inventory analysis mm – om – session 6 henry yuliando
TRANSCRIPT
INVENTORY ANALYSIS
MM – OM – Session 6Henry Yuliando
...Cases
• Three largest booksellers in US: Borders Group, Barnes&Noble, and Amazon.
• Borders Group has 174 days of inventory in its network; Barnes&Noble 129 days in 2006.
• From a macroeconomic perspective, inventort-related cost accounted approx. 2.5% of the GDP of US in 2005.
Watch this..
Different Views of INVENTORY
Process stageProcess stageRaw materialRaw material
Work in ProcesWork in ProcesFinished goodsFinished goods
Annual $ VolumeAnnual $ VolumeABC analysisABC analysis
Demand TypeDemand TypeIndependentIndependent
DependentDependent
TypesTypesCycleCycle
PipelinePipelineSafety StockSafety StockAnticipationAnticipation
Other:Other:Maintenance/RepairMaintenance/RepairOperating SuppliesOperating Supplies
Inventory Classification of an Automobile Firm
Engine Plant Assembly Plant Dealership
Process Inputs Inventory In-Process Inventory Outputs Inventory
Engine Plant Castings Unfinished engines Finished engines
Assembly plant Finished engines, chassis, etc
Unfinished automobile Automobile
Dealership (sales) Automobile Automobile -
Autombile firm
Inventory Benefits• Economies of scale
1. Procuring inputs involves a fixed order cost – as a fraction of total cost, this cost is independent of order size.
2. In producing outputs, starting process may involve a fixed setup cost – the time and materials required to set up a process. (e.g. Clean equipment and change tools)
3. The order or production in response to the economies of scale effect is referred as a batch.
4. Depending on the type of activity being performed: production batch (lot); transfer batch; procurement batch (order).
5. Cycle inventory is the average inventory arising due to a batch activity.
Inventory Benefits• Production and Capacity Smoothing. When demand
fluctuates seasonally, it is more economical to maintain a constant processing rate and build inventories in periods of low demand and deplete them when demand is high (level-production strategy).
• Stockout Protection. Inventories maintained to insulate the process unexpected supply disruptions or surges in demand are called safety inventory or safety stock.
• Price Speculation.
Inventory Costs Inventory holding cost has two components :1. Physical holding cost, refers to the cost of storing inventory.
(e.g. Insurance, security, warehouse rental, lighting, and heating/cooling, etc). This cost is usually expressed as a fraction h of the variable cost C, thus physical holding cost = hC.
2. Opportunity cost, refers to the forgone return of the funds invested in inventory which could have been invested in alternate projects. Expressed as rC, where r is the firm rate of return and C is the variable cost.
Then,Total unit inventory holding cost (H) = (h + r) C
Inventory Cost,..example• Centura Health is a nine-hospital integrated delivery network based in
Denver, US. Presently, each hospital orders its own supplies and manages the inventory.
• A common item used is a sterile Intravenous (IV) Starter Kit.• The weekly demand for this kit is 600 units (weekly R), which a unit cost
of $3.• Centura has estimated that the physical holding cost (operating and
storage cost) of one unit medical supply is about 5% per year (h).• The hospital network’s annual cost of capital is 25% (or $0.25 = r).• Each hospital incurs a fixed order cost of $130 whenever places an order.• The supplier takes one week to deliver the order. • Presently, each hospital places 6000 units per order. • Centura has recently been concerned about the level of inventories held
of the hospitals and is exploring strategies to reduce them.
Inventory Cost
• Consider Centura Health case, the annual physical holding cost
H = (h + r) C = (0.05 + 0.25) 3 = $0.90• Then, the total inventory holding cost per unit
of time is H x I.
Inventory Dynamics of Batch Purchasing• The rest of this lesson is focused on the effect of economies
of scale.• For an instance, an important managerial question of Centura
Health:1. How much to purchase at a time?2. When to purchase a new batch of IV Starter Kits?
• Consider following inventory dynamics of process view of Centura Health
Order fullfilment(in-process inventory)
Input(IV starter kits)
Inputs inventory
Output(orders)
Inventory Dynamics of Batch Purchasing
• Recall case of Centura Health, it processes a demand of 600 units of the IV starter kit each week and places and order of 6000 kits at a time.
• The hospital must then be ordering once every 10 weeks.• Average IV starter kit inventory will be Icycle = 6000/2 =
3000 units, and a typical kit spend and average of five week in storage.
