Presentation 6 Inventory Management Sharda

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INVENTORY MANAGEMENT

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Lead TimeLead Time(small introduction)(small introduction)

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Estimated time from release of an order requesting the manufacture or procurement of an item until its delivery to the customer

Lead Time [LT]

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SUPPLY CHAIN LEAD TIME AND ITS COMPONENTS

Commercial &Planning LT

Materials LΤ’s

ProductionWarehousing& Distribution

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SUPPLY CHAIN LEAD TIME & ITS COMPONENTS

The longer the process the less the reaction in unforeseen changes

LT(days)

• Salesman• Supervisor• Head of Sales• DRP• Order

• Production abroad• Transportation to GR• Procurement of packing materials

• Warehousing• W/H Forwarder• Forwarder Customer

1 - 3 20 - 60 7 1 - 2 =30-70

• Production

Commercial &Planning LT

Materials LΤ’s


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The cycle “CASH-TO-CASH”

How long does it take to convert an order into cash?

CollectionCommercial &Planning LT

Materials LΤ’s


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Inventory managementInventory management

(small introduction, use material from (small introduction, use material from

operations management)operations management)

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Factory Wholesaler Distributor Retailer Customer

Replenishment order

Replenishment order

Replenishment order

Customer order

Production Delay

WholesalerInventory

Shipping Delay

Shipping Delay

DistributorInventory

RetailerInventory

Item Withdrawn

Inventory Management

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Definitions

• Inventory-A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state.

• Inventory System- A set of policies and controls that monitors levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

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Expensive Stuff

• The average carrying cost of inventory across all mfg.. in the U.S. is 30-35% of its value.

• What does that mean?

• Savings from reduced inventory result in increased profit.

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Two Forms of Demand DependentDependent

Demand for items used to produce final products Demand for items used to produce final products Tires stored at a Goodyear plant are an example

of a dependent demand item

A

B(4) C(2)

D(2) E(1) D(3) F(2)

IndependentIndependent Demand for items Demand for items

used by external used by external customerscustomers

Cars, appliances, computers, and houses are examples of independent demand inventory

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Independent Demand

• Demand from outside the organization

• Unpredictable usually forecasted

Demand for tables . . .

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Dependent Demand

• Tied to the production of another item

• Relevant mostly to manufacturers

Once we decide how many tables we want tomake, how many legs do we need?

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Arguments for Carrying Inventory

Balancing supply and demandBalancing supply and demand

Protection from uncertaintiesProtection from uncertainties

Buffer interfaceBuffer interface

Realizes economies of scale through reduction of fixed costs Realizes economies of scale through reduction of fixed costs

Allows quick response to customer demands

Allows quick response to customer demands

Keeps production line running Keeps production line running

Supports long production runsSupports long production runs

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Disadvantages for Carrying Inventory

May become obsoleteMay become obsolete

Can be damaged or deteriorateCan be damaged or deteriorate

May be hazardous to storeMay be hazardous to store

May take up excessive W/H spaceMay take up excessive W/H space

Could be totally lost or hiddenCould be totally lost or hidden

Opportunity CostOpportunity Cost

Could be duplicated at different W/HCould be duplicated at different W/H

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Financial Impact of Inventory [3]1. Inventory is often a company’s largest asset

2. Inventories can account for 20% of total assets

3. Inventory costs may run up to 40- 50% of the value of a product and ~ 40% of total integrated logistics costs


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Definitions

• Inventory accuracy refers to how well the inventory records agree with physical count

• Cycle Counting is a physical inventory-taking technique in which inventory is counted on a frequent basis rather than once or twice a year


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In our example of ABC classifications we used the monetary value of the annual usage of each item as a measure of inventory usage. Monetary value can also be used to measure the absolute level of inventory at any point in time. This would involve taking the number of each item in stock, multiplying it by its value (usually the cost of purchasing the item) and summing the value of all the individual items stored. This is a useful measure of the investment that an operation has in its inventories but gives no indication of how large that investment is relative to the total throughput of the operation. To do this we must compare the total number of items in stock against their rate of usage. There are two ways of doing this. The first is to calculate the amount of time the inventory would last, subject to normal demand, if it were not replenished. This is sometimes called the number of weeks’ (or days’, months’, years’ etc.) cover of the stock. The second method is to calculate how often the stock is used up in a period, usually one year. This is called the stock turn or turnover of stock and is the reciprocal of the stock-cover figure mentioned earlier.

