Week 4 | Session 4: Decentralised vs. Centralised SC — News Vendor Problem (Deterministic)

Course: Supply Chain Digitization — Module 3: Digital Business in SC

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Session Agenda & Context

Note

Why this example? SC coordination asks: how should decisions be made within a supply chain — centrally or independently? The News Vendor Problem (NVP) is the classic model that reveals what goes wrong when each player optimises for themselves alone.

Focus decision: “How much to order?” — a lot-sizing and order quantity decision.

Relationship to EOQ: Both deal with order quantity, but they are different models. EOQ = multi-period, continuous demand. NVP = single-period, one-shot ordering decision.

Link to platform economy: This session builds the foundation — SC coordination failures → platform economy as the structural solution (covered in later sessions).

Tip

★ Exam Tip: News Vendor Problem = single-period ordering decision. This definition distinguishes it from EOQ. Always state this when introducing the model.

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The News Vendor Setting — Players & Objectives

Players

Player	Role	Objective
News Vendor (NV)	Observes market demand → places order → sells to end market	Maximise own profit
Regional Supplier (RS)	Receives NV’s order → decides whether to print and supply	Maximise own profit — can choose not to supply if the order is not viable

Note

In practice, multiple News Vendors and multiple Regional Suppliers can exist simultaneously. This analysis simplifies to one NV and one RS to isolate the coordination and incentive problem cleanly.

Other possible objectives for SC players include cost minimisation and emission targets — but this model uses profit maximisation throughout.

Decision Sequence (Chronological)

1. NV observes demand → decides order quantity S → places order to RS
2. RS receives order → decides whether to accept and supply (based on RS’s own profitability assessment)

Tip

★ Exam Tip — The critical distinction:

• Decentralised = each player maximises their own profit independently — NV and RS each decide alone
• Centralised = a central planner maximises total SC profit — both players’ outcomes are optimised together

This distinction drives every scenario analysis that follows.

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Revenue & Cost Parameters

Parameter	News Vendor (₹/unit)	Regional Supplier (₹/unit)
Retail price (p)	₹30 (price charged to end customer)	—
Wholesale price (w)	₹10 (paid to RS per unit ordered)	₹10 (received from NV per unit supplied)
Distribution cost (c_d)	₹10 per unit sold	—
Manufacturing / operating cost (c_m)	—	₹5 per unit printed
Fixed facility cost (F)	No fixed cost → always viable if demand > 0	₹1,50,000 per period
Net margin per unit sold	₹30 − ₹10 − ₹10 = ₹10 per unit	₹10 − ₹5 = ₹5 per unit (above breakeven)
Breakeven quantity	No fixed cost — always profitable if any unit sells	₹1,50,000 ÷ ₹5 = 30,000 units

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Key Formulas

News Vendor Profit

Note

Units sold = min(Demand D, Order S) → The NV can only sell what demand allows or what was ordered — whichever is lower.

NV Profit = [min(D, S) × (p − c_d)] − [S × w] = [min(D, S) × ₹20] − [S × ₹10]

Condition	Outcome
D = S	NV sells everything → Profit = S × ₹10
D < S	NV sells only D units → overstocking loss on (S − D) units procured but unsold
D > S	NV sells only S units → lost sales (underage)

Regional Supplier Profit

Note

RS Profit = [S × (w − c_m)] − F = [S × ₹5] − ₹1,50,000

Condition	Outcome
S < 30,000	RS makes a loss → has a rational motive to refuse the order
S = 30,000	RS breaks exactly even → barely viable
S > 30,000	Each additional unit earns ₹5 contribution margin → profitable

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Deterministic Setting — What It Means

Note

Deterministic demand: Demand is known with certainty before the order is placed. It can be a fixed constant or a function of price (as price increases, demand decreases).

Why use it? It is the analytical baseline — it isolates the incentive misalignment problem from the demand uncertainty problem. Removing demand uncertainty lets us see the coordination failure in its purest form.

Is it realistic? No — but that is not its purpose. The probabilistic setting (next session) adds demand uncertainty back in.

Tip

★ Exam Tip: Deterministic ≠ realistic. Always explain why a setting is chosen — deterministic is used to isolate and analyse the incentive problem without adding the complexity of demand uncertainty simultaneously.

