Module 3 Probabilistic Inventory Management

Question 1

What are sources of uncertainty?

Answer 1

In the EOQ model we assumed that shortages are not allowed
(we could do that because demand is deterministic)

In many practical situations, the assumption of deterministic
demand is inappropriate. So, demand is stochastic (probabilistic)

Uncertainty makes it difficult to match supply and demand

Forecasting doesn’t always solve the problem

Sources of uncertainty:
- Supply uncertainty
- Lead time uncertainty
- Resource availability
- Disasters
- Demand uncertainty

Question 2

What is the impact of Uncertainty?

Answer 2

Shortages are unavoidable; unless you keep ample stock which is
economically not feasible

Question 3

What do we need to know when demand is uncertain?

Answer 3

see docs

Question 4

What are different definitions of stock level?

Answer 4

On-hand stock (OH): the stock that is physically on the shelf. It
can never be negative. Relevant for determining whether a
particular customer demand can be satisfied directly from the shelf

Inventory position (IP): OH + (On-order) - BO.
The stock that is
really available. The “On-order” stock is the stock that has been
requested but not yet received.

Safety stock (s): average inventory level just before receiving an
order

Question 5

What is the news-vendor problem?

Answer 5

A one-period decision.

Excess inventory at the end of the period is sold for a salvage
cost.

demand is assumed to be uncertain/stochastic

There is no setup cost

Question 6

What are the cost function and expected cost of the News-vendor problem?

Answer 6

see docs

Question 7

What is the optimal order quantity of the news-vendor problem?

Answer 7

see docs

Question 8

What is the continuous review inventory model?

Answer 8

see docs

Question 9

What is the notation of (Q,R) policy

Answer 9

τ : The lead time

D : The demand distribution during lead time τ with pdf f(x) and
cdf F(x)

λ : The expected demand (units/time unit)

h : The holding cost (euro/held unit/time unit)

p : The shortage cost
(euro/unsatisfied unit)

K : The setup cost per order (euro)

Question 10

What are the expected on-had inventory, expected backorders/cycle, expected cost per time unit?

Answer 10

see docs

Question 11

What are the optimal policy parameters Q* and R* and the procedure for calculating (Q, R)?

Answer 11

see docs

Question 12

What are the 2 types service for the (Q, R) policy?

Answer 12

see docs