Materials Management(3)

8/2/2019 Materials Management(3)

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UNIT III

MATERIALS MANAGEMENT

DEFINITION

Planning and control of the functions supporting the complete cycle (flow) of materials, and the associated

flow of information. These functions include (1) identification, (2) cataloging, (3) standardization, (4)

need determination, (5) scheduling, (6) procurement, (7) inspection, (8) quality control, (9) packaging

(10) storage, (11) inventory control, (12) distribution, and (13) disposal. Also called materials planning

It is concerned with planning, organizing and controlling the flow of materials from their initial purchase

through internal operations to the service point through distribution.

Material management is a scientific technique, concerned with Planning, Organizing &Control of flow of

materials, from their initial purchase to destination.

AIM OF MATERIAL MANAGEMENT

To get

• The Right quality

• Right quantity of supplies

• At the Right time

• At the Right place

• For the Right cost

SCOPE OF MATERIALS MANAGEMENT

Materials Management strives to ensure that the material cost component of the total product cost be the least. In

order to achieve this, the control is exercised in the following fields.

•Materials Planning.

• Purchasing.

• Store Keeping.

• Inventory Control.

• Receiving, Inspection and Despatching.

• Value Analysis, Standardization and Variety Reduction.

• Materials Handling & Traffic.

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• Disposal of Scrap and Surplus, Material Preservation.

The function of material planning department is to plan for the future procurement of all the required materials as

per the production schedule. At the time of material planning, the budget allocated for the materials will also be

critically reviewed, for better control. After material planning, purchasing is to be done. Purchasing department

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buys material based on the purchase requisitions from user departments and stores departments and annual

production plan.

There are four basic purchasing activities:

WHAT IS INVENTORY?

Inventory is the total amount of goods and/or materials contained in a store or factory at any given time. Store

owners need to know the precise number of items on their shelves and storage areas in order to place orders or

control losses. Factory managers need to know how many units of their products are available for customer orders.

Restaurants need to order more food based on their current supplies and menu needs.

The word 'inventory' can refer to both the total amount of goods and the act of counting them. Many companies

take an inventory of their supplies on a regular basis in order to avoid running out of popular items. Others take an

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While accountants often discuss inventory in terms of goods for sale, organizations - manufacturers, service-

providers and not-for-profits - also have inventories (fixtures, furniture, supplies, ...) that they do not intend to sell.

Manufacturers', distributors', and wholesalers' inventory tends to cluster in warehouses. Retailers' inventory may

exist in a warehouse or in a shop or store accessible to customers. Inventories not intended for sale to customers or

to clients may be held in any premises an organization uses. Stock ties up cash and, if uncontrolled, it will be

impossible to know the actual level of stocks and therefore impossible to control them.

There are four types of inventory with which a manufacturing firm must concern itself –

• Raw materials and purchased components: These are raw - materials, parts and components which

enter into the product Direct during the production process and generally form part of the product.

• In process inventory: Semi-finished parts, work-in-process and partly finished products formed at various

stages of production.

• Finished Products: Complete finished products ready for sale.

• Maintenance, repair and tooling inventories: Maintenance, repairs and operating supplies which are

consumed during the production process and generally do not form part of the product itself (e.g

Petroleum products like petrol, kerosene, diesels, various oils and

lubricants, machinery and plant spares, tools, jibs and fixtures, etc.)

For example:

A canned food manufacturer's materials inventory includes the ingredients to form the foods to be canned, empty

cans and their lids (or coils of steel or aluminum for constructing those components), labels, and anything else

(solder, glue, ...) that will form part of a finished can. The firm's work in process includes those materials from

the time of release to the work floor until they become complete and ready for sale to wholesale or retail

customers.

To manage these various kinds of inventories, two alternative control procedures can be used –

• Order Point Systems : This has been the traditional approach to inventory control. In these systems, the

items are restored when the inventory levels become low. Order point systems are often considered the

appropriate procedure to control inventory type 3 & 4.

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• Materials requirement planning – MRP: It is important that the proper control procedure be applied to

each of the four types of inventory. In general, MRP is the appropriate control procedure for inventory

types 1 &2

SPECIAL TERMS USED IN DEALING WITH INVENTORY

• Stock Keeping Unit (SKU) is a unique combination of all the components that are assembled into the

purchasable item. Therefore, any change in the packaging or product is a new SKU. This level of detailed

specification assists in managing inventory.

