inventory- a stock or store of goods dependent demand items- components or sub-assemblies (in a...
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Inventory- a stock or store of goods
• Dependent demand items- components or sub-assemblies (In a Roland piano, the bench, for example). Forecast is based on # of related finished goods
• Independent demand items- finished goods that have their own demand curve (subject to randomness we discussed during forecasting section
Types of inventories- piano example
• Raw materials & parts (e.g. piano keys)
• Work In Process (keyboard assembly)
• Finished Goods (keyboard, stand and bench)
• Replacement items (keyboard cover handle)
• In-transit inventory
Why keep inventory if it costs so much?
• There are times in which the cost of keeping inventory is less than the benefits derived:
• smooth production requirements as seen in Agg. Planning examples
• decouple operations A distribution company wants to keep distributing even if the ship carrying the next shipment is late!
• To meet our stockout goals. Software is quick-decision purchase- many companies have 0% stockout strategies as a result (I.e. opportunity cost = 100%; inventory cost may equal 50%)
• To capitalize on opportunities. If we have excess warehouse and staff capacity, we may save by buying a lot at a great price.
Why keep inventory if it costs so much?
Ordering: quantity & timing Realities in the real world
• Your order quantity may have to be done for political reasons (new product the president is behind- Edirol example)
• We may not be able to affect the timing of orders. Distribution companies usually have to place 3 or even 6 month orders for highly technological products to smooth production planning. So fixed interval models are developed.
Counting Inventory
• Periodic systems count physically at regular intervals and re-order when necessary. Your accounting audit will require this.
• Perpetual systems (that count inventory as it changes in real time and re-ordering when we hit a reorder point) are almost universally used as the cost of computing has decreased.
• Most companies combine use of both.
Adding math models to your tool kit
• What is the lead time of your order (time between submission & receipt)
• What is your holding cost (includes interest, insurance obsolescence, theft, wear, warehousing, etc.)
• What is your ordering cost (including the cost of the transaction and receipt
• What is your Shortage cost (opportunity)
What inventory do we evaluate?
• Pareto principle tells us that 20% of our items will account for 80% of our orders/ supply requests
• So, use the ABC system to classify value Item demand Unit Cost Annual $ value Class
1 10 50 5002 100 1 1003 75 300 225004 5 2500 125005 50 35 17506 130 50 6500
More on ABC System
• Can be used to determine number of re-counts in physical counts (e.g. A’s get 3; B’s get 2; C’s get 1)
• Can also be used to determine who does counts (A’s counted by controller, staff & warehouse; B’s by staff & warehouse; C’s by warehouse only)
The Inventory Cycle
Profile of Inventory Level Over Time
Quantityon hand
Q
Receive order
Placeorder
Receive order
Placeorder
Receive order
Lead time
Reorderpoint
Usage rate
Time
So we’ve evaluated the right inventory. Now let’s order.
• EO Q Model minimizes the sum of holding and ordering costs by finding the optimal order quantity.
• Assumptions: 1) one product at a time; 2) we’re confident in our annual demand forecast; 3) demand is even; 4) lead time is constant (management issue); 5) orders received in one delivery; 6) no qty discounts
Getting to EOQ: we’re balancing...
• ANNUAL CARRYING COST = (Q/2)*H (Q= order quantity units; H- carrying cost/unit)
• ANNUAL ORDERING COST = (D/Q)*S (D= annual unit demand; Q= order
size; and S= ordering cost
• calculus then gives us EO Q, the optimal order quantity
Total cost = annual carrying cost + annual order cost
The Total-Cost Curve is U-Shaped
Ordering Costs
QO Order Quantity (Q)
An
nu
al C
os
t
(optimal order quantity)
TCQ
HD
QS
2Carrying
Costs
Q = 2DS
H =
2(Annual Demand)(Order or Setup Cost)
Annual Holding CostOPT
• Given that demand = 405/month
• Carrying cost = $30/yr/unit Order Cost = $4/order
• 1) EOQ= SQR(2*(405*12)*4)/30)= 36
• 2)What is average # of bags on hand? Q/2= 18
• 3) # of orders per year= (405*12)/36 =135
• 4) Carrying cost = (36/2)*30=540; ordering cost= (4860/36)*4=540 total cost = 540 +540 =1080
• **We need figures represented as annual costs.
Determining the economic run quantity of production
• When company is producer and user, determines optimum production run size (since production usually happens faster than usage)
• When we’re producing our own goods, assumes setup costs are the same as order costs in formula
• so total cost = carrying cost +setup cost• TC = (Max. Inventory/2)*H + (D/Q)*S• Economic Run quantity = SQRRT(2DS/H)* SQRRT(p/(p-u))
where p=prod. Rate u=usage rate• cycle time =Q/u run time = Q/p
Quantity discounts if carrying costs are constant
• Goal: minimize total cost, where TC =(Q/2)*H + (D/Q)*S + PD
where P= unit price
• Step 1: compute the common EOQ (if carrying cost is a constant $ figure, it won’t vary)
• Step 2: compute total cost at EOQ and price breaks and compare
Assume: D5000,/yr h= $2/unit/yr s=$48
Units Price
1-399 $10
400-599 $9
600+ $8
Quantity discounts if carrying costs are constant
• STEP 1: compute the common EOQ= SQR ((2DS)/H) =SQR((2*5000*48)/2)= 489.90
• STEP 2: compute the TC @ EOQ (490) = (Q/2)*H + (D/Q)*S + PD = (490/2)*2 + 5000/490)*48 + (9*5000) = $45980 (with rounding)
• STEP 3: compare with TC at discount levels TC = (Q/2)*H + (D/Q)*S + PD TC @600 = (600/2)*2 + (5000/600)*48 + (8*5000)= 41000
• 600 is the optimum order quantity account for discounts
We know how much to order… now, when do we reorder?
