05 Inventory Management

UNIT - 3

Syllabus

1.

Inventory Management: Definition of

Inventory, Purposes of Inventory, Inventory

Costs

2.

Independent versus Dependent Demand

3.

Inventory Systems, ABC, EOQ, FSN, VED

and VMI

What is inventory?

1.

The amount of material, a company has in

stock at a specific time is known as inventory.

2.

In terms of money inventory can be defined

as the total capital investment over all the

materials stocked in the company at any

specific time.

3.

Inventory is an idle resource, which has some

What all constitutes inventory?

1.

Raw material inventory

2.

In process inventory

3.

Finished goods inventory

4.

Spare parts inventory

5.

Office stationary

Independent vs. Dependent Demand

1.

Independent Demand



Finished goods, spare parts for repair and

maintenance



Continuous Demand

Uncertainty of Demand

2.

Dependent Demand



Component parts of a product



_{Eg. Tyres for bicycle,}

Types of Inventory

1.

Seasonal Inventory

: Organizations carry inventory to

meet fluctuations in demend. Seasonality in demand is

absorbed using inventory

2.

Decoupling Inventory

: Complexity of production control

is reduced by splitting manufacturing into stages and

maintaining inventory between these stages

3.

Cyclic Inventory

: Periodic replenishment causes cyclic

inventory

4.

Pipeline Inventory

: Exists due to lead time for order

5.

Safety Stock

: Used to absorb fluctuations in demand due

Decoupling Inventory

An illustration

Cyclic, Pipeline and Safety Stocks

1.

Order Cycle.

The period between two

Successive Orders.

2.

Two Methods of Inventory Management:



_{Fixed Order Quantity System or EOQ Model}

Periodic Review Model

3.

Lead Time.

Time between placing an order for

replacement of an item to actually receiving the

item into stock.

Some more Terms related to Inv. Mgt. …

 _{Indicates highest stock level}

2. Safety Stock/ Buffer Stock

 _{Additional stock provided to allow for delays in delivery or}

unexpected demand

3. Reorder Level/ Reorder Point

 _{Stock level at which new order is placed}

4. Reorder Quantity

 _{Quantity of replacement order}

Example

1. An aerated drinks manufacturing company requires 2000 Kg

of sugar a week for its plant. The plant buys sugar from the sugar factory directly and it takes 2 weeks for the sugar to arrive at the plant after the order is placed. The manufacturer places demand on a monthly basis. Determine:

 _{Storage capacity required at the plant (maximum inventory)?}  _{Lead time?}

 _{Average inventory (cyclic inventory)?}  _{Pipeline inventory?}

Storage capacity required at the plant (maximum inventory) = 2000 x 4 = 8000 Kg Lead time = 2 weeks

Average inventory (cyclic inventory) = (8000 / 2) = 4000 Kg

What decisions you need to take?

How much to order?

2.

When to order?

3.

From whom to purchase?

4.

How much safety stock to be kept?

For making these decisions what information you

need?

1. Demand of the item. (consumption pattern) 2. Costs associated

3. Type of item (storage requirement, perishability, availability etc) 4. Type of production system.

5. Lead time (delivery type, time)

6. Certainty of demand (fluctuations in demand) 7. Penalty of non availability of inventory

Why Inventories?

1.

Inventories are needed because demand and supply

can not be matched for physical and economical

reasons.

2.

To safe guard against the uncertainties in price

fluctuations, supply conditions, demand conditions,

lead times, transport contingencies etc.

3.

To reduce machine idle times by providing enough

in-process inventories at appropriate locations.

4.

To take advantages of quantity discounts, economy

Why Inventories? (contd..)

5.

To decouple operations i.e. to make one operation's supply

independent of another's supply. This helps in minimizing the

impact of break downs, shortages etc. on the performance of

the down stream operations. Moreover operations can be

scheduled independent of each other if operations are

decoupled.

6.

To reduce the material handling cost of semi-finished

products by moving them in large quantities between

operations.

7.

To reduce clerical cost associated with order preparation,

Why Inventory Management?

1.

As a lot of money is engaged in the inventories along with

their high carrying costs, companies cannot afford to have

any money tied in excess inventories.

2.

At the same time shortfalls in inventory has its damaging

effects.

3.

Any excessive investment in inventories may prove to be a

serious drag on the successful working of an organization.

Thus there is a need to manage our inventories more

effectively to free the excessive amount of capital engaged

in the materials.

Inventory Management

1.

Video Case Study: Inventory

Inventory Costs

1.

Unit cost or Unit Purchase Cost

: it is usually

the purchase price of the item under

consideration.



Direct Cost.



Purchase Cost = Unit cost x Demand = (C x D)

_{If unit cost is related with the purchase quantity,}

Inventory Costs:

Procurement costs or Ordering Cost (Co):

2. Price negotiation, contracting and purchase order generation 3. Follow-up and receipt of material

4. Eventual stocking in the stores after necessary accounting and

verification

 _{Fixed cost per order}

 _{Not dependent on quantity ordered}

 _{Total Ordering Cost = No of orders placed x Co}

 _{A larger order quantity will require less number of orders to}

Inventory Costs:

Carrying costs or Holding Cost (Cc or Ch)

This represents the cost of maintaining inventories in the

plant.