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7 Scenarios — Decentralised Decision Making (Deterministic)

NV places order S given known demand D. Both players make independent profit-maximising decisions.

Scenario	Demand (D)	Order (S)	NV Profit (₹)	RS Profit (₹)	Who Profits?	Would NV Choose This?
1	0	2,000	−₹20,000	−₹1,40,000	Neither	No — better to order 0
2	2,000	40,000	−₹3,60,000	+₹50,000	Supplier only	No — NV loses badly
3	2,000	1,500	+₹15,000	−₹1,42,500	NV only	No — S4 is better
4	2,000	2,000	+₹20,000	−₹1,40,000	NV only	Yes (D < 30K; best NV option)
5	30,000	30,000	+₹3,00,000	₹0 (breakeven)	NV only	Yes (NV profitable)
6	40,000	40,000	+₹4,00,000	+₹50,000	Both ✓	Yes — both win
7	> 40,000	= D	Increases with D	Increases with D	Both ✓	Yes — best outcome

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Scenario-by-Scenario Analysis

Scenarios 1–3: Demand Very Low (D ≪ Breakeven)

D = 0 or 2,000 | RS Breakeven = 30,000

Scenario 1 (D=0, S=2,000): NV sells 0 units → loses ₹20,000. RS prints 2,000 → loses ₹1,40,000. Neither player profits. NV would never choose this — ordering 0 is better.

Scenario 2 (D=2,000, S=40,000): NV massively overstocks → loses ₹3,60,000. RS gets a large order → profits ₹50,000. Supplier profits but NV is destroyed. NV would never rationally choose this.

Scenario 3 (D=2,000, S=1,500): NV slightly understocks → profits ₹15,000. RS order is far below breakeven → loses ₹1,42,500.

Note

Critical insight: Scenarios 1–3 will not actually occur in a decentralised setting. The NV always has a better option available — Scenario 4. These scenarios are included only to show why the NV always converges to ordering S = D.

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Scenario 4: D = 2,000, S = 2,000 (NV Matches Demand)

NV Profits — RS Loses — SC Conflict

• NV sells all 2,000 units → Profit = 2,000 × ₹10 = +₹20,000 ✓
• RS prints 2,000 (well below 30,000 breakeven) → Loss = −₹1,40,000 ✗

Note

★ Key conflict point: NV is profitable and has rationally made the best decision available to it. RS is deeply unprofitable.

RS’s rational response: Refuse to supply the order. If RS refuses → NV has no product to sell → SC collapses. The NV’s individually rational decision inadvertently destroys the supply chain.

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Scenario 5: D = 30,000, S = 30,000 (Demand = RS Breakeven)

NV Profits — RS Breaks Even

• NV Profit = 30,000 × ₹10 = +₹3,00,000 ✓
• RS Profit = 30,000 × ₹5 − ₹1,50,000 = ₹0 (exactly breakeven)

NV is profitable. RS is indifferent — barely viable, no incentive to invest or expand capacity. The SC technically functions, but only just.

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Scenarios 6 & 7: D ≥ 40,000 (Both Players Profitable)

Both Profit — Aligned Incentives

Scenario 6 (D = 40,000, S = 40,000):

• NV Profit = +₹4,00,000 ✓
• RS Profit = (40,000 × ₹5) − ₹1,50,000 = +₹50,000 ✓

Scenario 7 (D > 40,000, S = D):

• Both profits increase proportionally with demand
• Both players prefer S7 > S6 > S5 — incentives are fully aligned when D ≥ 30,000

Tip

Application of Concepts: Note that NV and RS have aligned incentives only when demand is high enough to cover the supplier’s fixed costs. This is the fundamental coordination problem — the NV’s order quantity decision has externalities for the RS, but the NV has no incentive to internalise those externalities when deciding how much to order.

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Key Insights — Decentralised vs. Centralised

News Vendor’s Decision Rule (Decentralised)

Note

In a decentralised, deterministic setting, the NV’s dominant strategy is always:

Order exactly S = D (match demand precisely)

Rule	Reason
Never order S > D	Overstocking hurts the NV — unsold units generate a procurement cost but no revenue
Never order S < D	Understocking leaves money on the table — profitable sales foregone
Always order S = D	Maximises NV’s own profit in every demand scenario

The NV holds the power: The NV’s order quantity determines what the RS earns. The supplier’s commercial fate is entirely in the NV’s hands.

