Module 3 Deterministic Inventory Management

Question 1

What is inventory

Answer 1

the stock of any item or resource used in an
organization to meet future demand, and can include: raw
materials, finished products, component parts, supplies, and
work-in-process

Question 2

What is inventory system

Answer 2

the set of policies and controls that monitor
the levels of inventory and determines what levels should be
maintained, when stock should be replenished, and how large
orders should be

Question 3

What is the objective of inventory management?

Answer 3

The objective of inventory management is to strike a balance
between inventory investment and customer service
- How many units to order?
- When to order?

Question 4

What are the types of inventory?

Answer 4

Raw materials: needed for the production or processing activity
of a firm

Work-In-Process (WIP): products waiting for processing of being
processed

Finished items: final product of the production process awaiting
to be/being transported

Tools and equipment (e.g. repair kits): needed to perform the
maintenance of the resource used in the production process.

Question 5

What are the characteristics of inventory systems/

Answer 5

Demand:
- May be known or uncertain
- May be changing or unchanging in Time

Lead Times: time that elapses from placement of order until it’s
arrival. Can be known or uncertain.

Review Time: are inventory levels reviewed periodically or is
system state known at all times?

Treatment of Excess Demand:
- Backorder all Excess Demand
- Lose all excess demand
- Backorder some and lose some

Question 6

What are the holding, ordering, and penalty costs?

Answer 6

Holding (or carrying) costs: cost of capital, costs for storage,
taxes and insurance, breakage and spoilage,. . .

Ordering costs:
- Fixed cost: costs of placing an order: order forms, inspection,
phone calls,. . .
- Variable cost: simply the price paid to supplier (including freight),
plus any cost incurred to make the products ready for use

Penalty (or shortage) costs: costs of running out of stock:
penalty late delivery, lost sales, loss of goodwill,. . .

Question 7

How are the holding costs expressed?

Answer 7

Inventory is usually measured in units rather than euros, so it is
convenient to express holding costs in euros per unit per year. Let
c : be the euro value of one unit of inventory
I : be the annual interest rate
h : be the holding cost in terms of euros per unit per year

Then we have the relationship
h = c × I

Question 8

What are the holding costs?

Answer 8

The value of the interest rate of opportunity cost of alternative
investment is
- related to a number of standard accounting measures, including the internal rate of return, the return on assets etc
- estimated by the firm’s accounting department
usually refereed to as ”cost of capital”

Holding costs can be estimated as an aggregated (annual)
interest rate

Question 9

What are the assumptions of EOQ (economic order quantity model)

Answer 9

• Demand is assumed to be constant over time
• No shortages are allowed
• Lead time tau for the receipt of orders is constant (e.g. τ = 0)
• Order quantity is received all at once
• Unit variable cost doesn’t depend on the replenishment quantity
  (no discounts)
• Cost factors do not change significantly over time (no inflation)
• Item is treated entirely independently of other items (benefits from
  joint replenishment are negligible)

Question 10

What is the notation of the EOQ model?

Answer 10

Q : the replenishment order quantity (unit) ⇒ Decision variable

K : the fixed ordering cost regardless of the ordered quantity (euro)

c : the unit variable cost of the item (the value of the item and not
its selling price (euro/unit))

h : the carrying charge, the cost of holding an item in inventory for
a unit time interval (euro/unit/time unit)

λ : the demand rate of the item (unit/time unit)

G(Q) : the total cost per time unit (euro/time unit)

Question 11

What is the cost function?

Answer 11

see cost function in Docs

Question 12

What is the optimal order quantity?

Answer 12

see Docs

Question 13

What are the quantity discounts?

Answer 13

We assume quantity discounts can be obtained.

We denote cd the unit cost when a discount d(%) is offered.

So, c_0 is the unit cost when no discount is offered.

Ordering large quantities may result in cost savings, but is offset by increasing inventory holding cost.

Question 14

What is the assumed cost structure and the G(Q) of that one?

Answer 14

see docs

Question 15

What is the procedure of the algorithm?

Answer 15

Procedure:

Step 1: Compute the EOQ for each discount d (including d = 0%)

Step 2: For each discount, compare Q∗d with Qb.
If Q∗d < Qb (it doesn’t qualify for discount) then adjust Q∗d to Qb

Step 3: Evaluate the total cost for each discount at Q∗d
(use the adjusted values of Q∗d)

Step 4: Select Q∗
d with the lowest total cost.

Question 16

What are the assumptions of the economic production quantity model?

Answer 16

• Order is received gradually, as inventory is simultaneously being
  depleted
• Non-instantaneous receipt model
• Assumption that order quantity is received all at once is relaxed

Question 17

What is the notation of the economic production quantity model?

Answer 17

P : daily rate at which an order is received over time (production
rate)

λ : daily rate at which inventory is demanded

Q : size of each production run ⇒ Decision variable

T = T1 + T2 : the cycle length (time between successive
production startups). T1 is uptime and T2 is downtime

H be the maximum level of on-hand inventory during a cycle
(H < Q)

Question 18

What is the analysis of the economic production quantity model?

Answer 18

see docs