It includes the interest on capital engaged



_{Cost of storage (power/AC/Dust free room), cost of}

insurance, security, warehouse rent, taxes, spoilage,

breakage, obsolescence etc.



_{Depended on quantity of inventory held.}



Carrying Cost = Average Inventory x Holding Cost Per

Unit



_{Larger the ordering quantity, higher will be the carrying}

Inventory Costs:

Stock out/Shortage costs or Back Order Cost (Cs)

This represents the cost of losses due to shortage in

supplies.



_{Penalty costs associated with delay in meeting}

demand or inability to meet at all.



This includes cost of loss of profit, loss of

customer goodwill, penalty, cost of re-scheduling

production, cost of idle time of resources,

increased freight etc.



The effects of shortage are vastly intangible, it is

EOQ Model

Total cost of carrying

Total cost of ordering Sum of the two costs

Minimum Cost

Economic

Order Qty. Order Quantity/Level of Inventory

Co st of In vent or y

Total annual inventory cost

= Purchase Cost of items +

Annual procurement cost +

Annual carrying cost+

Stockout costs

=

C x D + No of orders placed x Co

Inventory Costs

The objective of inventory management team is to minimize the total annual inventory cost. A simplified

graphical presentation in which cost of items,

procurement cost and carrying cost are depicted.

EOQ = Q* (Size of the order representing std qty of material)

Inventory Control for deterministic

demand:

EOQ Model

o C       o C Q D *

Demand during the planning period = D

Order quantity = Q

The cost of ordering per order = Inventory carrying cost per unit per unit time =

The total ordering cost is given by

2 Q       c C Q * 2

The average inventory carried by an organisation= The cost associated with carrying inventory =

c C       c C Q * 2      o C Q D *

Total cost of the plan =

Total cost of carrying inventory + Total cost of ordering

Inventory Control for deterministic

demand:

EOQ Model…

c o C D C Q*  2 2 2 ) ( Q D C C dQ Q dTC _{ c  o}

When the total cost is minimum, we obtain the most economic order quantity (EOQ). By taking the first derivative of with

respect to Q and equating it to zero we can obtain the EOQ Differentiating total cost equation with respect to Q we obtain,

The second derivative is positive and hence we obtain the minimum cost by equating the first derivative to zero.

Denoting EOQ by Q*_{, we obtain the expression of Q}* _as:

The optimal number of orders = _*

Q D

Time between orders =

D

Economic Order Quantity (EOQ) Model

Assumptions

1. Demand per year is

deterministic in nature

2. Planning period is one year 3. Lead time is zero or constant

and deterministic in nature

4. Replenishment of items is

instantaneous

5. Demand/consumption rate is

uniform and known in advance

6. No stockout condition exist in

Example 1

1. ABC manufacturers produces 1,25,000 oil seals each year to

satisfy the requirement of their client. They order the metal for the bushing in lot of 30,000 units. It cost them $40 to place

the order. The unit cost of bushing is $0.12 and the estimated carrying cost is 25% unit cost. Find out the economic order quantity? What percentage of increases or decrease in order quantity is required so that the ordered quantity is Economic order quantity ?

 _{How many orders the company will be placing in a year?}  _{What will be the average inventory?}

 _{What will be the order cycle?}

 _{What is the Total Cost of Inventory per year?}

Example 1 solution contd …

No of Order per year = D/EOQ = 125000/ 18258 = 6.8 ≈ 7 Average Inventory = EOQ/2 = 18258/2 = 9129

Order Cycle = 365/ N = 365/ 7 = 52 Days

Total Inv. Cost (for EOQ) = C.D + Co.D/Q + Cc. Q/2

= 0.12 x 125000 + 40 x 125000/ 18258 + 0.25 x 0.12 x 18258/2 = $15,560

Total Inv. Cost (for Q = 30000 Units) = C.D + Co.D/Q + Cc. Q/2

Example 2

A manufacturer uses Rs. 10,000 worth of an

item during the year. He has estimated the

ordering costs as Rs 25 per order and carrying

costs as 12.5% of average inventory value.

Find the optimal order size, number of order

per year, time period per order and total cost.

Inventory expressed in terms of cash Deterministic model with continuous demand and

Use Excel to solve

1. The annual Demand (D) of raw material of a company is 1000

Units. Ordering cost (S) is Rs 5 per order. Holding Cost (H) is Rs 1.25 per Unit per year. Cost per unit is Rs. 12.50. What would be the minimum Total Cost of Inventory per year (TC) and the economic order quantity (Q)?

Represent the holding cost and ordering cost Vs . Order quantity on a line graph.

Example 3

1. An item is used at a uniform rate of 50,000 units per year. No

shortage is allowed and delivery is at an infinite rate. The

ordering, receiving and hauling costs is Rs 13 per order, while inspection cost is Rs 12 per order. Interest costs are Rs 0.056 and deterioration and obsolescence cost Rs. 0.004 respectively per year for each item actually held in inventory plus Rs. 0.02 per year per unit based on the maximum number of units in inventory. Calculate EOQ. If lead time is 20 days, find re-order level.

