operations management session 24: inventory systems
TRANSCRIPT
Operations Management
Session 24: Inventory Systems
Session 24 Operations Management 2
Previous Lectures
EOQ Model Known demand, multi-periods
Newsvendor Model Uncertain demand, but only 1 period The tension between setup cost and inventory holding
cost is not relevant.
How do we handle uncertain demand and multiple periods?
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Today’s Lecture
Inventory systems
Inventory turns/turnover
Briefing on the simulation game
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Inventory Level in Real Life
First lead time, LT1
d1
Q
Amount used duringfirst lead time
Safety stock, SS
LT2
Order 1 placed
Order 2 placed
Order 3 placed
Shipment 1 received
Shipment 2 received
Time
Inventory on Hand
Reorder point
Order quantity, Q
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Inventory Systems
Continuous (perpetual) system: Continuous (perpetual) system: System that keeps track of removals from inventory continuously, thus monitoring current levels of each item. Fixed quantity is ordered when a certain level is reached.
Good: (1) Keeps constant count of inventory and (2) fixed order quantity.
Bad: (1) Higher record keeping cost; (2) Periodic inventory counting is still require; (3) Time of delivery is random.
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Continuous System with Positive Lead-time
(ROP,Q) policy Order when the inventory reaches the ROP The order size is always Q
What is the optimal Q?
How do we decide when to order? Should the re-order point be greater than dL?
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Safety Stock
Safety Stock:Safety Stock: Stock that is held in excess of expected demand due to variable demand rate and/or lead time.
An expense of doing business. Necessary to ensure good customer service.
Safety stock is determined by demand variability and target service level.
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Example
Daily demand for a certain product is normally distributed with a mean of 60 and a standard deviation of 7. The source of supply is reliable and maintains a constant lead time of six days. The cost of placing the order is $10 and annual holding costs are $0.50 per unit. There are no stockout costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over the entire 365 days of the year. Find the order quantity and reorder point to satisfy a 95% probability of not stocking out during the lead time. (Example 17.4, page 562)
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Example
Let us first ignore the random/uncertainty part.
If daily demand is 60 for sure, what is the order quantity and the reorder point?
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Example
zdLR :pointReorder
Average daily demand Leadtime
z value
st. dev. of demand over the leadtime
units 93650.0
10*365*60*22 :isquantity order optimal The H
DS
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Example
zdLR :pointReorder
15.177*6 2
1
2
L
i d
The z-value associated with 0.95 is 1.64.
The re-order point R is 60(6)+1.64*17.15 = 388 units.
To summarize, an order for 936 units is placed whenever the number of units remaining in inventory drops to 388.
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Example
What happens if demand is not normal?
Demand Probability2 0.023 0.054 0.095 0.146 0.27 0.178 0.159 0.110 0.0511 0.03
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Example
What is the average on hand inventory level?
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Example
What if the supplier is able to reduce the leadtime from 6 days to 3 days?
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Example
What if the cost of placing an order is reduced from $10 to $2.5?
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Inventory Level in Real Life
RP RP
Review period
d1
Q2
Target inventory level, TIL
Amount used during RP+first lead time
Safety stock, SS
First lead time, LT1
LT2 LT3
Order 1 placed
Order 2 placed
Order 3 placed
Shipment 1 received
Shipment 2 received
Shipment 3 received
Time
Inventory on Hand
First order quantity, Q1
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Inventory Systems
Periodic system: Periodic system: Physical count of items made at periodic intervals (weekly, monthly)
Good: (1) Economics of scale and (2) Delivery is performed on a known schedule
Bad: (1) Lack of control between reviews; (2) Carry extra stock to protect against shortages between reviews; (3) Order quantity is random
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Periodic System
(Order-up-to,T) policy
How do we compute how much to order at every review period?
If there was no variability in the system, we would order exactly the amount needed to satisfy demand over the period T+L.
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Example
Daily demand for a product is 10 units with a standard deviation of 3 units. The review period is 30 days, and the lead time is 14 days. Management has set a policy of satisfying 98 percent of demand from items in stock. At the beginning of this review period, there are 150 units in inventory.