• Stockout means running out of the inventory of an SKU.

• "New old stock " (sometimes abbreviated NOS) is a term used in business to refer to merchandise being

offered for sale that was manufactured long ago but that has never been used. Such merchandise may not

be produced anymore, and the new old stock may represent the only market source of a particular item at

the present time.

TYPOLOGY IN INVENTORY MANAGEMENT

• Buffer/safety stock - Buffer Stock is a stock held to reduce the negative effects (stock-out costs) of an

unusually large usage of stock.

•Cycle stock (Used in batch processes, it is the available inventory, excluding buffer stock)

• De-coupling (Buffer stock that is held by both the supplier and the user). Inventory “decouples” in

different stages. It might be raw material, WIP, finished goods inventory. Ex: customer has inventory for

10 days for consumption. For 10 days customer is decoupled from producer. So, decoupling inventory is

the one which decouples customer and producer.

• Anticipation stock (Building up extra stock for periods of increased demand - e.g. ice cream for summer)

• Pipeline stock (Goods still in transit or in the process of distribution - have left the factory but not arrived

at the customer yet). It can be raw material, work in progress or finished goods inventory Ex: Assume

supplier is far away. Consumption per day is 20 units, 5 days for transportation 20X5= 100 units are

required for the period of transportation. So if you keep 100 units in your stock it becomes your pipeline

inventory.

• Lead Time: Lead time is the period between a customer's order and delivery of the final product. A small

order of a pre-existing item may only have a few hours lead time, but a larger order of custom-made parts

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may have a lead time of weeks, months or even longer. It all depends on a number of factors, from the

time it takes to create the machinery to the speed of the delivery system.

WHAT IS INVENTORY CONTROL?

Inventory consists of the goods and materials that a retail business holds for sale or a manufacturer keeps in raw

materials for production. Inventory control is a means for maintaining the right level of supply and reducing

loss to goods or materials before they become a finished product or are sold to the consumer.

Inventory System

The simplest language, inventory control may be said to be a planned method

whereby investment in inventories held in stock is maintained in such a manner

that it ensures proper and smooth flow of materials needed for production

operations as 'well sales, while at the same time, the total costs of investment

in inventories is kept at a minimum.

Inventory control is one of the greatest factors in a company’s success or failure. Proper inventory control will

balance the customer’s need to secure products quickly with the business need to control warehousing costs. To

manage inventory effectively, a business must have a firm understanding of demand, and cost of inventory.

OBJECTIVES OF INVENTORY CONTROL

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- Demand--

- Inventory Costs--

- Lead time--

Constraint

Inventory

PolicyPP Objective

Minimize

CostCC

Decision

1. How much to

order ?

2. When to

order?



• To ensure adequate supply of products to customer and avoid shortages as far as possible.

• To make sure that the financial investment in inventories is minimum (i.e., to see that the

working capital is blocked to the minimum possible extent).

• Efficient purchasing, storing, consumption and accounting for materials is an importan

objective.

• To maintain timely record of inventories of all the items and to maintain the stock within

the desired limits.

• To ensure timely action for replenishment.

• To provide a reserve stock for variations in lead times of delivery of materials.

• To provide a scientific base for both short-term and long-term planning of materials.

BENEFITS OF INVENTORY CONTROL

It is an established fact that through the practice of scientific inventory control, following are the

benefits of inventory control:

• Improvement in customer’s relationship because of the timely delivery of goods and

service.

•

Smooth and uninterrupted production and, hence, no stock out.

• Efficient utilisation of working capital. Helps in minimising loss due to deterioration

obsolescence damage and pilferage.

• Economy in purchasing.

• Eliminates the possibility of duplicate ordering.

INVENTORY COSTS

There are four main types of cost in inventory. There are the costs to carry standard inventories and safety stock

Ordering and setup costs come into play as well. Finally, there are shortfall costs. A good inventory contro

system will balance carrying costs against shortfall costs.

