INVENTORY PLANNING &

CONTROL

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 Systems-A set of policies and controls that monitors levels of inventory and determines what levels should be maintained and how large orders should be placed

INVENTORY PLANNING FOR INDEPENDENT DEMAND ITEMSIn a manufacturing organization, finished goods and spare parts typically belong to the category of independent demand items.Planning for a dependent demand item is done to meet manufacturing requirements but incase of independent demand item,it is done to meet customer requirements.

CONTINUOUS DEMANDIndependent demand items are always in continuous demandConsider the sale of consumer appliances of manufactures such as Videocon and LG. The demand for 32”LCD color television panel in a particular city will be continuous. When there is a continuous demand for an item, constant availability of items and periodic replacement of stock are important elements of the planning process.

UNCERTAINITY OF DEMANDThere is an element of considerable uncertainty of demand in the case of independent demand items. On the other hand, in the case of dependent demand items, the demand is always derived and hence known with certainty.

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TYPES OF INVENTORY

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Types of inventory

Decoupling inventory

Pipeline inventory

Safety stock

Seasonal

inventory

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SEASONAL INVENTORY Organisations carry out to meet the fluctuations in demand arising out of seasonality.

During the festivals the demand for consumer durable may be high due to increase in disposable income from consumers

To meet such this inventory is prepared Example During lunch hours hotels and fast food chains to handle increase and decrease demand inventory helps them for short term capacity.

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DECOUPLING INVENTORY Manufacturing normally involves many steps and many workstations, raw materials pass through many process to meet the finished goods so the planning so such process is important and it becomes complex as well

To solve this decoupling inventory can be used

Decoupling inventory

Stage 1

Stage 2

Stage 3

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CYCLIC INVENTORY Its customary for organisations to order inventory in repeated cycles and consume them over time.

Example Hospital uses disposable syringes of 10k, if average consumption is 500 then it takes 20 days delicate the order, and another day for 10k and so on it will continue.

time

quantity

The average cyclic inventory=

Q+0 = q2 2

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PIPE LINE INVENTORY Organisations carry in long run due to no zero lead time for order. Due to distance between the supplier and the host so the time between the order placement and the order delivery is known as pipeline inventory

Example Suppose it takes 3 days for supply of disposable sriynges, then hospital must place order at end of 7th day to replenish the order of 10000 that means the order will be placed when inventory reaches 1500(3days at the rate 500 per day)

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SAFETY STOCKSafety Stock:If the actual usage increases or the delivery of the inventory is delayed, firm can face a problem of stock-out. So firm may maintain the safety stock.In this case Reorder point is calculated asReorder point=Lead*Average usage + safety stock.

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CARYING COSTSl.no Items of expenditure{annual}

Amount

1 Stationary 750002 Insurance premium 3750003 Establishment expenses and

overheads275000

4 Salary of stores personnel 1,100,000Total expenditure 1,750,000Average value of the inventory in stores

5.00%

A Cost of warehousing 5.00%B Cost of capital 15.00%C Obsolescence(estimated

historically)2.00%

D Damages,spoliers,etc 1.00%CARYING COST?

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COST OF ORDERINGSL.NO ITEMS OF

EXPENDITUREAMOUNT

1 Stationary 80,0002 Telephone 40,0003 Other communication

expenses60,000

4 Salary of purchase department personnel

1,100,000

5 Inwards goods inspection section expenses

350,000

6 Other expenses and overheads

200,000

TOTAL EXPENDITURE 1,830,000no of purchase orders generated

600.00

average cost of ordering 3,050

WHAT IS ABC ANALYSIS? ABC analysis is an inventory categorization method which consists in dividing items into three categories (A, B, C): A being the most valuable items, C being the least valuable ones.

This method aims to draw managers’ attention on the critical few (A-items) not on the trivial many (C-items).

ABC analysis also called as : HML (High Moderate Low) Analysis Pareto Analysis Selective Stock Control

STEPS Find out the unit cost and and the usage of each material over a given period.

Multiply the unit cost by the estimated annual usage to obtain the net value

(Annual demand) x (item cost per unit) Find % of each material/item in total inventory . All items are then ranked according to their % rupee value as either A, B, or C as per rule.