How many units should be ordered? (Example 17.5, page 563)
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Example
Let us first ignore the random/uncertainty part.
If daily demand is 10 for sure, what is the order- up-to level?
d(T+L)
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The Safety Stock Level and Order Quantity
Safety stock = z*(st. dev. of demand over review and lead time)
q = d(T+L) + zσ - IPart in light blue is the target inventory level.
q = Quantity to be orderedT = number of days between reviewsL = lead timed = forecast avg. daily demandz = z-value for a specified service levelσ = st. dev. of demand over review and lead timeI = current inventory level
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Example
d = 10; T = 30; L = 14; I = 150We must calculate z and σ.The z value for 0.98 is 2.05.
Formula: q = d(T+L) + z*σ - I
90.19)3)(1430()( 22
1
2
d
LT
i d LT
The quantity to order is:q = 10(30+14)+2.05*19.90-150 = 331 unitsto ensure 98% probability of not stocking outover the review period.
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Example
What is the average on hand inventory level?
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Inventory Level
Safety stock, SS
Time
T
L T-L
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Inventory Level
Safety stock, SS
3 7
6
6+20
20
6
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Inventory Level
Safety stock, SS
3 7
6
20
6
3
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Inventory Level
Safety stock, SS
3 7
6
20
3
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Inventory Level
Safety stock, SS
L T-L
dL
dT
L
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Example
What if the supplier is able to reduce the leadtime from 14 days to 7 days?
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Example
What if the review period is reduced from 30 days to 15 days?
What is the main trade-off that determines T, the review cycle?
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Inventory Turn
Inventory Turn
= (Annual) Cost of goods sold/Average inventory value
= [(Annual) Sales quantity * Unit Cost] /
(Average inventory quantity * Unit Cost)
= (Annual) Sales quantity / Average inventory quantity
= Throughput Rate / Average WIP
= 1 / Throughput Time
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Inventory Turn
Continuous System
Inventory turn = D / (Q/2 + SS)
Periodic System
Inventory turn = D / (DT/2 + SS)
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Comparison: Continuous Review vs Periodic
Continuous review inventory system: The order quantity Q is constant (i.e., the same amount is ordered every time), and an order is placed every time the inventory drops to the reorder level R. The time between orders is variable.
Periodic review inventory system: There is a target inventory level, and an order is placed every T time units. The size of the order is variable, and equals the target inventory level minus the inventory currently on hand. The time between orders is constant.
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The Simulation Game: First Run
Monitoring utilization rate Buy machines when the utilization rate is high
Forecasting and planning Occasional information updating and monitoring
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The Simulation Game: First Run
Monitoring utilization rate It is very hard to play catch-up game What the cause of peak rate? Noise? Underlying demand? What is the right utilization rate for the desired leadtime?
Forecasting and planning Capacity requirement Capacity requirement with 85% target utilization rate Spreadsheet waiting time calculation for leadtime
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The Simulation Game: First Run
Do we want to delay the purchase?
Do we want to sell the machines in the end?
Do we want to change the queue priority?
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The Simulation Game: Second Run
Preparing Testing
CentrifugingDecisions:1. Three pricing contract type (7 day, 1 day, and half day)2. The number of machines at each station. (Start with 1.)3. The inventory policy (reorder point, reorder quantity)4. The priority at the testing queue (FIFO, initial, or final).
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The Simulation Game: Second Run
Observation period for the second simulation game starts at 7:00 pm, 4/15/09 (Wed.).
Second Simulation Game Starts at 4/16/09 7:00pm (Thurs.)
The simulator stops running at 7 pm on 4/23/09 7:00pm (Thurs.)
50% is your standing against the other teams in this class.
50% is a 2 page write-up.
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Next Class
Supply Chain Coordination Article reading: "Back to the Future: Benetton
Transforms it’s Global network" MIT Sloan management Review, Fall 2001.
Beer Game Please download the game before class at
http://scm.bus.umich.edu/BeerNet/Beerwin32.exe Bring laptops to the class next time