Manufacturing System Inventory Management

Dr. Jack Su

505-277-3618

su@mgt.unm.edu

ASM 2154

Office Hour: M, W 2-4

Why Study Inventory Management

Broadly used Common language Central to modern management

concept such as JIT and MRP

What is inventory

InventorySupplier Customer

Materials that has been purchased from a supplier, may have been partially or completely converted, but not yet sold to the customer.

Types of Inventory

Inventory

Raw materials

Components Work-in-process

Finished goods

Why hold inventory?

Buffer against uncertainty– Demand, Supply, Down time

To ensure a high level of customer service

Economies of scale Processing and movement Speculation of future events Independence of stages

Cost of holding inventory

Capital cost (Interest) Storage cost Obsolete cost Consist of about 20% of total cost in the

United States

Inventory decisions

When, What, and how many to order

Inventory issues

Demand– Constant vs. variable– deterministic vs. stochastic

Lead time Review time

– Continuous vs. periodic Excess demand

– Backorders, lost sales Inventory change

– Perish, obsolescence

EOQ Assumptions

Production is instantaneous Delivery is immediate (Infinite capacity) Demand is deterministic Demand is constant over time A production run incurs a constant

setup cost Products can be analyzed singly

EOQ Notations

D: demand rate (units per period) c: unit cost (dollars per unit) A: fixed setup cost (dollars per order) h: holding cost (dollars per unit per

period) Q: order quantity (units); this is decision

variable

Variable and Deterministic Demand

t 1 2 3 4 5 6 7 8 9 10

Dt 20 50 10 50 50 10 20 40 20 30

ct 10 10 10 10 10 10 10 10 10 10

At 100 100 100 100 100 100 100 100 100 100

ht 1 1 1 1 1 1 1 1 1 1

Notations

t: time period (t= 1, 2, ..., T) Dt: demand in period t

ct: unit cost in period t

At: setup cost in period t

ht: unit holding cost in period t

It: inventory left over at the end of period t

Qt: order quantity in period t (decision variables)

Lot for lot rule

t 1 2 3 4 5 6 7 8 9 10

Dt 20 50 10 50 50 10 20 40 20 30

Qt 20 50 10 50 50 10 20 40 20 30

It 0 0 0 0 0 0 0 0 0 0

setup cost

100 100 100 100 100 100 100 100 100 100

holding cost

0 0 0 0 0 0 0 0 0 0

Total cost

$1000

Fixed Order Quantity

t 1 2 3 4 5 6 7 8 9 10

Dt 20 50 10 50 50 10 20 40 20 30

Qt 100 0 0 100 0 0 100 0 0 0

It 80 30 20 70 20 10 90 50 30 0

setup cost

100 100 100

holding cost

80 30 20 70 20 10 90 50 30 0

Total cost

$300+$400=$700

Wangner-Whitin Procedure

Optimal for variable and deterministic demand scenario

News Vendor Assumptions

Product are separable Planning is done for a single period Demand is stochastic Deliveries are made in advance of

demand Cost of overage and underage are

linear

News Vendor Notations

X: demand (units), a random variable G(x) = P(X ≤ x) μ: mean demand (units) σ: standard deviation of demand (units) co: overage cost (dollars per unit)

cs: shortage cost (dollars per unit) Q: order quantity (units); the decision variable

Assumption of Base Stock Models Products can be analyzed individually Demands occur one at a time Unfilled demand is backordered Replenishment lead times are fixed and

known Replenishments are ordered one at a

time

Notations of Base Stock Models

l: replenishment lead time X: demand during lead time, a random

variable p (x): P(X = x) G (x): = P(X ≤ x) θ: mean demand during lead time σ: standard deviation of demand during

lead time

Notations of Base Stock Models

r: reorder point (decision variable) R = r+1, base stock level s = r-θ, safety stock level S(R) : fill rate (percentage of orders

filled from stock) B(R) : average number of outstanding

backorders I (R) : average inventory level

Terms

On-hand inventory (Physical inventory in stock can never go to negative)

Inventory position = on-hand inventory – backorders + orders

Inventory Model with Stationary Stochastic Demand

Three Key issues– How often the inventory status should be

determined (review frequency)– When a replenishment order should be

placed (when to order)– How large the replenishment order should

be (order quantity)

Continuous vs. Periodic Review (1 of 2)

R: review period Continuous review (R=0) also call

transactions reporting Even with POS inventory decision often

made in after-hours (R=1 days)

Continuous vs. Periodic Review (2 of 2)

Benefit of Periodic Review– easy coordination across supply chain– More predictable work load– cheaper than continuous review system– for a slow moving item PR can detect spoilage

Benefit of Continuous Review– Provide same level of customer service– Requires less safety stock because manager can

take actions any time

Four Types of Control Systems

(s,Q): Continuous review, reorder point (s), order quantity (Q)

(s,S): Continuous review, reorder point (s), order-up-to level (S) system

(R,S): Periodic Review, review period (R), order-up-to level (S) system

(R,s,S): Periodic Review, review period (R), reorder point (s), order-up-to level (S) system

(s,Q) system

A fixed quantity, Q, is ordered whenever the inventory position drops to the reorder point, s, or lower.

Base stock is a special form of (s,Q) Two bin system is another a special

form of (s,Q)

(s,S) system

Replenishment is made whenever the inventory position drops to the order point s or lower and order enough to the order-up-to level, S.

If all demand transaction are unit-sized (s,S) system is equivalent to (s,Q) system by setting S=s+Q

Also call min-max system Best (s,S) outperform best (s,Q) However, Computational effort to find optimal solution

for (s,S) is substantially more than that for (s,Q)

(R,S) system

Periodic review system Every R unit of time enough is ordered

to raise the inventory position to order-up-to level, S.

Also called replenishment cycle system Carrying cost is higher than continuous

review system

(R,s,S) system

Combination of (s,S) and (R,S) system Every R units of time we check the

inventory position. If it is at or below reorder point, s, we

order enough to raise it to S. If the position is above s, nothing is

done until at least next review.

The (s, Q) model

Also called the (Q, r) model Assumptions are the same as base

stock except– Fixed ordering cost or– Constraint on the number of order allow

per period Purpose of s and Q Cycle stock vs. safety stock

Stock out vs. Backorder

A fixed stock out cost is charged whenever the demand can not be filled immediately regardless of the duration or quantity of the unfilled demand

A unit backorder cost is charged per stock out per period of time

Basic (s, Q) insights

D ↑⇒ Q↑ θ ↑⇒ r ↑ σ ↑⇒ r ↑ h ↑⇒ Q↓ and r↓

Conclusion

Tradeoff between setup and inventory

Tradeoff between customer service and inventory

Tradeoff between variability and inventory

ABC Classification

Stock keeping unit (SKU) 20/80 rule

– 20 percent of the SKUs account for 80 percent of the total annual dollar usage

Class A– first 5 to 10 percent of SKUs– Account for about 50 percent of total annual dollar usage

Class B– Largest number of SKUs fall into this category, usually around 50

percent.– Account for almost the remaining total annual dollar usage

Class C– Remaining SKUs that are rarely used– Important to identify this large groups of SKUs that can potentially

consume large amount of data inputs and managerial times

Rule of Thumb

A item: (s, S) or (R, s, S) B item: (s, Q) or (R, S) C item: two bin system