1. Slides 2 Inventory Management
Global Supply Chain Management
Inventory Management

2. Agenda Inventory Management Intro Economic Lot Size Model
Continuous Review Policy
Service level optimization
Risk Pooling / Centralization
Inventory Management

3. Inventory Management (IM)
We will introduce here the basics….
Later, course cases GM, Meditech, Reebok present a diagnosis of a typical problem: low service levels & too high inventory levels. This is actually an Oxymoron…..
Solutions: co-ordination within or across, better forecasts, reduction of lead time, use Pull, Push-Pull boundaries, postponement.
Emphasis is on quick diagnosis (like a Kaizen event), using simple tools and principles, to identify high leverage points
Actual project– specialty industrial chemicals
Note – there is not much real information in case, so we’ll need to make some inferences; depending on what one assumes, analysis and rec’s might change.
Inventory Management

4. IM implies Order (or Production) Management
Key Question: what, when and how much to order (or: to produce – assume order)
Simple models and principles can provide valuable guidance
At start not like continuous replenishment policy (case of Tesco): we order, the order arrives before we need to order again. Later: orders are underway when we order.
My next session --- Instron case– think about how do you want to run the operation? What are the main tactics and operating polices to use?
Inventory Management

5. Why do we keep Inventory?
Logical: incentives for orders or arriving shipments that are larger (and hence less frequent) compared to leaving sales based on demand: think of a grocery retailer
Uncertainty in supply levels, in lead times
To address uncertainty in demand in combination with long lead times
demand may be hard to forecast, demand may suddenly go up, with high “unsatisfied demand” costs we rather keep some stock, especially if it takes a long time to replenish.
Risks associated with inventories
Shorter lifecycles, more competing products
Inventory Management

6. Typical Inventory Policy Factors
Expectations about customer demand
Expectations about lead time
Length of the planning horizon (e.g. seasonal ?)
Costs:
Fixed (order) costs, consisting of fixed costs in
Materials and components, storage, admin costs, production costs, transportation costs,
Assume that variable costs are covered with sales
Inventory holding costs and associated costs
Taxes and Insurance costs, Maintenance costs
Obsolescence costs and Loss of Opportunity costs
Service level (availability) requirements
Inventory Management

7. Economic Lot Size Model
FIGURE 2-3: Inventory level as a function of time
Assumptions
- Constant demand rate of D items per unit of time
- Q items per order: Order quantities are always the same
- Lead Time = 0 : Time between placement of an order and its receipt is assumed to be zero.
- Planning horizon is long, infinite (for that product)
Inventory Management

8. Other Assumptions
K fixed setup cost: Every time the warehouse places an order, a fixed setup cost of K is incurred
h inventory carrying cost: A holding cost of h is incurred per unit held in inventory per unit of time
Requested is Q* or EOQ, the Economic Order Quantity
Inventory Management

9. EOQ: Minimizing Total Costs
FIGURE 2-4: Economic lot size model: total cost per unit of time
as a function of the order quantity
Inventory Management

10. Deriving EOQ
Whatever Q is, at the start of cycle time T we order Q units
The average inventory during a cycle is: Q/2, see diagram
Per T this means a total holding cost of: T * h * Q/2
For every cycle T we also incur a fixed order cost: K
So the average total cost per cycle: K T * h *Q/2
Average total cost per unit of time: K/T h * Q/2
Total demand during a cycle is Q = D * T, so T = Q/D
Average total cost per unit of time: K * D/Q + h * Q/2
This sum of the Order Cost per of unit time and Holding Cost per unit of time can be shown in a Diagram…..
Inventory Management

11. Where is the minimum ? Function f(Q) = K*D/Q + h*Q/2
Gives f ’(Q) = -1*K*D/Q^2 + h/2
This being 0, implies that the optimal order quantity is
Example: K = 2000$, D = 180 units per day and h = 0.5$ per unit per day
What is Q*? How often will we order?
Inventory Management

12. Sensitivity Analysis
Total costs relatively insensitive to order quantities
Actual order quantity: Q
Q is a multiple b of the optimal order quantity Q*.
For a given b, the quantity ordered is Q = bQ*
Nevertheless: it makes a difference b
0.5
0.8
0.9
1.0
1.1
1.2
1.5
2.0
Cost Increase
25%
2.5%
0.5% 0%
0.4%
1.6%
8.9%
Inventory Management

13. What if the Manufacturer (or Retailer) has an Initial Inventory?
Trying to use the existing inventory to meet the demand has….
Advantage: no need to pay production (order) cost
Disadvantage: it may be impossible to meet demand
Producing/ordering on the other hand has….
Advantage: more likely to meet demand
Disadvantage: implies a production (order) cost, which is relatively high a as we will produce (order) a smaller quantity
Inventory Management