Cost Of Ordering/ Replenishment cost :

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Every time an order is placed for stock replenishment, certain costs are involved, and for most practical

purposes, it can be assumed that the cost per order is constant. The ordering cost (Co) may vary, depending upon

the type of items; raw material like steel against production components like casting. However, it is assumed that

an estimate Co can be obtained for a given range of items. This cost of ordering, Co includes:

o Paper work costs, typing and despatching an order.

o Follow-up costs required to ensure timely supplies – includes the travel cost for purchase follow-

up, telephone, telex and postal bills.

o Costs involved in receiving the order, inspection, checking and handling in the stores.

o Any set up cost of machines if charged by the supplier, either directly indicated in quotations or

assessed through quotations for various quantities.

o The salaries and wages to the purchase department.

Holding\Inventory Carrying cost\Safety stock:This cost is measured as a percentage of the unit cost of the item. This measure, gives a basis for

estimating what it actually costs a firm to carry stock. This cost includes:

interest on capital.

insurance and tax charges.

storage costs – any labour, the costs of provisions of storage area and facilities like bins, racks, etc.

allowance for deterioration or spoilage.

salaries of stores staff.

Obsolescence.

These charges increase as inventory levels rise. To minimize carrying costs, management makes frequent

orders of small quantities. Holding costs are commonly assessed as a percentage of unit value, rather than

attempting to derive monetary value for each of these costs individually. This practice is a reflection of the

difficulty inherent in deriving a specific per unit cost, for example, obsolescence or theft.

Ordering costs:

Ordering costs have to do with placing orders, receiving and storage. Transportation and invoice

processing are also included. Lowering these costs would be accomplished by placing small number of

orders, each for a large quantity. Unlike carrying costs, ordering expenses are generally expressed as a

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monetary value per order. If the business is in manufacturing, then to production setup costs are

considered instead.

Stock-out costs:

Stockout or shortfall costs(Ks) represent lost sales due to lack of supply for consumers. How these costs

are calculated can be a matter of contention between sales and logistics managers. Sales departments

prefer these numbers be kept low so that an ample stock will always be kept. Logistics managers prefer to

err on the side of caution to reduce warehousing costs. They include sales that are lost, both short and long

term, when a desired item is not available; the costs associated with back ordering the missing item; or

expenses related to stopping the production line because a component part has not arrived. These charges

are probably the most difficult to compute, but arguably the most important because they represent the

costs incurred by customers when an inventory policy falters.

INVENTORY CONTROL TECHNIQUES

Some important analysis carried out are :

ABC Analysis - based on annual consumption.

VED Analysis - criticality for production.

SDE Analysis - availability.

GOLF analysis-based on suppliers

HML Analysis - weight / cost permit.

FSN Analysis - consumption rate.

SOS Analysis-based on seasonality

XYZ Analysis-Left out stock value

Two-Bin System

a) ABC ANALYSIS :

ABC is said to connote “Always Better Control”. ABC analysis is the analysis of the store items cost criteria. Of

the various techniques, ABC classification is the most important technique. The cost of each item is multiplied by

the number used in a given period and then these items are tabulated in descending numerical value order. It wil

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be seen that first 10% of items approximately account for 70%, the next 20% for 20% of value and the last 70%

account for 10% of value.

It has been seen that a large number of items consume only a small percentage of resources and vice- versa. A –

Items represent the high cost centre, B items represent the immediate cost centres, and C- items represent low cost

centres. A very close control is exercised over A items while less stringent control is adequate for those in the

category B, and less attention for category C.

By concentrating on controlling A- items, and to a lesser degree on B items, it will be possible to control the

inventory quiet effectively both in the way of cost control and lessening the risk of ‘stock out’. Since A items are

of the highest value and are required in large numbers they could be purchased more frequently and the others, B

& C items less frequently. In so far as inventory control is concerned the following guidelines will help in keeping

the system optimum (i.e. Healthy balance between financial constraints and purchase of required quantity of

materials)

A- Items: on

1. Tight controls

2. Rigid estimates of requirements

3. Strict and close watch ( monitoring)

4. Safety stocks should be low

5. Management of items should be done at top management level.

B- Items

1. Moderate control

2. Purchase based on rigid requirements

3. Reasonably strict watch and control

4. Safety stocks moderate

5. Management be done at middle level

C- Items

1. Ordinary control measure

2. Purchase based on usage estimates

3. Controls exercises by store keeper.

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4. Safety stocks high

5. Management be done at lower levels.

Class Number of items Rupee value in items

A 10% of total items 70%

B 20% of total items 20%C 70% of total items 10%

Steps in computing A-B-C analysis: procedure of A-B-C analysis

• First we are trying to prepare a list of items and calculate their annual usage in rupees. This can be

obtained by multiplying the quantity ( number of units) of the item consumed in one year by its unit price.