A-B-C APPROACHA item

B item

C item

High

Moderate

Low

Low High Moderate

Annu

al ru

pee

valu

e of

item

s

Percentage of items

PROBLEM 1 From the following information classify the inventory items into A,B and C categories-Item Quantit

yPrice per unit

Items Quantity

Price per unit

A 200 201 G 400 25

B 600 83 H 280 400C 250 250 I 400 55D 470 50 J 300 40E 250 64 K 250 30F 300 85 L 1000 15

Material Quantity Price per unit

Inventory Value(Qty*rat

e)

% in value

Category

A 200 201 100200 21.97% AB 600 83 49800 10.92% AC 250 250 62500 13.71% AD 470 50 23500 5.15% BE 250 64 16000 3.51% CF 300 85 25500 5.59% BG 400 25 10000 2.19% CH 280 400 112000 24.56% AI 400 55 22000 4.82% BJ 300 40 12000 2.63% CK 250 30 7500 1.64% CL 1000 15 15000 3.29% C

TOTAL 456000 100%

SOLUTION:

PROBLEM 2Item Annual demand Unit cost (Rs.)

1 250 3302 100 703 190 5004 150 1005 390 7006 100 9157 20 2108 100 40009 800 10

10 900 211 50 20012 40 300

Items Annual demand(qty)

Price per unit

(rate)

Inventory Value(qty * rate)

% in value

Classification

1 250 330 82500 8.25% B2 100 70 7000 0.7% C3 190 500 95000 9.5% B4 150 100 15000 1.5% C5 390 700 273000 27.3% A6 100 915 91500 9.15% B7 20 210 4200 0.42% C8 100 4000 400000 40% A9 800 10 8000 0.8% C10 900 2 1800 0.18% C11 50 200 10000 1% C12 40 300 12000 1.2% CTOTAL 1000000 100%

Solution:

PROBLEM 3 Classify Inventory Items into ABC Category:Items Unit Cost Annual Demand

1 5 480002 11 20003 15 3004 8 8005 7 48006 16 12007 20 180008 4 3009 9 500010 12 500

Items Unit Cost Annual Demand

Inventory Value

(qty*rate)

% in Value

Classification

1 5 48000 240,000 32.5% A2 11 2000 22,000 3% B3 15 300 4,500 0.6% C4 8 800 6,400 0.9% C5 7 4800 33,600 4.6% B6 16 1200 19,200 2.6% B7 20 18000 360,000 48.8% A8 4 300 1,200 0.2% C9 9 5000 45,000 6.1% B10 12 500 6,000 0.8% C

TOTAL 737,900 100%

Solution :

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ECONOMIC ORDER QUANTITY It is the order size that minimizes the total annual cost. The Question to how much to order is determind by Economic order quantity.

It identifies the optimal order quantity by minimizing the sum of certain annual costs that vary with order size.

Three order size models are:1.The basic economic order quantity model2.The economic production quantity model3.The quantity discount model

ASSUMPTIONS OF EOQ MODEL Only one product is involved Annual demand requirements known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts

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Order Quantity (Q)

The Total-Cost Curve is U-Shaped

Ordering Costs

QO

Ann

ual C

ost

(optimal order quantity)

TC QH DQS

2

THE BASIC ECONOMIC ORDER QUANTITY MODEL Annual Carrying cost=(Q/2)H

Q =order quantity per unit H=Holding (carrying)cost per unit.

Annual Ordering cost=(D/Q)SD=Annual demandS=Ordering cost

D = Annual demand (units) C = Cost per unit ($) Q = Order quantity (units) S = Cost per order ($) I = Holding cost (%) H = Holding cost ($) = I x C

Number of Orders = D / Q

Ordering costs = S x (D / Q)

Average inventory units = Q / 2 $ = (Q / 2) x C

Cost to carry average inventory = (Q / 2) x I x C = (Q /2) x H

Total cost = (Q/2) x I x C + S x (D/Q) inv carry cost order cost

Take the 1st derivative:

d(TC)/d(Q) = (I x C) / 2 - (D x S) / Q²

To optimize: set d(TC)/d(Q) = 0

DS/ Q² = IC / 2

Q²/DS = 2 / IC

Q²= (DS x 2 )/ IC

Q = sqrt (2DS / IC)

Deriving the EOQ

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Total Cost=(Q/2)H+(D/Q)S Economic Order Quantity(Q0)= √(2DS/H) Length of the order cycle=Q/D; Number of orders=(D/Q)

Example 1:. Piddling Manufacturing assembles security monitors .It purchases

3600 black and white cathode ray tubes a year at $65 each.Ordering costs are $31,

and annual carrying costs are 20% of the purchase price.Compute the optimal

quantity and the total annual cost of ordering and carrying the inventory?