Formulas for Measuring Inventory

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Time

QO

n-ha

nd I

nven

tory

Time

Q

On-

hand

Inv

ento

ryMany orders, low inventory level

Few orders, high inventory level

While carrying costs increase,

ordering costs fall and vice versa

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OBJECTIVES: To determine the best ordering policy, i.e.

1. To decide how much, and

2. when to order

Economic Order Quantity [EOQ] model

•One of the oldest and most commonly used in inventory control

•Based on a number of assumptions

HOW MUCH?


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EOQ Model Cost Curves

Slope = 0 Total Costcurve

Ordering Cost = CoD/Q

Order Quantity, Q

Annualcost ($)

Minimumtotal cost

Optimal order Q*

(EOQ)

Carrying Cost = CcQ/2

Total Costs = Carrying Cost + Ordering CostCt = CcQ/2 + CoD/Q

EOQ, Q = 2 D Co

Cc

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Inventory managementInventory management

(real thing ….)(real thing ….)

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Production Quantity ModelProduction lot-size Model

Gradual replacement (or usage) modelEconomic batch quantity (EBQ)

EOQ model with noninstantaneous receipt

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EOQ Assumptions

1. Continuous and known demand rate

2. Lead time/replenishment cycle is known and constant

3. Price to purchase is independent of the amount needed

4. Transportation costs remain constant

5. No stock outs (or shortages) are permitted

6. No inventory is in transit

7. The order quantity is received all at once


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Production Quantity Model

• An inventory system in which an order is received gradually, as inventory is simultaneously being depleted, i.e. assumption that Q is received all at once is relaxed

• p - daily rate at which an order is received over

time, i.e. production rate

• d - daily rate at which inventory is demanded, usage

rate

• P>= d, never the opposite so that …no shortages

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Assumptions1. Only one item is involved

2. Annual demand is known

3. The usage rate is constant

4. Usage occurs continually, but production occurs periodically

5. Production rate is constant

6. Lead time not vary

7. There are no quantities discounts

8. No stock outs (or shortages) are permitted


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QQ(1-(1-d/pd/p))

Inventory level,Inventory level,unitsunits

TimeTime00

Replenishment order cycleReplenishment order cycle

Begin orderBegin orderreceiptreceipt

End orderEnd orderreceiptreceipt

MaximumMaximuminventory levelinventory level


EPQ, the No. of units producedPr

oduc

tion

rate

= p

Usage rate = d

Inve

ntory

build

-up =

p-d

OrderOrderreceipt periodreceipt period Q/pQ/p

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QQ(1-(1-d/pd/p))

InventoryInventoryLevel,Level,unitsunits

(1-(1-d/pd/p))QQ22

TimeTime00

OrderOrderreceipt periodreceipt period Q/pQ/p

BeginBeginorderorder

receiptreceipt

EndEndorderorder

receiptreceipt

MaximumMaximuminventory inventory levellevel

AverageAverageinventory inventory levellevel


Slope = p - d

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pp = production rate = production rate dd = demand rate = demand rate

Maximum inventory level =Maximum inventory level = QQ - - dd

== QQ 1 - 1 -

QQpp

ddpp

Average inventory level = Average inventory level = 1 - 1 -QQ22

ddpp

TCTC = + 1 - = + 1 -ddpp

CCooDD

QQ

CCccQQ

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QQoptopt = =22CCooDD

CCcc 1 - 1 - ddpp


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Production Quantity ModelEXAMPLE 1

Assume that an outlet store has its own manufacturing facility in which it produces Supper Shag carpet. The ordering cost is $150 and the carrying cost $0.75 per yard and D=10,000 yards per year. The manufacturing facility operates the same days the store is open, i.e. 311 days and produces 150 yards of the carpet per day. Determine Qopt, total

inventory cost, the length of time to receive an order, the number of orders per year, and the maximum inventory level.

