05 Inventory Management

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 Text : Chapter 12

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 economic value.

What all constitutes inventory? 1. Raw material inventory 2. In process inventory

3. Finished goods inventory 4. Spare parts inventory

5. Office stationary 6. Maintenance material.

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,

 Demand is certain

Types of Inventory 1. Seasonal Inventory: Organizations carry inventory to

2.

3. 4. 5.

meet fluctuations in demend. Seasonality in demand is absorbed using inventory Decoupling Inventory: Complexity of production control is reduced by splitting manufacturing into stages and maintaining inventory between these stages Cyclic Inventory: Periodic replenishment causes cyclic inventory Pipeline Inventory: Exists due to lead time for order Safety Stock: Used to absorb fluctuations in demand due to uncertainty

Decoupling Inventory An illustration

Production System without any decoupling inventory

1

2

3

2

5

6

4

1 Stage 1

4

5 Stage 2

3 7

7

8

9

8

10

9

Stage 3

6

Decoupling Inventory

10

Cyclic, Pipeline and Safety Stocks A graphical illustration

Quantity

Cyclic Stock

Pipeline inventory L

Time

Safety stock

Average Cyclic Inventory 

Q0 Q  2 2

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. … 1.

Maximum Stock.  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

5.

Economic Order Quantity (EOQ)

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 Pipeline inventory = Lead Time x Demand/unit time = 2 x 2000 = 4000 Kg.

What decisions you need to take? 1. 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. 2. 3. 4. 5. 6. 7.

Demand of the item. (consumption pattern) Costs associated Type of item (storage requirement, perishability, availability etc) Type of production system. Lead time (delivery type, time) Certainty of demand (fluctuations in demand) 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 of scale in transportation etc.

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, order procurement etc.

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

Management at Pearson Education

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, it is called as discount price.

Inventory Costs: Procurement costs or Ordering Cost (Co): Search and identification of appropriate sources of supply 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 1.

 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

meet a known demand and vice versa

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 cost

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 difficult to accurately estimate

EOQ Model

Cost of Inventory

Sum of the two costs

Total cost of carrying

Minimum Cost

Total cost of ordering

Economic Order Qty.

Order Quantity/Level of Inventory

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 + Average inventory x Cc + Stockout costs

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) Aggregate of the costs of procuring the inventory and costs of holding inventory are the minimum.

Inventory Control for deterministic demand: EOQ Model Demand during the planning period

=D

Order quantity

=Q

The cost of ordering per order

=

Co Inventory carrying cost per unit per unit time = C c The average inventory carried by an organisation=

Q 2

Q  The cost associated with carrying inventory =  * C c  2  D  The total ordering cost is given by  * C o  Q 

Total cost of the plan = Total cost of carrying inventory + Total cost of ordering

D  Q   * C * C TC(Q) =  o  c +   2  Q 

Inventory Control for deterministic demand: EOQ Model… 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,

dTC (Q) Cc Co D   2 dQ 2 Q 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

The optimal number of orders =

Q* Time between orders = D

D Q*

Q*

as: Q

*



2C o D Cc

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 the organization

Example 1 (Deterministic model with continuous demand and instantaneous supply. ) 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? What will be the saving for the company by following EOQ?

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 = 0.12 x 125000 + 40 x 125000/ 30000 + 0.25 x 0.12 x 30000/2 = $15,616

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 instantaneous supply

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.

2.

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: QUANTITY PRICE (Rs) 1 – 49

14000

50 – 89

11000

90 +

9000

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?

TC (C= Rs14000) TC (C= Rs11000) TC (C= Rs9000)

2CoD 2  25000  200   72.5 ~ 73 Cc 1900

1.

EOQ =

2.

For 73 order qty, the price would be Rs 11000.

3.

TC (min) = Rs 2337840

For order size of 90; and C= Rs 9000; find TC 5. TC = Rs 194105. 4.

Production Quantity Model 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 1.

EPQ Qmax

t1

t2

EPQ Qmax

t1

t2 EPQ 

t1 = Duration of Production Co = Set up cost; Cc = 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 Area under ABC ( p  d ).Q Q max = (p-d) . T1  (t  t ) 2p Average Inventory = 1

2

2.Co.D Cc

(p

(p  d)

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 (Gradual supply and shortages not allowed).

D = 100 x 360 = 36000 Units; 2. d = 600 / day; p = 100/day 3. Co = Rs. 2000; Cc = 0.01 1.

2.D.Co. p 2.  3600  2000  600 EPQ    41570 Cc.( p  d ) 0.1  (600  100)

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)

3. FSN Analysis (on the basis of movement of inventory) 4. VED Classification (on the basis of criticality of items) 5. On the basis of sources of supply

Significant Few Insignificant Many

PARETO’s Law

ABC Analysis Based on the annual value of the item. 2. ABC – Always Better Control 3. Procedure: 1.

 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

A Class – Monitor Closely, Continuous rigourous control 5. B Class – Monitor periodically, relaxed control 6. C Class – Rule of thumb 4.

Sample Data for ABC Calculation ITEM NO.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

UNIT VALUE (Rs) 30000 450 590 25000 600 4500 400 30 145 2300 9 11 2000 4 120 20 10 80 25 1

ANNUAL DEMAND 80 1200 400 9 200 15 100 1000 200 12 1500 1000 5 4000 120 500 1000 100 100 1500

CONSUMTION VALUE (Rs) 2400000 540000 236000 225000 120000 67500 40000 30000 29000 27600 13500 11000 10000 16000 14400 10000 10000 8000 2500 1500

CUMULATIVE NUMBER OF ITEMS (%) 0 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 35.00% 40.00% 45.00% 50.00% 55.00% 60.00% 65.00% 70.00% 75.00% 80.00% 85.00% 90.00% 95.00% 100.00%

CUMULATIVE VALUE (%)

0.00% 62.96% 77.12% 83.32% 89.22% 92.37% 94.14% 95.19% 95.97% 96.73% 97.46% 97.81% 98.10% 98.36% 98.78% 99.16% 99.42% 99.69% 99.90% 99.96% 100.00%

ABC Classification

A graphical illustration 100% 90% Class C Class B

70% 60% Class A

50% 40% 30% 20% 10%

No. of items (% )

0% 10

% 90

% 80

% 70

% 60

% 50

% 40

% 30

% 20

10

%

0%

0%

Consummption value (%)

80%

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 D – Low level of service

FSN Analysis On the basis of movement of inventory Fast Moving Slow Moving Non-moving

Selective Control of Inventories

N S F

V E D

A

B

C