SUPPLY CHAIN DESIGN AND PLANNING
Tilburg University
September 2025
,LECTURE 2: INVENTORY, RISK POOLING & DISTRIBUTION
Key inventory decisions:
1. How much to order?
2. When to order?
3. Where to stock my inventory?
Why is inventory required?
1.Uncertainty in customer demand
i) Shorter product lifecycles
ii) More competing products
2.Uncertainty in supplies (Quality/Quantity/Costs/Delivery Times)
3.Delivery lead times
4.Incentives for larger shipments (economies of scale in transportation / purchasing)
Economic lot size (Order Quantity) model
Considers a constant and deterministic demand with an infinite planning horizon. The goal of
the economic lot size model is to minimize annual ordering and holding costs.
Q* = optimal order quantity
D = demand
K = fixed order cost
h = holding cost per unit held
However: we do not know demand…
Demand uncertainty
- Forecast is always wrong
- The longer the forecast horizon, the worse the forecast is
- Aggregate forecasts are more accurate
Single period models: newsvendor model
There is only one ordering opportunity before demand occurs. Make use of historical data to:
- Identify a variety of demand scenarios
- Determine probability each of these scenarios will occur
The highest probability sells 12,000 items.
How much to order?
Above, below or equal to the expected demand?
1.Calculate average (expected profit) given a specific
order quantity.
2.Choose order quantity that maximizes expected profit
Optimal quantity is 12,000 units < 13,000 (avg demand)
Why?
2
,Relationship between optimal quantity and average demand
Compare marginal profit of a sale and marginal cost of not selling
Marginal profit/unit = selling price – variable ordering (or production) costs
Marginal cost/unit = variable ordering (or production) cost – salvage value
If marginal profit > marginal cost => Optimal quantity > Average demand
If marginal profit < marginal cost => Optimal quantity < Average demand
How much units shall we order if we want an X% chance of not stocking-out?
Optimal service level (SL)= Marginal profit / (Marginal profit + marginal cost)=Cu / (Cu+Co)
Risk-reward trade-offs
If producing 9,000 units or producing 16,000 units will lead to about the same average profit.
Which one would you prefer?
Increasing Q increases the possible risk and the possible reward!
Consider the distribution of the profit (the probability of what profit)
Multiple order opportunities – Continuous review policy
(Q,R) policy – whenever inventory level falls to a reorder level
R, place an order for Q units.
The reorder point (R) should be high enough to:
- Satisfy demand during the lead time
- Protect against demand (and lead time) uncertainty
Stable lead times:
Variable lead times:
The order quantity (Q) balances inventory holding costs and fixed order costs
Multiple order opportunities – Periodic review policy
Inventory level is reviewed periodically at regular intervals. And appropriate quantity is
ordered after each review.
A: Short intervals (daily): (s,S) policy
During each inventory review, if the inventory position falls below s, order enough to raise
the inventory position to S.
- Set s = R, and S = R + Q
B: Intervals (weekly, monthly): Base-stock level policy
- Always order after an inventory level review
- Determine a target inventor level, the base-stock level
- During each review period, the inventory position is reviewed
- Order enough to raise the inventory position to the base-stock level
3
, How to determine the base stock level? Should be enough to cover demand until the next
order arrives (in r+L days) and the safety stock.
r = length of review period
L = lead time
z = safety factor
Service level:
- The higher the service level, the higher the inventory level
- The lower the inventory level, the higher the impact of a unit of inventory on service
level and hence on expected profit
- For the same inventory level, the longer the lead time to the facility, the lower the
level of service provided by the facility
Service level will be higher for products with:
- High profit margin
- High volume
- Low variability
- Short lead time
Risk pooling
Risk pooling suggests that demand variability is reduced if one aggregates demand across
locations. With risk (location) pooling inventory is kept at a central location to satisfy demand
in multiple markets. The demand variability is reduced when there is aggregation across
locations.
Critical points:
- The higher the initial coefficient of variation, the greater the benefit from location
pooling
- The benefits from location pooling depend on the behaviour of the demand from one
market relative to demand from another
- Reallocation of items from one market to another easily accomplished in centralized
systems
There are also other forms of risk-pooling:
- Location pooling
- Product pooling (standardized design)
- Postponement (delayed differentiation)
- Capacity pooling (production flexibility)
Distribution strategies
- Items can be directly shipped from supplier or manufacturer to the retail stores or end
customer
- Use intermediate inventory storage points
Direct shipment
+ the retailer avoids the expenses of operating a distribution center
+ total lead times are reduced (and pipeline inventory)
- risk-pooling effects are negated (higher safety stock inventory)
- manufacturer and distributor transportation costs increase
4
Tilburg University
September 2025
,LECTURE 2: INVENTORY, RISK POOLING & DISTRIBUTION
Key inventory decisions:
1. How much to order?
2. When to order?
3. Where to stock my inventory?
Why is inventory required?