• Consider a cost effective to order (or produce) in batches, such as a case ATM, training, shuttle bus service, trash collection, etc.
Economies of Scale and Optimal Cycle Inventory
• Two causes of scale economies:1. Economies arising from a fixed-cost component
of costs in either procurement (e.g. order cost), production (e.g. setup cost), or transportation.
2. Economies arising from price discount offered by suppliers.
Economies of Scale and Optimal Cycle Inventory
Fixed Cost of Procurement: Economic Order Quantity• Process manager can control inflow into the buffer.• The total annual fixed order cost = S X R/Q • Total holding cost per year : H x Icycle = H x (Q/2)
• Total annual cost of material procured = unit cost x ouflow rate = C x R• Thus the total annual cost, TC, is given by :
• Recall Centura Health case, fixed cost per order of IV starter kit = $130. The unit cost C = $3, and weekly outflow rate of 600 or equal to an annual outflow rate = 31,200 per year (assuming 52 weeks).
RxCQxH
Q
RxSTC
2
Economies of Scale and Optimal Cycle Inventory
Fixed Cost of Procurement: Economic Order Quantity• As Centura holding cost per year H = $0.90, and Q = 6000 units in
each order, the component of the total annual cost:Total annual fixed order cost = S x R/Q = 130 x 31,200/6000 = $676Total annual holding cost = H x (Q/2)
= 0.90 x 3000 = $2700 Total annual cost of materials = C x R = 3 x 31,200 = $93,600 Thus, total annual cost
= $96,976 RxCQxH
Q
RxSTC
2
Ip
0 tz 2tz
Q QQ
Ip + Q
I(t)
t
-R
Economies of Scale and Optimal Cycle Inventory
Batch Size (Q)
Number of Orders (R/Q)
Annual Order Cost (S x R/Q)
Average Cycle
Inventory (Q/2)
Annual Holding
Cost (H x Q/2)
Annual Procurement Cost (C x R)
Total Annual Cost (TC)
500100015002000250030003500400045005000550060006500
62.4031.2020.8015.6012.4810.40
8.917.806.936.245.675.204.80
8,112.004,056.002,704.002,028.001,622.001,352.001,158.861,014.00
901.33811.20737.45676.00624.00
250500750
1000125015001750200022502500275030003250
225.00450.00675.00900.00
1,125.001,350.001,575.001,800.002,025.002,250.002,475.002,700.002,925.00
93,60093,60093,60093,60093,60093,60093,60093,60093,60093,60093,60093,60093,600
101,937.0098,106.0096,979.0096,528.0096,347.4096,302.0096,333.8696,414.0096,526.3396,661.2096,812.4596,979.0097,149.00
Order Q = 3000 gives the total minimum cost
TC*
Fixed order cost
Total cost
Costs
Variable (material) cost
Inventory holding cost
Q* = EOQ
Economies of Scale and Optimal Cycle Inventory
Fixed Cost of Procurement: Economic Order Quantity• Based on the above graph, The economic order quantity (EOQ) is the
optimal order quantity that minimizes total fixed and variable cost of a batch order (Q*).
• Based on EOQ: Total annual fixed costs per order = total annual holding costs, thus S x R/Q* = H x (Q*/2), and the minimum in actual total cost, TC* = 2 S R H + CR
• Using example of Centura Health hospitals network:
H
SRQ
2
yearper cost holdingUnit
rate outflow annualorder x per cost fixed x 2 sizeorder Optimal
*
002,390.0$
200,31130$22* xx
H
SRQ
Economies of Scale and Optimal Cycle Inventory
Fixed Order Cost Reduction• The optimal order size increase if the fixed order cost increases.• Fixed cost in procurement usually include administrative costs of creating a
purchase order, activities or receiving the order, so on. • Technology can be used significantly to reduce such costs, for example Electronic
Data Interchange (EDI) success story of Wal Mart.
Economies of Scale and Optimal Cycle Inventory
Inventory versus Sales Growth• Te EOQ formula is relevant to proof that a doubling of a company’s annual sales does not require a doubling of invetory cycle.
Centralization and Economies of Scale• The idea of inventory centralization (logistics in practices) ireferred to the fact that the optimal batch Q* is proportional to the
square root of the outflow rate R.• Consider Centura Health case, it could centralize purchasing of all supplies and perhaps store these in a central warehouse.