• Arranging all these items in the descending order of their individual dosage in rupees. That means the first

item in the list will now show the maximum annual usage in rupees, the second item the second maximum,

the third item the third maximum and so on. After having done this the total of annual usage in rupees is

put at the bottom of the list.

• Those items which together form about 70% of the total annual usage may be total annual usage may be

categorized as A items. Similarly. Items which contribute the next 20 to 25 % of the aggregate are listed as

B items. The rest which contributes 5 to 10% of the total percentage of annual usage are called C items.

• Placing of the orders on the basis of this classification.

Example: The company has 10 items mentioned in the table .

Table: 1 A-B-C analysis usage in rupees

Items Annual

usage units

Unit cost in

rupees

Annual usage

Rs: (2)×(3)

Ranking

1 2 3 4 5

101

102

103

104

20,000

30,000

10,000

500

0.25

0.20

0.10

0.30

5000

6000

1000

150

4

3

6

9

12



105

106

107

108

109

110

50,000

8000

60,000

700

9000

50

0.20

.05

0.40

1.00

0.50

2.00

10000

400

24000

700

4500

100

2

8

1

7

5

10

Total Rs: 51,850

Table :1 shows a representative ABC analysis where 10 items have been studied and annual usage extended by

unit cost to get annual usage in rupees.

Table: 2 A-B-C ranking

Ranking Item Annual

usage

Rs.

Cumulative

annual usage

Rs.

Cumulative

percentage

Category

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1

2

3

4

5

6

7

8

9

10

107

105

102

101

109

103

108

106

104

110

24000

10000

6000

5000

4500

1000

700

400

150

100

24000

34000

40000

45000

49500

50500

51200

51600

51750

51850

46.28

65.57

77.14

86.78

95.47

97.39

98.14

99.51

99.81

100.00

A

A

B

B

C

C

C

C

C

C

Table 2 shows the ranking and assignment of A, B and C categories of items.

Table 3: Summary of A-B-C analysis:

Class Item % of

items

Rs: (per

group)

Cumulative

percentage of

Rs.

A

B

C

107,105

102,101

109,103,104

106,108,110

20

20

60

34000

11000

6850

65.57

21.21

13.22

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Table 3 shows a summary ABC analysis showing that 20% of the items represent 65.57 % of annual usage 20

percent of the item represent 21.21% of annual usage and 60% of the items represent only 13.22 % of annual

usage.

A items are ordered more frequently and I small quantities ( i.e. few weeks requirements) while C items are

ordered just once or twice a year to obtain the entire year’s requirement.

The general picture of ABC Analysis will show the following position:-

b) VED ANALYSIS :

ABC analysis does not tell anything about the criticality of the items. VED analysis is done to control a critical

inventory situation. Through this analysis, we identify the criticality of production situation and accordingly plan

for the inventory. Materials are classified into the three types as under:

V-Vital: items without which production will completely stop. i.e. non- availability can not be tolerated

Eg. Due to the absence of bearing, rolling machine cannot operate. Airlines industry is bound to keep

stand-by engines as its absence; at times, the industry may require flight cancellation, which costs to the

industry an enormous revenue loss.

E-Essential: items whose cost of non availability can be tolerated for 2-3 days, because similar or

alternative items are available. For example, some paper mills, bamboo is an important raw material.

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Availability of bamboo from the forests, at times, becomes uncertain because of number of reasons due to

climate, natural calamities etc.,

Desirable: items whose non availability can be tolerated for a long period.

Although the proportion of vital, essential and desirable items varies from organisation to organisation.

Although not included in scientific VED analysis, in some public organizations which are static or inefficiently

managed, there is a peculiar category of ‘U’ items which can be grouped as unnecessary. These unnecessary items

get purchased due to the following reasons.

a) Thoughtless continuation of previous purchase.

b) Indifferent attitude towards hospital formulary

c) Fear of change

d) Poor supervision and control

e) Unfair practice due to vested interest.

The vital items are stocked in abundance; essential items are stocked in medium amounts, and desirable items we

stocked in small amounts. By stocking the items in order of priority, vital and essential items are always in stock

which means a minimum disruption in the services offered to the people.

