Week 5 | Session 2: NVP — Supplier Payoffs, SC Conflict & Revenue Sharing Contracts

Course: Supply Chain Digitization — Module 2: Digital Business in SC

Session Agenda

Recap — Probabilistic NVP (Session 1)

Demand distribution: 5 scenarios → 10K(20%), 20K(15%), 30K(10%), 40K(25%), 50K(30%)
NV profit formula: min(D, S) × ₹20 − S × ₹10
NV optimal order: S* = 40,000 units → E[Profit] = ₹2,00,000 (highest)
RS profit formula: S × ₹5 − ₹1,50,000 | Breakeven at S = 30,000
This session: What does NV’s choice of S = 40K mean for RS and the SC? → conflict → contracts

Supplier Payoff — Probabilistic Setting

RS profit does NOT depend on demand D — only on the order size S placed by NV. Why? RS fulfils the order and gets paid wholesale price ₹10/unit. Market demand is NV’s problem, not RS’s.

RS profit = S × (₹10 − ₹5) − ₹1,50,000 = S × ₹5 − ₹1,50,000
RS prefers: As large an order as possible — more units = more marginal profit at ₹5/unit

Supplier Potential Order Size	10000	20000	30000	40000	50000
Fixed Cost of Facility (Rs.)	150000	150000	150000	150000	150000
Potential Mfg & Operating Costs (Rs.)	50000	100000	150000	200000	250000
Supplier’s Potential Revenues (Rs.)	100000	200000	300000	400000	500000
Supplier’s Potential Profits (Rs.)	-100000	-50000	0	50000	100000
Supplier’s Choice of Order Size (units)					50000
Supplier’s Final Order Size to Retailer (units)				40000
Potential Profits as per Newsvendor’s Best Order				50000
Suppliers Actual Profit (Rs.)				50000

Table 1: RS profit for each possible order size — NV picks 40K, RS wants 50K

RS break-even and engagement decision by order size

Order Size (S)	Fixed Cost	Var. Cost (₹5/unit)	Revenue (₹10/unit)	RS Profit	RS engage?
S = 10,000	₹1,50,000	₹50,000	₹1,00,000	−₹1,00,000 ✗	No
S = 20,000	₹1,50,000	₹1,00,000	₹2,00,000	−₹50,000 ✗	No
S = 30,000	₹1,50,000	₹1,50,000	₹3,00,000	₹0 (breakeven)	Maybe ⚠
S = 40,000 ← NV picks	₹1,50,000	₹2,00,000	₹4,00,000	+₹50,000 ✓	Yes ✓
S = 50,000 ← RS wants	₹1,50,000	₹2,50,000	₹5,00,000	+₹1,00,000 ✓✓	Yes ✓✓

Entity-wise outcomes — NV, RS, and SC total profit by order size

Entity-wise decisions and outcomes Potential Order Size	10000	20000	30000	40000	50000
a. Expected Profit of Newsvendor (Rs.)	100000	160000	190000	200000	160000
b. Newsvendor’s order size (units)				40000
c. Supplier’s Potential Profits (Rs.)	-100000	-50000	0	50000	100000
d. Supply Chain’s Potential Profits (Rs.) (a. + c.)	0	110000	190000	250000	260000
Supply Chain’s Preferred B2B Order Size (units)					50000
Supply Chain’s Final B2B Order Size (units)				40000

At S = 40,000 (NV’s choice): RS earns +₹50,000 → profitable, so RS will engage ✓
At S = 50,000 (RS’s preferred): RS earns +₹1,00,000 → twice the profit
NV will NOT order 50,000: E[NV Profit] at S=50K = ₹1,60,000 < ₹2,00,000 at S=40K → NV has no incentive

Three-Way Conflict — NV vs RS vs SC

Order Size	NV E[Profit]	RS Profit	SC Total E[Profit]	Preferred by?
S = 40,000 (NV optimal)	+₹2,00,000 ✓ (NV best)	+₹50,000 ✓	+₹2,50,000	NV → Yes. RS → OK but wishes more. SC → Not best.
S = 50,000 (SC/RS optimal)	+₹1,60,000 ✗ (NV worse)	+₹1,00,000 ✓✓	+₹2,60,000 ★	NV → No (loses vs. S=40K). RS → Yes. SC → Yes (global best).