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CCcc = $0.75 per yard = $0.75 per yard CCoo = $150 = $150 DD = 10,000 yards = 10,000 yards

dd = 10,000/311 = 32.2 yards = 10,000/311 = 32.2 yards//dayday pp = 150 yards = 150 yards//dayday

QQoptopt = = = 2,256.8 yards = = = 2,256.8 yards

22CCooDD

CCcc 1 - 1 - ddpp

2(150)(10,000)2(150)(10,000)

0.75 1 - 0.75 1 - 32.232.2150150

TCTC = + 1 - = $1,329 = + 1 - = $1,329ddpp

CCooDD

QQ

CCccQQ

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Production run = = = 15.05 days per orderProduction run = = = 15.05 days per orderQQpp

2,256.82,256.8150150


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Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 yards

dp

32.2150


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EXAMPLE 2

A toy manufacturer uses 48,000 rubber wheels peryear for its popular dump truck series. The firmmakes its own wheels, which it can produce at a rateof 800 per day. The toy trucks are assembleduniformly over the entire year. Carrying cost is €1per wheel a year. Set-up cost for a production run ofwheels is €45. The firm operates 240 days peryear. Determine each of the following :(i) Optimal run size(ii) Minimum total annual cost for carrying and set-up(iii) Cycle time for optimal run size(iv) Run time


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ANSWER

D = 48,000 wheels per yearCCοο = = €45

CCcc = = €1 per wheel per yearp = 800 wheels per dayd = 48,000 wheels/240 days, or 200 wheels/day


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QQoptopt = = = 2, = = = 2,400 400 wheelswheels

22CCooDD

CCcc 1 - 1 - ddpp

2(2(4545)()(4848,000),000)

1 1 1 - 1 - 220000800800

TCTC = + 1 - = = + 1 - = € 900 + €900 = €1800€ 900 + €900 = €1800ddpp

CCooDD

QQ

CCccQQ

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Production run = = = 12 days for every run of wheelsProduction run = = = 12 days for every run of wheelsQQpp

2,2,400400800800


Cycle time = = = Cycle time = = = 3 3 days per rundays per runQQdd

2,2,400400220000

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EXAMPLE 3a

The manager of a bottle-filling plant which bottles soft drinks needs to decide how long a run of each type of drink to process. Demand for each type of drink is reasonably constant at 80,000 per year (a year has 160 production hours). The bottling lines fill at a rate of 3000 bottles per hour, but take an hour to clean and reset between different drinks. The cost of (labour and lost production capacity) of each of these changeovers has been calculated at €100 per hour. Stock-holding costs are counted at €0.1 per bottle per month.

Determine the Optimal run size, EBQ


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ANSWER

D = 80,000 per year

CCοο = = €100

CCcc = = €0.1 per bottle per month

p = 3000 bottles per hour

d = 80,000 per year = 500 per hour


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ANSWER


QQoptopt = = = 13,856 = = = 13,856 bottlesbottles

22CCooDD

CCcc 1 - 1 - ddpp

2(100)(80,000)2(100)(80,000)

0.0.1 1 1 - 1 - 55000030300000

TCTC = + 1 - = = + 1 - =ddpp

CCooDD

QQ

CCccQQ

22

Production run = = = Production run = = = QQpp

138561385630300000

Cycle time = = = Cycle time = = = QQdd

1385613856550000

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EXAMPLE 3b

The manager of a bottle-filling plant which bottles soft drinks needs to decide how long a run of each type of drink to process. Demand for each type of drink is reasonably constant at 80,000 per year (a year has 160 production hours). The bottling lines fill at a rate of 3000 bottles per hour, but take an hour to clean and reset between different drinks. The cost of (labour and lost production capacity) of each of these changeovers has been calculated at €100 per hour. Stock-holding costs are counted at €0.1 per bottle per month.

Determine the Optimal run size, EBQ

The staff who operates the lines have devised a method of reducing the changeover time from 1 hour to 30 minutes. How would that change the EBQ?