Model 3: Quantity Discounts

1. Avtek, wants to reduce its large stock of televisions. So it has

offered a local chain of stores a quantity discount pricing schedule, as follows:

2. As the procurement manager for the chain of stores, you have

arrived at the following estimates. The annual carrying cost for a TV is Rs. 1900; the ordering cost is Rs 25000 and the annual demand for this TV is estimated as 200 units. Would you take the discount offer or go for the EOQ?

QUANTITY PRICE (Rs)

1 – 49 14000 50 – 89 11000 90 + 9000

TC (C= Rs14000) TC (C= Rs11000)

1. EOQ =

2. For 73 order qty, the price would be Rs 11000. 3. TC (min) = Rs 2337840

4. For order size of 90; and C= Rs 9000; find TC 5. TC = Rs 194105. 73 ~ 5 . 72 1900 200 25000 2 2 _   _ Cc CoD

Production Quantity Model

1. Gradual Usage and Non-instantaneous receipt model 2. Order qty is received gradually over time.

3. Eg. Inventory user is the producer also; batch manufacturing

EPQ Qmax

t₂ t₁

EPQ Qmax

t₂ t₁

t_{1 =} Duration of Production

C_o = Set up cost; C_c = Holding Cost or carrying cost p= Rate of production or Rate of Supply (item/day) d= Rate of consumption/ Rate of demand (item/day)

Rate of inventory rise during production (during t₁ ) = p- d Production Qty or Batch size (EPQ) = p . t₁

Q max = (p-d) . T₁ Average Inventory = p Q d p t t ABC under Area 2 ). ( ) ( 1 2    ) ( ( . . 2 d p p Cc D Co EPQ  _

Economic Production Qty Model

(Gradual supply and shortages not allowed).

1.

A component for a product is used at the rate of 100 per

day and can be manufactured at the rate of 600 per day. It

costs Rs. 2000 to set up the manufacturing process and

Rs. 0.1 per unit per day held in inventory based on the

actual inventory any time. Shortage is not allowed.

2.

Find:

 _{Optimum number of units per manufacturing run (Economic}

production quantity.

 _{Find the minimum annual variable cost.}  _{Time for each production run.}

Economic Production Qty Model

1. D = 100 x 360 = 36000 Units; 2. d = 600 / day; p = 100/day 3. Co = Rs. 2000; Cc = 0.01 41570 ) 100 600 ( 1 . 0 600 2000 3600 . 2 ) .( . . . 2          d p Cc p Co D EPQ

Selective Control of Inventories

Alternative Classification Schemes

1.

ABC Analysis (on the basis of consumption value)

2.

XYZ Classification (on the basis of unit cost of the item)

FSN Analysis (on the basis of movement of inventory)

VED Classification (on the basis of criticality of items)

On the basis of sources of supply

Significant Few

ABC Analysis

1. Based on the annual value of the item. 2. ABC – Always Better Control

3. Procedure:

 _{Calculate Unit Price and Annual Demand of the items}  _{Unit Price x Annual Demand = Annual Value}

 _{List in the Ascending order of Annual Value}  _{Calculate the cumulative annual values}

4. A Class – Monitor Closely, Continuous rigourous control 5. B Class – Monitor periodically, relaxed control

Sample Data for ABC Calculation

ITEM NO. UNIT VALUE _{(Rs) DEMAND}ANNUAL CONSUMTION _{VALUE (Rs)}

CUMULATIVE NUMBER OF ITEMS (%) CUMULATIVE VALUE (%) 0 0.00% 1 30000 80 2400000 5.00% 62.96% 2 450 1200 540000 10.00% 77.12% 3 590 400 236000 15.00% 83.32% 4 25000 9 225000 20.00% 89.22% 5 600 200 120000 25.00% 92.37% 6 4500 15 67500 30.00% 94.14% 7 400 100 40000 35.00% 95.19% 8 30 1000 30000 40.00% 95.97% 9 145 200 29000 45.00% 96.73% 10 2300 12 27600 50.00% 97.46% 11 9 1500 13500 55.00% 97.81% 12 11 1000 11000 60.00% 98.10% 13 2000 5 10000 65.00% 98.36% 14 4 4000 16000 70.00% 98.78% 15 120 120 14400 75.00% 99.16% 16 20 500 10000 80.00% 99.42% 17 10 1000 10000 85.00% 99.69% 18 80 100 8000 90.00% 99.90% 19 25 100 2500 95.00% 99.96% 20 1 1500 1500 100.00% 100.00%

ABC Classification

XYZ Classification

On the basis of unit cost of the item



High Unit cost (X Class item)



Medium Unit cost (Y Class item)



Low unit cost (Z Class item)

VED Analysis

1.

On the basis of criticality of items



Vital



Essential



Desirable



V – High level of service, safety stock



E – Medium level of service, low safety

stock

FSN Analysis

On the basis of movement of inventory



_{Fast Moving}

Slow Moving

Non-moving

Selective Control of Inventories