The newsvendor’s best decision (40,000 units) is not the preferred choice for the supplier (50,000 units). The supplier is constrained to produce and sell 40,000 units to the newsvendor as the newsvendor initiates the order.
The newsvendor has no incentive to order 50,000 units instead of 40,000 units.
The newsvendor’s best decision (40,000 units) is the decentralized decision which represents the best decision for the single entity (local optimum).
The supply chain’s best option (50,000 units) is the centralized decision which represents the best decision for the supply chain (global optimum).
There is no incentive for the newsvendor to choose the centralized decision and hence, the same is not chosen for the supply chain.
SC global best: S = 50,000 → SC total E[Profit] = ₹2,60,000 (max possible)
NV decentralised best: S = 40,000 → SC total = ₹2,50,000 (₹10,000 short of global best)
Gap: ₹10,000 of value lost to the SC because NV rationally prefers S=40K over S=50K
SC is “forced” to accept: 40,000 units because NV is the decision-maker and will not voluntarily order more

Why Contracts? — The Coordination Need

Problem: NV’s individually rational decision (S=40K) leaves ₹10,000 of SC profit unrealised
Solution needed: A mechanism that incentivises NV to voluntarily order S=50K → while still being profitable
Contract: A formal agreement between parties with agreed terms and conditions. Contract parameters can include: Price | Order quantity | Ordering schedule | Payment terms | Credit period | Duration | Returns policy.
Effective contract: Moves ALL players to a better-off position than without the contract — Pareto improvement
Information shared via contracts: Market demand info | Inventory levels | Risk | Costs

Types of Coordination Contracts

Contract Type	Mechanism	Who shares risk?	Key Effect
Revenue Sharing ★	NV shares % of revenues with RS. RS gives wholesale price discount in return.	NV shares revenue risk with RS	Incentivises NV to order more; lowers NV procurement cost
Buyback	RS agrees to buy back excess unsold stock from NV at agreed price after selling period.	RS absorbs overstock risk	NV orders more (lower downside); RS shares demand info
Quantity Flexibility	NV can return PART of excess stock (not all) at agreed price — partial buyback.	Partial risk sharing	More flexible than buyback; intermediate order incentive
Quantity Discount	RS gives lower wholesale price per unit for larger order quantities (e.g. ₹8/unit for 50K vs ₹10/unit for smaller orders).	NV takes on volume risk	Directly incentivises larger NV orders
Sales Rebate	NV gets a reward/rebate for selling above a threshold quantity. Encourages discounts to end customers.	NV incentivised to push demand	NV shares demand info; boosts market throughput
Cost Sharing	NV shares cost information with RS; RS reduces price accordingly. Not applicable to current NVP scenario.	Cost visibility shared	Enables larger production runs by RS
Payback	RS has excess unsold inventory; NV agrees to purchase it. Reverse of buyback — RS has market info here.	NV absorbs RS overstock	Applicable when RS has more market knowledge than NV

Contracts explored in this example: Revenue Sharing (detailed) + Quantity Discount (mentioned). Cost sharing & Payback: Not directly applicable to this NVP scenario — RS does not have more market info than NV here.

Concept

NV offers RS: X% of revenues earned from sales
RS gives NV: A discount on wholesale price (w < ₹10)
Logic: Lower w → NV’s procurement cost falls → NV willing to order more | Revenue share → RS compensated for giving discount
Revenue formula: Revenue = min(D, S) × ₹30 → NV keeps (1−X)% | RS gets X%
NV profit formula (with contract): min(D,S) × ₹30 × (1−X) − min(D,S) × ₹10 − S × w = min(D,S) × [₹30(1−X) − ₹10] − S × w

With X = 32% revenue share and w = ₹2.75, the tables below work through the contract step by step. First, NV’s total revenues [min(D,S) × ₹30] for each demand-order combination:

Newsvendor Demand (Prob) \ Potential Order Size	10000	20000	30000	40000	50000
10000 (20%)	300000	300000	300000	300000	300000
20000 (15%)	300000	600000	600000	600000	600000
30000 (10%)	300000	600000	900000	900000	900000
40000 (25%)	300000	600000	900000	1200000	1200000
50000 (30%)	300000	600000	900000	1200000	1500000

Applying the contract formula gives NV’s adjusted profits. Under these parameters, NV’s best order shifts to S = 30,000 units (Note: Table data reflects a different parameter set leading to 30K; 32% with ₹2.75 leads to 50K optimally).

Demand (Prob) \ Potential Order Size	10000	20000	30000	40000	50000
10000 (20%)	70000	-30000	-130000	-230000	-330000
20000 (15%)	70000	140000	40000	-60000	-160000
30000 (10%)	70000	140000	210000	110000	10000
40000 (25%)	70000	140000	210000	280000	180000
50000 (30%)	70000	140000	210000	280000	350000
Expected Profit of Newsvendor	70000	106000	116500	110000	61000
Newsvendor’s order size (units)			30000

The supplier’s payoff under the RS contract — including the expected revenue share received from NV — is shown below:

Supplier Potential Order Size	10000	20000	30000	40000	50000
Fixed Cost of Facility (Rs.)	150000	150000	150000	150000	150000
Potential Mfg & Operating Costs (Rs.)	50000	100000	150000	200000	250000
Supplier’s Potential Revenues (Rs.)	100000	200000	300000	400000	500000
Supplier’s Expected Revenue Share	30000	54000	73500	90000	99000
Supplier’s Potential Profits (Rs.)	-70000	40000	73500	140000	199000
Supplier’s Choice of Order Size (units)					50000
Supplier’s Final Order Size to Retailer (units)			30000
Potential Profits as per Newsvendor’s Best Order			73500
Supplier’s Actual Profit (Rs.)			73500

(Note: The above tables illustrate a suboptimal contract parameter set resulting in S=30,000).

