Manufacturing System Inventory Management
Dr. Jack Su
505-277-3618
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
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