It should be realized that vital- V items and A items are not the same. All the vital items are not expensive and all

the expensive items are not vital. Domestic examples of salt and matchbox proves that though these items are

vital, they are not expensive, similarly microwave oven and air conditioning unit are expensive, but they are not

essential.

It is possible to conduct a two dimensional analysis taking into consideration cost on one hand , i.e. A,B,C

categories, and critically VED on the other.

c) SDE ANALYSIS :

This analysis is based spares availability of an item –

S-Scarce Items

D-Difficult Items

E-Easy Items

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S - refers to Scarce Items, especially imported and those which are very much in short supply. Due to their

nature, these items are procured on yearly interval.

D - are Difficult items which are procurable in market but not easily available. For example, items which have to

come from far off cities or where there is not much competition in market or where good quality supplies are

difficult to get or to be procured.

E - refers to Easy items – Items are those which are easily available; mostly local items. Due to their easy

availability, organizations may not require to hold these items in large volume in their stock.

It is normally advantageous to consider A, V & S items for selective controls.

d) GOLF ANALYSIS:

It is similar to SDE analysis, and it is based on the nature of market and suppliers. Suppliers or Vendors are

classified as under:

G-Government

O-Ordinary or Non-government

L-Local

F-Foreign

All these suppliers have their own payment terms, own administrative procedure and soon. For a materials

Manager, therefore, it is important to keep in mind all these issues to function efficiently and smoothly.

e) HML ANALYSIS :

The cost per item (per piece) is considered for this analysis.

High cost items (H),

Medium Cost items (M) and

Low Cost item (L) help in bringing controls over consumption at the departmental level.

f) FSN ANALYSIS :

This analysis is to help control obsolescence and is based on the consumption pattern of the items. The items are

analyzed to be classified as

Fast-moving (F),

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Slow-moving (S) and

Non-moving (N) items.

The Non-moving items (usually not consumed over a period of two years) are of great importance. Scrutiny of

non-moving items is to be made to determine whether they could be used or be disposed off. The fast and slow-

moving classifications help in arrangement of stock in stores and their distribution and handling methods.

g) SOS ANALYSIS:

SOS Analysis is done, keeping in view the seasonality or non-seasonality of the item.

S- Seasonal Items

OS – non-seasonal Items

Depends on seasonality and non-seasonality of the items, procurement actions vary. Example: in case of sugar

mills whose procurement is seasonal, these companies need to procure their requirement for a longer duration so

as to adjust their production plans. Green tea leaves are available for a longer duration from February to October.

Non-seasonal items are available throughout the year without any major price variation. Since seasonal items

which are available for a limited period, are procured in bulk to manage the production process throughout the

year.

h) XYZ ANALYSIS

This analysis is made based on the value of left out stock in the stores. ‘X’ items are those whose value of left out

stock is very high. ‘Y’ items are those whose left-out stock value is moderate. ‘Z’ items are the residual items,

whose left-out stock value are neither high nor moderate. Materials managers, based on such analysis, can plan not

only for procurement but also for secured storage of items.

i) THE TWO-BIN SYSTEM

One of the earliest systems of stock control is two-bin system, which is a simple method of control exercised by

two simple rules. One is when the order should be placed, and the other is what quantity should be covered. The

following diagram shows this simple method. The bins contain, say, mild-steel bolts and

nuts. The bolts and nuts are issued from the first bin as and when required

and as soon as the first bin is empty, more bolts and nuts are ordered

The replenishment arrives just when the second bin is empty. While delivery is

awaited, the nuts and bolts from the second bin are issued. When the delivery

arrives, then both the bins are again filled in.

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Such a method is appropriate only when consumption rate is constant, that is

to say, it is a deterministic system. We know from our experience what quantity

of bolts and nuts are necessary for a given period as well as we know their rate

of consumption.

INVENTORY MODELS

The inventory models are broadly classified as follows:

Deterministic models [Known Demand]

Probabilistic models [Unknown Demand]

DETERMINISTIC AND PROBABILISTIC METHODS

What is Deterministic and Probabilistic inventory control?

To value it better, let us imagine deterministic and probabilistic conditions.