14. Multiple Order Opportunities
Suppose: demand is uncertain & lead times exist
Question: when and how much to order each time?
to balance annual inventory holding costs and annual fixed order costs
to satisfy demand occurring during lead time
to protect against uncertainty in demand
Major strategies
Continuous review policy
inventory is continuously reviewed (computerized inventory system) and an order is placed when the inventory reaches a particular level, the reorder point
Periodic review policy (less relevant today)
Inventory Management

15. Continuous Review Policy
An entity faces demand according to a normal distribution, the mean demand is AVG and its standard deviation STD.
Every time the entity places an order to its supplier (or decides to manufacture), the entity pays a fixed cost K (plus an amount proportional to the quantity).
Inventory holding cost h is charged per item per unit time.
Inventory level is continuously reviewed, and if an order is placed, the order arrives after the (constant) lead time L.
If customer demand occurs when there is no inventory on hand (i.e. when the entity is stocked out), the order is lost.
The entity specifies a required service level α. This implies that the probability of stocking out during L out is 1 – α.
Inventory Management

16. Continuous Review Policy
(Q,R) policy – whenever inventory level falls to a reorder level (point) R, place an order for Q units (optimal order quantity)
What is the optimal value of R?
What is the safety stock level?
What is the demand during the lead time ?
What is the optimal value of Q?
The expected time between orders TBO?
How many inventory turns per unit of time?
Inventory Management

17. Inventory development over time
Order
received Q
placed
Inventory + Pipeline
Time
inventory R
TBO1
TBO2
TBO3 L

18. Continuous Review Policy
Expected demand during lead time L x AVG
Required safety stock
Reorder level R=
Order quantity
Expected time between orders = Q / AVG
Inventory Management

19. Relation between Service Level α and Safety Factor z
90%
91%
92%
93% 94 %
95%
96%
97%
98%
99%
99.9%
Z - value
1.29
1.34
1.41
1.48
1.56
1.65
1.75
1.88
2.05
2.33
3.08
z is chosen from statistical tables to ensure
that the probability of stock-outs
during lead time is exactly 1 - α
Inventory Management

20. Inventory Level Over Time
FIGURE 2-9: Inventory level as a function of time in a (Q,R) policy
Inventory level before receiving an order =
Inventory level after receiving an order =
Average Inventory (AvInv) =
Inventory Turn = AVG / AvInv
Inventory Management

21. Continuous Review Policy Example: calculate (Q,R)
A distributor of TV sets that orders from a manufacturer and sells to retailers
Fixed ordering cost = $4,500
Cost of a TV set to the distributor = $250
Annual inventory holding cost = 18% of product cost (so 18% of $260)
Lead time = 2 weeks
Expected service level = 97%
AVG = 49 per week.
STD = √50 per week (variance is 50)
Inventory Management

22. Service Level Optimization
Optimal inventory policy assumes a specific service level target.
What is the appropriate level of service?
May be determined by the downstream customer
The customer may require its supplier (the entity), to maintain a specific service level
The supplier will use that target to manage its own inventory
The Supplier (the Entity) may have the flexibility to choose the appropriate level of service
Inventory Management

23. Service Level Optimization
FIGURE 2-11: Service level versus inventory level as a function of lead time
Inventory Management

24. Trade-Offs Everything else being equal:
the higher the service level, the higher the inventory level and vice versa (see graph),
the lower the inventory level, the higher the impact of a unit of inventory on service level and hence on expected profit (form of curves),
for the same inventory level, the longer the lead time to the facility, the lower the service level provided by the facility (dotted curve).
Inventory Management

25. Defining a Retail Strategy
Given a target overall service level across all products
Determine the service level for each SKU so as to maximize expected profit
Everything else being equal, service level will be higher for products with:
high profit margin
high volume
low variability
short lead time
Inventory Management

26. Service Level Optimization
FIGURE 2-12: Service level optimization by SKU (Example)
Note that the size of the circles is an indication of the profitability
Inventory Management

27. Profit Optimization
A target service level of 97% across all products combined typically leads to a:
Service level > 99% for products with high profit margin, high volume, low variability.
Service level < 95% for products with low profit margin, low volume and high variability.
Inventory Management

28. Risk Pooling (based on location)
Demand variability is reduced if one aggregates demand across locations.
More likely that high demand from one customer will be offset by low demand from another customer.
Reduction in variability allows a decrease in safety stock and therefore reduces average inventory.
Other RP factors are time and product
Inventory Management