Assuming that the cost parameters unchanged, it could expect that for total outflow rate that is nine hospitals, the average inventory would be only three times (equal to 9)
Economies of Scale and Optimal Cycle Inventory
Centralization and Economies of Scale• Consider Centura Health case, S = $130; and H = $0.90, weekly outflow rate (R)= 600 for each hospital. The EOQ (Q*) = 3,002 units;
Icycle = 1,502 units. Total annual order and holding cost = $2,702.
• If 9 hospital assummed to be identical: The total cycle inventory = 9 x 1,501 = 13,509 units The total annual and holding costs = 9 x $2,702 = $24,318
Annual outflow rate of 9 hospitals = 9 x 31,200/year = 280,800 units/year Here, the new EOQ =
The inventory cycle = 9,006/2 = 4,503; with the total annual order and
holding costs = which is 67% lower than for the decentralized operation.
006,990.0$
800,280130$2
xx
yearxxx /106,8$90.0800,2801302
Effect of Lead Times on Ordering Decision
• Lead time (L) is the time lag between the arrival of the replenishment and the time the order was placed.
• Reorder point (ROP) is the availble inventory at the time of placing an order.
ROP = L x R • Ex., recall Centura Health case, the replenishment
lead time for ordering IV starter kits is L = 1 week. Then ROP = L x R = 1 week x 600 units/week = 600.
Effect of Lead Times on Ordering Decision
Ordering Decisions and The Reorder Point, case L < Q/R
EOQ without the instantaneous receipt assumption
• This model is applicable when inventory continuously flows or builds up over a period of time after an order has been placed or when units are produced and sold simultaneously. (called production run model)
Inventory level
Maximum inventory
t Time
Part of inventory cycle duringwhich production is taking place
There is no production during this part of the inventory cycle
Annual cost for production run model
• Q = number of pieces per order, or production run• Cs = setup cost• Ch = holding cost per unit per year• p = daily production rate• R = annual outflow (annual demand rate)• d = daily demand rate• t = length of production run in days• Total produced = Q = pt or t =Q/p• The maximum inventory level = pt – rt = Q(1-r/p)• Average inventory = Q/2(1-r/p)• Annual holding cost = Q/2(1-r/p)Ch
• Annual setup cost = (R/Q)Cs
• The optimal production quantity is
pd
C
RCQ
h
s
1
2*
Single-item static model with price breaks
Quantity Discount Model• The total cost =
material cost + ordering cost + carrying costTotal cost = DC + (D/Q)Co + (D/Q)Ch
where D = annual demand in unitsCo = ordering cost of each order
C = cost per unitCh = holding or carrying cost per unit per yearCh = hC (h = percentage of the unit cost C)
• For each discount price ( C ), EOQ =
• If EOQ < minimum for discount, adjust the quantity to Q = minimum for discount.• For each EOQ or adjusted Q, total cost = DC + (D/Q)Co + (D/Q)Ch • Choose the lowest cost quantity.
Order quantity
Totalcost $
1000 2000
TC curve forDiscount 1 TC curve for
Discount 3
TC curve forDiscount 2
EOQ forDiscount 2
hC
DCo2
Price Discounts: Forward Buying
• For a trade promotion, it is often that a supplier give a short-term discount policy.
• The supplier offers incentives in the form of one-time opportunities to sell materials at reduced unit costs or perhaps notifies the buyer of an upcoming price increase and offers one last chance to order at the lower price.
• Consider that instead of a normal price of $C per unit, a supplier offers a one-time discount of $d per unit. Then for a certain period the price is $(C-d)/unit
• After which the regular price will resume, the buyer must decide the quantity Qf to order at the discounted price.
• The optimal forward-buying quantity is computed as follows:
*
)(Q
dC
C
dCHx
RdQ f
…• Example: Kmart-retail store to order toothpaste Colgate
S = order cost = $100 R = unit demand per year = 120,000
C = unit price = $3 h = unit annual holding cost = 0.2 d = discounted amount of price
(ex : for one time discount 5%, at regular price C = $3 / unit, d = 0.05x$3 = $0.15)
H = unit annual holding cost = $0.60Q* = regular optimum order quantity
325,660,0$
000,120100$22
xx
H
SR
236,3815.000.3
325,63
)15.000.3(2.0
15.0000,120
x
x
xQ f
SAFETY INVENTORY and SERVICE LEVEL
Service Level Measures:• Cycle service level, refers to either the
probability that there will be no stockout within an order cycle, or, equivalently, the proportion of order cycles without a stockout, where an order cycle is the time between two consecutive replenishment orders.