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A deterministic circumstance is one in which the system parameters can be ascertained precisely. This is also

known as a situation of sureness since it is realized that whatever are ascertained, things are sure to occur the same

way. Also the information about the system under thought should be whole so that the parameters can be

determined with confidence. But this kind of system rarely exists, and it is for sure that some uncertainty is always

associated with the system.

Deterministic optimization models presume the state of affairs to be deterministic and consequently render the

numerical model to optimize on system arguments. Since it conceives the system to be deterministic, i

automatically means that one has full information about the system.

Probabilistic situation is also known as a situation of uncertainty. Although this is present everywhere, the

vagueness always makes us comfortless. So people keep attempting to lessen uncertainty.

Probabilistic inventory prototypes consisting of probabilistic demand and supply are more suitable in many real

circumstances. But, such models also create larger trouble in analysis and often become uncontrollable.

Deterministic models are further classified as follows:

A. Elementary Models:

1) Economic Order Quantity [EOQ] models without shortages

a) Instantaneous production

b) Finite production

2) Reorder level models [ROL] with shortages

a) Instantaneous production

b) Finite production

B. EOQ models with restrictions (multi items models)

C. EOQ models with lead time

D. EOQ models with price breaks (quantity discounts)

In general Inventory Models are classified as:

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5. That the only costs pertinent to the inventory model are the cost of placing an order and the cost of holding

or storing inventory over time

EOQ is the quantity to order, so that ordering cost + carrying cost finds its minimum. (A common

misunderstanding is that the formula tries to find when these are equal.)

Variables

Q = order quantity

Q * = optimal order quantity

D = annual demand quantity of the product

P = purchase cost per unit

S = fixed cost per order (not per unit, in addition to unit cost)

H = annual holding cost per unit (also known as carrying cost or storage cost) (warehouse space,

refrigeration, insurance, etc. usually not related to the unit cost)

Calculating EOQ through Different Models

Economic order Quantity will be optimal for the basic assumptions made in the inventory management and these

assumptions for each model are specified below. These assumptions are essential for evolving the best effective

inventory management systems. But in reality, situation arises with deviations to the assumptions, thus resulting in

conflicting issues while seeking the best possible solutions. Hence it may become imperative to consider different

lot sizes, uneven demand rates, purchase with or without discounts, while calculating the EOQ that serves the best

possible solution. Five EOQ models, which cater to these requirements, are discussed in this unit.

• Model – 1: EOQ with Uniform Rate of Demand & Instantaneous Replenishment

In this model the assumptions made are:

a) Demand is known for the item and is consumed at uniform rate

b) Stock replenishment is instantaneous (lead time is zero) i.e. the quantity of items will be realized instantly as

soon as the consumption reaches a point.

c) Price of materials is fixed (no quantity discount is assumed)

d) Inventory carrying cost per unit is constant.

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Figure shown below is the graphical representation of the above said model with assumption

When reach down to a level of inventory at R, you place your next order for Q sized order

R = Reorder Level. Q = Economic order Quantity AND L = Lead time

How to Calculate EOQ

The objective is to determine the quantity to order which minimizes the total annual inventory management cost.

Total Cost = purchase cost + ordering cost + holding cost

Purchase cost: This is the variable cost of goods, indicated by per unit purchase price × annual demand

quantity. This is indicated as P×D

Ordering cost: This is the cost of placing orders, each order has a fixed cost S, and we need to order D/Q

times per year. Where

Order Cost = The Number of Orders Placed in the period x Order Costs .

This is indicated as S × D/Q

Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2. and Holding

cost/Carrying Cost = Average Inventory Level x the Carrying Costs of 1 unit of Stock for one period

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so this cost is H × Q/2

.

To determine the minimum point of the total cost curve, set the ordering cost equal to the holding cost:

Solving for Q gives Q* (the optimal order quantity):

Therefore: .

Note that interestingly, Q* is independent of P(purchase price); it is a function of only S, D, H.

Graphical Solution

If we minimize the sum of the ordering and carrying costs, we are also minimizing the total costs. To help

visualize this we can graph the ordering cost and the holding cost as shown in the chart below:

This chart shows costs on the vertical axis or Y axis and the order quantity on the horizontal or X axis. The

straight line which commences at the origin is the carrying cost curve, the total cost of carrying units of inventory.