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Impact of NV’s Decision on the Regional Supplier

Demand Level	NV’s Rational Order	NV Outcome	RS Outcome	SC Outcome
D < 30,000	S = D (< 30,000)	Profitable	Loss — may refuse to supply	SC conflict → potential collapse
D < 30,000, S forced > 30,000	NV would never choose this	Loss	Profitable	NV refuses — not chosen
D ≥ 30,000	S = D (≥ 30,000)	Profitable	Profitable or breakeven	SC works ✓

Note

★ The core finding of decentralised SC analysis:

The NV maximises its own profit → inadvertently causes SC conflict when market demand is below the supplier’s breakeven. The SC is not optimised as a whole — it is optimised only from the NV’s perspective.

This is called double marginalisation in SC literature — each player takes a margin, and the cumulative effect reduces system-wide efficiency below what a central planner could achieve.

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What Would Change Under Centralised Decision Making?

A central planner optimising total SC profit would:

• Only operate the SC when D ≥ 30,000 — ensuring both players are viable
• Choose order quantities that guarantee RS profitability alongside NV profitability
• Recognise that an order of S < 30,000 makes the system unviable — and either refuse to operate or find a way to compensate RS

Note

The key challenge: How do you get the NV to voluntarily order more than what demand dictates — even when doing so hurts the NV’s own margin?

This requires coordination contracts — mechanisms that change the incentive structure so that the NV’s individually rational decision also becomes the collectively optimal decision.

Examples of coordination contracts (covered in upcoming sessions): Buyback contracts | Revenue sharing | Quantity discounts

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Limitation of the Deterministic Setting

Note

The deterministic setting assumed demand was known with certainty before the order was placed. This is analytically clean but unrealistic in practice.

Real demand is probabilistic: The NV does not know exactly how many papers will sell tomorrow. Demand is a random variable — it could be high or low.

The conflict scenarios (1–4) above become structurally more complex when demand is uncertain — because the NV must now decide S before knowing D, adding a new source of misalignment.

Next session: The same NVP in a probabilistic demand setting → additional analytical challenges emerge → sets up the full coordination mechanisms and platform economy discussion.

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Session Summary

Element	Detail
Model	News Vendor Problem — single-period ordering with 2 players (NV and RS)
NV profit formula	min(D, S) × ₹20 − S × ₹10
RS profit formula	S × ₹5 − ₹1,50,000 | Breakeven at S = 30,000 units
NV’s dominant strategy (deterministic)	Always order S = D — matches demand exactly
SC conflict zone	D < 30,000 → NV profitable, RS not → RS may exit → SC collapses
Both viable zone	D ≥ 30,000 → both NV and RS profitable → SC functions
Centralised improvement	Needs coordination contracts to align NV’s individual decisions with system-wide optimum
Next session	Probabilistic demand setting + coordination mechanisms

Tip

★ Exam Tip — 10-mark answer on Decentralised vs. Centralised SC:

1. Define both: Decentralised = each player maximises own profit independently. Centralised = central planner maximises total SC profit.
2. Introduce the NVP: Single-period ordering model with NV (retailer) and RS (supplier). State parameters — retail price ₹30, wholesale ₹10, distribution cost ₹10, manufacturing cost ₹5, RS fixed cost ₹1,50,000.
3. State the formulas: NV Profit = min(D,S) × ₹20 − S × ₹10 | RS Profit = S × ₹5 − ₹1,50,000 | RS breakeven = 30,000 units.
4. Use the scenario table: Show that NV always chooses S = D → when D < 30,000, NV profits but RS does not → RS may refuse to supply → SC conflict and collapse.
5. State the centralised solution: Central planner would only operate when D ≥ 30,000 and needs coordination contracts (buyback, revenue sharing) to get the NV to internalise the RS’s fixed costs.
6. End with what comes next: Probabilistic setting adds demand uncertainty → coordination mechanisms + platform economy as structural solutions.