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ANSWER 3b

D = 80,000 per year

CCοο = = €50

CCcc = = €0.1 per bottle per month

p = 3000 bottles per hour

d = 80,000 per year = 500 per hour


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Quantity discounts are price reductions for large orders offered to customers to induce them to buy in large quantities.

For example, a box supplier publishes the price list shown in table for boxes of ½ Kg. Note that the price per box decreases as order quantity increases.

Quantity Discounts

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Total Costs with Purchasing Cost

Annualcarryingcost

PurchasingcostTC = +

Q2

Cc DQ

CoTC = +

+Annualorderingcost

PD +

EOQ models with constant purchase price:

Quantity Discounts

Where P = Unit price

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Adding PD doesn’t change the EOQ.

The rationale for not including unit price in the EOQ is that under the assumption of no quantity discounts, price per unit is the same for all order sizes.

Quantity Discounts

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The total-cost curve with quantity discounts is composed of a portion of the total-cost curve for each price.

Including unit prices merely raises each curve by a constant amount. However, because the unit prices are different, each curve is raised by a different amount, i.e. smaller unit prices will raise the a total-curve less than larger unit prices.

Quantity Discounts

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Quantity Discounts

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A. When carrying costs are constant, all curves have their minimum points at the same quantity.

B. When carrying costs are stated as a percentage of unit price, the minimum points do not line up.

Quantity DiscountsComparison of TC curves for constant carrying costs and carrying costs that are a percentage of unit costs

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For carrying costs that are constant, the procedure is as follows:

1. Compute the common minimum point.

2. Only one of the unit prices will have the minimum point in its feasible range since the ranges do not overlap. Identify that range.

a. If the feasible minimum point is on the lowest price range, that is the optimal order quantity.

b. If the feasible minimum point is in any other range, compute the total cost for the minimum point and for the price breaks of all lower unit costs. Compare the total costs; the quantity (minimum point or price break) that yields the lowest total cost is the optimal order quantity.

Quantity Discounts with constant carrying cost

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QQoptopt

Carrying cost Carrying cost

Ordering cost Ordering cost

Inve

ntor

y co

st (

$)In

vent

ory

cost

($)

QQ((dd1 1 ) = 100) = 100 QQ((dd2 2 ) = 200) = 200

TC TC ((dd2 2 = $6 ) = $6 )

TCTC ( (dd1 1 = $8 )= $8 )

TC TC = ($10 )= ($10 ) ORDER SIZE PRICE

0 - 99 $10

100 – 199 8 (d1)

200+ 6 (d2)

Quantity Discounts

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EXAMPLE [PCs]

Annual carrying cost is $190/pc, ordering cost = $2,500 and annual demand is estimated to be 200 PCs. Should it take the advantage of this discount or order EOQ?


ORDER SIZE PRICE

1 – 49 $1,400

50 – 89 1,100

90+ 900

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QUANTITYQUANTITY PRICEPRICE

1 - 491 - 49 $1,400$1,400

50 - 8950 - 89 1,1001,100

90+90+ 900900

CCoo = = $2,500 $2,500

CCcc = = $190 per computer $190 per computer

DD = = 200200

QQoptopt = = = 72.5 PCs = = = 72.5 PCs22CCooDD

CCcc

2(2500)(200)2(2500)(200)190190

TCTC = + + = + + P P D D = $233,784 = $233,784 CCooDD

QQoptopt

CCccQQoptopt

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For For QQ = 72.5 = 72.5

TCTC = + + = + + P P D D = $194,105= $194,105CCooDD

QQ

CCccQQ

22

For For QQ = 90 = 90

$ 1100

$ 900


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QUANTITYQUANTITY PRICEPRICE

1 - 491 - 49 $1,400$1,400

50 - 8950 - 89 1,1001,100

90+90+ 900900

TCTC = $233,784 = $233,784 For For QQ = 72.5 = 72.5

TCTC = $194,105 = $194,105For For QQ = 90 = 90


Since this total cost is lower (194,105 < 233,784), the max discount price should be taken, and 90 units should be ordered.

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Example

The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12, carrying costs are $4 per case a year, and the new price schedule indicates that orders of less than 50 cases will cost $20 per case, 50 to 79 cases will cost $18 per case, 80 to 99 cases will cost $17 per case, and larger orders will cost $16 per case. Determine the optimal order quantity and the total cost.


