efficiency
then:
• The supplier would always prefer RSWP to maximize its own profits;
• The optimal UWP is always lower than the optimal RSWP to the more efficient
retailer;
• The optimal UWP is always higher than the optimal RSWP to the less efficient
retailer; and
• The more efficient retailer would prefer the UWP while the less efficient retailer
would prefer the RSWP.
Source: Vakharia and Wang 2014

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Suggestions of extensions (from the authors)
• To compare other pricing schemes (e.g. quantity discounts) in a similar setting
• To investigate how market parameters (which is held constant across retailers in this
article) would impact and/or moderate some of the finding in this work.
Source: Vakharia and Wang 2014

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Contents
1. Introduction
2. The model
3. RSWP vs. UWP and Total Supply Chain Profits
4. Conclusions
5. Extension

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Suggestions of extensions
• To employ a game theoretical approach in a similar setting, considering competing
suppliers.
• To evaluate a similar setting with stochastic demand.
Source: Vakharia and Wang 2014