• Fill rate, is the fraction of total demand satisfied from inventory on hand.
SAFETY INVENTORY and SERVICE LEVEL
Service Level Measures:• For example: a process manager observes that
within 100 order cycles, stockouts occurs in 20. Cycle service level is then 80/100 = 80%
• Now suppose that total demand during 100 cycles was 15,000 units and the total number of units short in the 20 cycles with stockouts was 1,500 units. The fill rate, therefore, 13,500/15,000 = 0.9 or 90%.
SAFETY INVENTORY and SERVICE LEVEL
Continuous Review, Reorder Point System• Lead Time Demand (LTD), is the total flow-unit
requirement during replenishment lead time (L). • In general, if either flow rate R or lead time L is
uncertain, the LTD will also be uncertain. • To reduce stockout risk, we may decide to order
earlier by setting the reorder point larger than LTD.• The excess amount is safety inventory (Isafety)
Isafety = ROP – LTD or ROP = LTD + Isafety
SAFETY INVENTORY and SERVICE LEVEL
Service Level Given Safety Inventory• Service level (SL) is the probability that the
actual LTD will not exceed ROP, or SL = Prob(LTD ROP)• To compute this probability, it is necessary to
know the probability distribution of the random variable LTD (assumed normally distributed) with mean LTD and standard deviation LTD.
SAFETY INVENTORY and SERVICE LEVEL
Service Level Given Safety Inventory
SAFETY INVENTORY and SERVICE LEVEL
• Correspoding to the z value: SL = Prob(LTD ROP) = Prob (Z ≤ z)
Isafety = z x LTD or
SL = NORMDIST (ROP, LTD, LTD ,True)
• Example: GE Lightings has the average LTD = 20,000 units with LTD = 5,000. The warehouse currently orders a 14-day supply of lamps at ROP = 24,000 units. Determine SL?
Isafety = ROP – LTD = 4,000
SL = Prob (Z ≤ 0.8) = 0.7881 or SL = NORMDIST(24,000,20,000,5,000,True) = 0.7881
SAFETY INVENTORY and SERVICE LEVEL
LTD
safetyIz
8.0000,5
000,4
LTD
safetyIz
• To summarize, in 78.81% of the order cycles, the warehouse will not have a stockout.
• Recall that Q = 28,000 units, thus:Icycle = 28,000/2 = 14,000
Isafety = 4,000 Inventory total = 18,000 units
H = $20 x 18,000 = $360,000/yearT = I/R = 18,000/2,000 = 9 days
SAFETY INVENTORY and SERVICE LEVEL
Safety Inventory Given Service Level • Service level (SL) is known and need to determine safety inventory and
ROP. SL = Prob (Z ≤ z) or z = NORMSINV (SL)Isafety = z x LTD and ROP = LTD + Isafety
ROP = NORMINV (SL, LTD, LTD )
• Example: Reverse case of GE Lightings, with know SL = 78.81, obtains Isafety = 4,000 and ROP = 24,000.
SAFETY INVENTORY and SERVICE LEVEL
Sevice Level (SL) Z ValueSafety Inventory
(Isafety)Reorder Point
(ROP)
85%90%95%99%
1.041.281.652.33
5,2006,4068,246
11,686
25,20026,40628,24631,686
Safety Inventory Given Service Level
SAFETY INVENTORY and SERVICE LEVEL
The effect of Everyday Low Pricing
• Order incerases designed to take an advantage of short-term discount.
• A policy of everyday low pricing (EDLP) – a pricing policy whereby retailers charge constant, with no temporary discount.
• The same argument can be used upstream in the supply chain.
Levers for Managing Inventory• Theoretical inventory: reducing critical activity times; eliminating non-
value-adding activities; moving work from critical to non-critical activities; redesigning the process to replace sequential with parallel processing.
• Cycle inventory: reduce fixed order (setup) cost by simplifying the order process with the use of information technology; negotiating everyday low prices with suppliers.
• Seasonal inventory: using pricing and incentive tactics to promote stable demand patterns.
• Safety inventory: ensuring reliable suppliers and stable demand patterns (discussed further in next session).
• Speculative inventory: reduce the total cost of purchasing materials; increases profits by taking advantage of uncertain fluctuations in a product’s price.