Here D=3600 cathode ray tubes per year S=$31 H= 0.20*65=$13

A)Qo=√(2DS/H) √(2(3600)(31)/13=131 cathode ray tubes

B)TC=carrying cost+ ordering cost(Qo/2)H+(D/Qo)S=(131/2)13+(3600/131)31=$1704

Example:2A local distributor for a national tire company expects to sell approximately 9,600 steel-belted radial tires of a certain size and tread design next year .Annual carrying cost is $16 per tier,and ordering cost is $75.The distributor operates 288 days a year.A)What is EOQ?B)How many times per year does the store order?C)What is length of an order cycle?D)What is total annual cost if the EOQ quantity is ordered?

D=9600 tires per year H= $16 per unit per year S= $75A)Q0= √(2DS/H)=√(2(9600)75)/16=300B)Number of orders pre year: (D/Q)

=9600/300=32c)Length of order cycle=(Q/D)=300tires/9600 tires/yr

1/32 of a year 1/32*288=9 days

D)TC=CC+OC=(Q/2)H+(D/Q)S=(300/2)16+(9600/300)75=2400+2400= $ 4800

ECONOMIC PRODUCTION QUANTITY (EPQ) Production done in batches or lots Capacity to produce a part exceeds the part’s usage or demand rate Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

Economic run size:

P=Production or delivary rateu=Usage RateS=Setup cost

Q DSH

pp u

02

ECONOMIC PRODUCTION QUANTITY ASSUMPTIONS Only one item is involved Annual demand is known Usage rate is constant Usage occurs continually Production rate is constant Lead time does not vary No quantity discounts

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Cycle time is time between orders or between the beginnings of the run) Cycle time= (Qo/u) Run time is a function of run(lot size) and the production rate: Run time=(Qo/p) Max inventory levels (Imax)=(Qo/p)(p-u) Avg inventory level(Iavg)=Imax/2

Example:A toy manufacturer uses 48000 rubber wheels per year for its popular dump truck series.The firm makes its own wheels,which it can produce at a rate of 800 per day .The toy trucks are assembled uniformly over the entire year.Carrying cost is $1 per wheel a year.Setup cost for a production run of wheels is $45.The firm operates 240 days per year.Determine the A)optimal run size B)Minimum total annual cost for carrying and setup C)Cycle time for carrying and setup D)run time

D=48000 wheels per year S=$45 H=$1 per wheel per year P=800 wheels per day U=48000 per 240 days A)

√(2*48000*45)/1* √(800/(800-200)=2400 wheels

Q DSH

pp u

02

B)TC min=CC+Setup cost=(Imax/2)H+(D/Qo)SImax=(Qo/p)(p-u)=1,800 wheels

TC min=1800/2*1+48000/2400*45=$1800C)Cycle time=(Qo/u)

2400 wheels/200 wheels per day=12 daysD)Run time=(Qo/p)=2400wheels/800 wheels per day=3 days

Example2:A firm in Sialkot produces 250,000 each world class footballs for both domestic and international markets . It can make footballs at a rate of 2000 per day. The footballs are manufactured uniformly over the whole year. Carrying cost is Rs. 100 per football and Setup cost for a production run is Rs.2500. The manufacturing unit operates for 250 days per yearDetermine the 1. Optimal Run Size. 2. Minimum total annual cost for carrying and setup cost. 3. Cycle time for the Optimal Run Size. 4. Run time by using the formula

 A)Optimal Run Size.(Qo)== √ (2 X 250,000 X 2500/100 )*  √(2 000 /2000-1000 )) = 2500( sq.root2X2)=5000 footballs.B) Minimum total annual cost for carrying and setup cost.

= Carrying Cost + Set up Cost=( I max/2)H+ ( D/Q0)S

Where I max= (Q0/p )(p-u)=5000/2000(1000) =2500 footballs

Now TC= 2500/2 X 100 + (250,000/5000 )(2500)=1250 X 100 + 125,000=125,000+ 125,000= Rs. 250,000.

C)Cycle time for the Optimal Run Size.Q0/U=5000/1000= 5 days

D) Run timeQ0/p=5000/2000= 2.5 days

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