• ROP: predetermined inventory level of an item at which a reorder is placed.
• Demand (d) and Lead TIME (LT)
• ROP= d*LT
• Example: Monthly demand is 400. Lead Time is two weeks (.50 months). ROP= 400 *.50 =200
• Reorder when inventory level reaches 200.
• This model assumes static d and LT
What if demand or lead time is variable?
• Then we add a safety stock to help us satisfy orders if demand is higher than expected.
• Company policy: What is our service level? It is the number: 1- stock-out risk. “Our service level goal is 95%. In other words, there’s a 95% probability we won’t stock out.
Handling variability, 2
• We assume the variability is characterized by the normal distribution.
• Turn to page 889. The shaded area under the curve represents the probability of us having inventory, given the variability in the average demand or average lead time.
• So let’s say we have a service level goal of 95%. What is the Z score that characterizes 95% of the area under the normal curve?
• About 1.645
When lead time is variable:
• First example: LEAD TIME variable.
• When lead time is variable, ROP= d* avgLT + z*d(LT) where d= demand rate; LT= lead time; LT=std. Dev. Of lead time
• Get the z score (based on your service level goal) from the table as we saw on the last slide based on company’s stockout policy..
• Given: demand during lead time =400/day
• Lead Time = 5 days, =2acceptable stockout risk= 5%
• STEP 1: get your Z score1-.05 = .95 z (.95) =1.65
• STEP 2: plug in400*5 + 1.65*400*2= 3320
• Reorder when inventory = 3320
ROP= d* avgLT + z*d(LT)
If demand rate is variable:
• ROP= avgd* LT + z* sqr.root of LT * (d)
• assume: avg d =1000; d= 14; LT=4; company stockout policy = 10% risk.
• Z score for .90 = 1.28
• 1000*4 + 1.28* 2 * 14= 4000+ 35.84= 4036
• in real world, d is derived by managers keeping careful records to determine it.
For next time
• PROBLEMS (not questions) Ch 12 #s 1,6,13,19,
• Page 587- know models 1,2,3, and 4a,b,c
Problem 1Item Usage Unit Cost Value Class
4021 90 1400 126000 A
9402 300 12 3600 C
4066 30 700 21000 B
6500 150 20 3000 C
9280 10 1020 10200 C
4050 80 140 11200 C
6850 2000 10 20000 B
3010 400 20 8000 C
4400 5000 5 25000 B
Problem 6• D=800/MO @ $10/UNIT S=$28
H= 35% OF UNIT COST/YR
• D- 9600/YR H= $3.50/UNIT/YR
• CURRENT TC = (q/2)*H + (D/Q)*S
• CURRENT TC= (800/2)*3.50 + (9600/800)*28 =1736
• EOQ= square root of ((2DS)/H)
• EOQ = SQR ((2*9600*28)/3.50)=SQR 153600 =391.91= 392
• TC at 392= (392/2 )*3.5 + (9600/392)*28=1371.71
• Cost savings =1736-1372=364
Problem 13: carrying costs are constant
• D=18000 H= $0.60/yr S=$96
• STEP 1: Common EOQ= SQR ((2DS)/H) =SQR((2*18000*96)/.6)= 2400
• STEP 2: TC @2400 = (Q/2)*H + (D/Q)*S + PD =(2400/2)*0.60 + (18000/2400)*96 + (1.20*18000)=$23040
• TC @5000 = (5000/2)*0.60 + (18000/5000)*96 + (18000*1.15)=$22545.60
• TC@10000= (10000/2)*.60 + (18000/10000)*96 + 18000*1.10=22972.80
• 5000 is the optimum order quantity account for discounts
Problem 19, page 597• see page 573, equation 12-12. The estimate of standard deviation of lead time demand
is available, so you can use this simpler equation
• Expected demand during LT = 300 Std dev of LT demand = 30
• a) Step 1 z=2.33• a) step 2 300+(2.33*30)=69.9=370• b) from a)--> 70 units• c)less safety stock is required because we’d be
carrying an amount of inventory causing us to stock out more often.
Problem 23• Hint: plot the information you do have under the equation, then solve for
what you don’t have.• When the book says “the delivery time is normal” that means we’ve got a
variable lead time problem.
• When lead time is variable, ROP= d* avgLT + z*d(LT) where d= demand rate; LT= lead time; LT=std. Dev. Of lead time
• 625= 85*6 + z*85*1.10• solving for z, z=1.22• from table on p. 883, that shows an 89% probability of
supply, implying an 11% probability the supply will be exhausted.