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D = 816 cases per year

Co = $12

Cc = $4 per case per year


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Compute the common EOQ:

The 70 cases can be bought at $18 per case because 70 falls in the range of 50 to 79 cases. The total cost to purchase 816 cases a year, at the rate of 70 cases per order, will be

TC = Carrying cost + Order cost + Purchase cost

TC = (Q/2)Cc + (D/Q0)Co + PD

TC70 = (70/2)4 + (816/70)12 + 18(816) = $14,968

TC80 = (80/2)4 + (816/80)12 + 17(816) = $14,154

TC100 = (100/2)4 + (816/100)12 + 16(816) = $13,354


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When carrying costs are expressed as a percentage of price, determine the best purchase quantity with the following procedure:

1. Beginning with the lowest unit price, compute the minimum points for each price range until you find a feasible minimum point (i.e., until a minimum point falls in the quantity range for its price).

2. If the minimum point for the lowest unit price is feasible, it is the optimal order quantity. If the minimum point is not feasible in the lowest price range, compare the total cost at the price break for all lower prices with the total cost of the feasible minimum point. The quantity that yields the lowest total cost is the optimum.

Quantity Discounts when carrying cost are % of price

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Homework - ExampleSurge Electric uses 4,000 toggle switches a year.

Switches are priced as follows: 1 to 499, 90 cents each; 500 to 999, 85 cents each; and 1,000 or more, 80 cents each. It costs approximately $30 to prepare an order and receive it, and carrying costs are 40 percent of purchase price per unit on an annual basis. Determine the optimal order quantity and the total annual cost.


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D = 4,000 switches per year

S = $30

H = .40P


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This is feasible; it falls in the $0.85 per switch range of 500 to 999.

Now compute the total cost for 840, and compare it to the total cost of the minimum quantity necessary to obtain a price of $0.80 per switch.

Thus, the minimum-cost order size is 1,000 switches.


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Company ABC has about 5000 items in its inventory. After hiring a bright SC manager, the firm determined that it has 500 A items, 1750 B items and 2750 C items.Company policy is to count all A items every month (every 20 working days), all B items every quarter (every 60 working days), and C items every 6 months (every 120 working days). How many items should be counted each day?

Company ABC has about 5000 items in its inventory. After hiring a bright SC manager, the firm determined that it has 500 A items, 1750 B items and 2750 C items.Company policy is to count all A items every month (every 20 working days), all B items every quarter (every 60 working days), and C items every 6 months (every 120 working days). How many items should be counted each day?

Cycle Counting

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Cycle Counting

ITEM

CLASS

QUANTITY CYCLE COUNTING

POLICY

NO. OF ITEMS COUNTED PER

DAY

A 500 Each month (20 working days

500/20 = 25/day

B 1750 Each quarter (60 working days

1750/60 = 29/day

C 2750 Every month (120 working days

52750/120 = 23/day

5000 77/day

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Quantity Discounts

Price per unit decreases as order quantity increasesPrice per unit decreases as order quantity increases

TCTC = + + = + + PDPDCCooDD

QQ

CCccQQ

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wherewhere

PP = per unit price of the item = per unit price of the itemDD = annual demand = annual demand

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Reorder Point

Level of inventory at which a new order Level of inventory at which a new order is placed is placed

RR = = dLdL

wherewhere

dd = demand rate per period = demand rate per periodLL = lead time = lead time

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Reorder Point: Example

Demand = 10,000 yards/yearDemand = 10,000 yards/year

Store open 311 days/yearStore open 311 days/year

Daily demand = 10,000 / 311 = 32.154 Daily demand = 10,000 / 311 = 32.154 yards/dayyards/day

Lead time = L = 10 daysLead time = L = 10 days

R = dL = (32.154)(10) = 321.54 yardsR = dL = (32.154)(10) = 321.54 yards

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CASE STUDY: The UK National Blood Service

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CASE STUDYManor Bakeries

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CASE STUDY: Trans – European Pastics

Presentation 6 Inventory Management Sharda

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