Parameter Tuning — What Happens at Different Values?

Rev Share %	W/sale Price (₹)	NV’s Best S	NV E[Profit]	RS Profit	SC Total	Both better?
0% (baseline)	₹10	40,000	₹2,00,000	₹50,000	₹2,50,000	— (reference)
10%	₹10	30,000	₹1,16,500 ✗	₹73,500 ✓	₹1,90,000 ✗	No — NV worse, SC worse
0%	₹7	40,000	₹2,30,000 ✓	₹20,000 ✗	₹2,50,000	No — RS worse
10%	₹7	40,000	₹2,30,000 ✓	₹20,000 ✗	₹2,50,000	No — RS still worse
32% ★	₹2.75 ★	50,000 ★	₹2,03,200 ✓	₹56,800 ✓	₹2,60,000 ★	YES — All better ✓

Reading the Table — Key Observations

Rev share 10%, w=₹10 (no discount): NV orders only 30K (lower than before) → NV worse, SC worse. RS slightly better but irrelevant — NV won’t sign.
Rev share 0%, w=₹7 (discount only): NV orders 40K → NV better (+₹30K). RS worse (loses discount revenue). NV might like this but RS won’t sign.
Rev share 10%, w=₹7: NV orders 40K → NV still better. RS still worse than baseline. SC same as baseline. Not sufficient.
Rev share 32%, w=₹2.75: NV orders 50K ✓ → NV better (+₹3,200) | RS better (+₹6,800) | SC = ₹2,60,000 (global best ✓). All players win.

Contract Design as an Optimisation Problem

Goal: Find (revenue share %, wholesale price w) that maximises total SC profit such that both NV and RS are individually better off than without the contract.
Constraints: NV E[Profit] ≥ ₹2,00,000 (NV’s outside option) | RS Profit ≥ ₹50,000 (RS’s outside option).
The 32%/₹2.75 solution is one valid point — many combinations exist that satisfy both constraints simultaneously.
Prof’s approach: Manual exploration (not formal optimisation) — demonstrates the concept.
Formal approach: Set up as LP/NLP and solve — covered in more advanced SCM/OR courses.

Final Summary — Decentralised vs. Centralised vs. Coordinated

The table below compares the key outcomes across all three SC regimes — no contract, central planner, and revenue-sharing contract:

Aspect	Decentralised (No contract)	Centralised (Central planner)	Coordinated (Revenue share contract)
NV order	40,000 (NV best)	50,000 (SC best)	50,000 ✓ (achieved via incentive)
NV E[Profit]	₹2,00,000	Less (NV wouldn’t comply)	₹2,03,200 ✓
RS Profit	₹50,000	₹1,00,000 (RS wants this)	₹56,800 ✓
SC Total E[Profit]	₹2,50,000	₹2,60,000 ★ (global best)	₹2,60,000 ★ ✓
Will it happen?	Yes — NV acts alone	No — NV has no incentive	Yes — both players voluntarily agree ✓

What Contracts Enable — Four Levers

Information visibility: NV shares market demand signals. RS understands actual market conditions.
Inventory visibility: Both parties know stock levels, order quantities, and sales outcomes.
Risk sharing: Revenue share → NV shares demand risk with RS. Buyback → RS absorbs overstock risk for NV.
Cost visibility: Cost sharing contracts → player reveals costs → enables trust-based pricing.

Bridge — SC Coordination → Platform Economy

Same coordination logic applies in platform economy scenarios:

Taxi driver: Join cab aggregator platform OR find customers directly OR both → tradeoffs in revenue share and market access
Seller on e-commerce: Sell on Amazon/Flipkart (share revenue) vs. own website → SC reach vs. margin tradeoff
Digital content: Free content (ad-supported) vs. subscription → demand vs. revenue model tradeoff
Platform: A coordination mechanism at scale — reduces search & selection problems + enables risk/revenue sharing across SC players

Session Summary

RS payoff: Increases with S. At S=40K (NV optimal): RS earns +₹50K. At S=50K (RS preferred): RS earns +₹1L.
Conflict: NV picks S=40K (maximises own E[Profit]). SC global best is S=50K. NV has no incentive to go there.
Contract types: Revenue sharing | Buyback | Qty flexibility | Qty discount | Sales rebate | Cost sharing | Payback
Revenue sharing contract: NV gives X% of revenue to RS. RS gives wholesale price discount. Must balance both parameters.
Optimal contract (this example): Rev share = 32%, wholesale price = ₹2.75 → NV orders 50K → all players better off → SC profit = ₹2,60,000
Key principle: Effective contract = all players individually better off (participation constraint) + SC total profit maximised
Bridge: Same coordination logic underpins platform economy — platforms enable info/risk/cost visibility at scale