1.Uncertainty in customer demand
i) Shorter product lifecycles
ii) More competing products
2.Uncertainty in supplies (Quality/Quantity/Costs/Delivery Times)
3.Delivery lead times
4.Incentives for larger shipments (economies of scale in transportation / purchasing)
Economic lot size (Order Quantity) model
Considers a constant and deterministic demand with an infinite planning horizon. The goal of
the economic lot size model is to minimize annual ordering and holding costs.
Q* = optimal order quantity
D = demand
K = fixed order cost
h = holding cost per unit held
However: we do not know demand…
Demand uncertainty
- Forecast is always wrong
- The longer the forecast horizon, the worse the forecast is
- Aggregate forecasts are more accurate
Single period models: newsvendor model
There is only one ordering opportunity before demand occurs. Make use of historical data to:
- Identify a variety of demand scenarios
- Determine probability each of these scenarios will occur
The highest probability sells 12,000 items.
How much to order?
Above, below or equal to the expected demand?
1.Calculate average (expected profit) given a specific
order quantity.
2.Choose order quantity that maximizes expected profit
Optimal quantity is 12,000 units < 13,000 (avg demand)
Why?
2
,Relationship between optimal quantity and average demand
Compare marginal profit of a sale and marginal cost of not selling
Marginal profit/unit = selling price – variable ordering (or production) costs
Marginal cost/unit = variable ordering (or production) cost – salvage value
If marginal profit > marginal cost => Optimal quantity > Average demand
If marginal profit < marginal cost => Optimal quantity < Average demand
How much units shall we order if we want an X% chance of not stocking-out?
Optimal service level (SL)= Marginal profit / (Marginal profit + marginal cost)=Cu / (Cu+Co)
Risk-reward trade-offs
If producing 9,000 units or producing 16,000 units will lead to about the same average profit.
Which one would you prefer?
Increasing Q increases the possible risk and the possible reward!
Consider the distribution of the profit (the probability of what profit)
Multiple order opportunities – Continuous review policy
(Q,R) policy – whenever inventory level falls to a reorder level
R, place an order for Q units.
The reorder point (R) should be high enough to:
- Satisfy demand during the lead time
- Protect against demand (and lead time) uncertainty
Stable lead times:
Variable lead times:
The order quantity (Q) balances inventory holding costs and fixed order costs
Multiple order opportunities – Periodic review policy
Inventory level is reviewed periodically at regular intervals. And appropriate quantity is
ordered after each review.
A: Short intervals (daily): (s,S) policy
During each inventory review, if the inventory position falls below s, order enough to raise
the inventory position to S.
- Set s = R, and S = R + Q
B: Intervals (weekly, monthly): Base-stock level policy
- Always order after an inventory level review
- Determine a target inventor level, the base-stock level
- During each review period, the inventory position is reviewed
- Order enough to raise the inventory position to the base-stock level
3
, How to determine the base stock level? Should be enough to cover demand until the next
order arrives (in r+L days) and the safety stock.
r = length of review period
L = lead time
z = safety factor
Service level:
- The higher the service level, the higher the inventory level
- The lower the inventory level, the higher the impact of a unit of inventory on service
level and hence on expected profit
- For the same inventory level, the longer the lead time to the facility, the lower the
level of service provided by the facility
Service level will be higher for products with:
- High profit margin
- High volume
- Low variability
- Short lead time
Risk pooling
Risk pooling suggests that demand variability is reduced if one aggregates demand across
locations. With risk (location) pooling inventory is kept at a central location to satisfy demand
in multiple markets. The demand variability is reduced when there is aggregation across
locations.
Critical points:
- The higher the initial coefficient of variation, the greater the benefit from location
pooling
- The benefits from location pooling depend on the behaviour of the demand from one
market relative to demand from another
- Reallocation of items from one market to another easily accomplished in centralized
systems
There are also other forms of risk-pooling:
- Location pooling
- Product pooling (standardized design)
- Postponement (delayed differentiation)
- Capacity pooling (production flexibility)
Distribution strategies
- Items can be directly shipped from supplier or manufacturer to the retail stores or end
customer
- Use intermediate inventory storage points
Direct shipment
+ the retailer avoids the expenses of operating a distribution center
+ total lead times are reduced (and pipeline inventory)
- risk-pooling effects are negated (higher safety stock inventory)
- manufacturer and distributor transportation costs increase
4