As expected, as we order more on the X axis, the carrying cost line increases in a proportionate manner. The

downward sloping curve which commences high on the Y axis and decreases as it approaches the X axis and

moves to the right is the ordering cost curve. This curve represents the total ordering cost depending on the size of

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the order quantity. Obviously the ordering cost will decrease as the order quantity is increased thereby causing

there to be fewer orders which need to be made in any particular period of time.

The point at which these two curves intersect is the same point which is the minimum of the curve which

represents the total cost for the inventory system. Thus the sum of the carrying cost curve and the ordering cost

curve is represented by the total cost curve and the minimum point of the total cost curve corresponds to the same

point where the carrying cost curve and the ordering cost curve intersect.

To determine Economic order quantity EOQ that minimizes the total annual inventory costs, we have to

differentiate total annual cost with respect to variable Q and set the derivative to zero and by using calculus, the

formula for calculating the EOQ works out to:

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Worked Example on Modle – 1:

An electronic product uses 32000 PCB’s per year costing Rs.1000 per unit. Cost of ordering Rs.250 per unit and

the inventory cost is Rs.100 per unit.

a) How many PCB’s should be ordered at a time to maximize economy?

b) How many orders be placed per year

c) What is the duration between each order?

d) What are the total annual costs associated with inventory?

e) What are the total annual costs involved including that of materials?

Solution:

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• Model – 2: Economic Lot Size with Uniform Rate of Demand and Finite Rate of Replenishment

In this model the assumptions made are as follows:

a) Demand is known and is consumed at uniform rate

b) Stock replenishment is not instantaneous but it is gradual at uniform rate

c) Setup cost is fixed and it does not change with lot size.

d) Inventory carrying cost per unit is constant

e) Shortages (stock outs) are not permitted.

Figure shown below indicates the uniform demand and finite rate of replenishment. Uniform demand means that

the stocked material goes on decreasing at a uniform rate as shown by the sloping line downwards.

Finite rate of replenishment means, when the order is placed, the inventory builds up gradually at a certain rate as

by the sloping line upwards. This cycle repeats at an interval. Since the stock out is not permitted, the rate of

replenishment should be greater than or equal to the rate of decrease in inventory.

This model is suitable for the manufacturing organization where there is a simultaneous production and

consumption. Since this type of production is very much in practice, this model can be considered as the

production model.

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It may please be noted that there is no ordering cost here as there are no outside vendors or suppliers considered

Instead of ordering cost Co, there is cost associated with the setup of machinery and tooling. Hence the set up cost

is fixed per run and no change with the lot size of production. In view of all these changes, the EOQ mentioned in

the previous model is referred here as ‘Economic Production Quantity’-EPQ or ‘Economic Batch Quantity’- EBQ,

i.e. the economic batch size in production.

We can calculate the total annual inventory, EBQ, and annual inventory cost from the following derivations:

Total annual inventory = [Annual ordering costs + annual Inventory carrying costs] ————— (1)

Annual ordering costs = Annual set up costs = No. of set ups x Cost/setup ——————————— (2)

Annual set up costs = [(D/Q) x Co] ——————————————– (3)

Annual Inventory carrying cost = [Average inventory x Inventory Carrying Cost] —————— (4)

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A transmission manufacturer supplying to a car manufacturer at the rate of 25 per day has a holding cost of the

complete unit at Rs. 20/month, produces in batches with a set up cost of Rs. 10000 each time when set up is

changed. Its production capacity is 40 transmissions per day and works for 300 days in a year. Cost of material

inputs per transmission is Rs. 3000. Calculate:

a) Most economical numbers that can be produced in one batch

b) How frequently should the batches be started in a day

c) What will be the minimum average inventory cost and production time

d) What is the production time

Answer for

• Model – III: Finite Rate of Replenishment with Shortages

The assumptions made in this model are as follows:

1) Demand is known and is consumed at uniform rate

2) Stock replenishment is not instantaneous but it is at a finite rate

3) Setup cost is as per production runs

4) No quantity discount is given for the supplies

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5) Shortages are allowed

6) No loss of sales due to the above said shortages

Figure given below represents the model which shows the finite replenishment with shortages.

Finite replenishment is a gradual and uniform increase in inventory due to continuous production just as in model

II. Here the shortages are allowed which means that demand is more than supply for certain duration. There is no

consumption during this shortage until fresh stocks arrive for production and the immediate supply is given first to

production before building up the inventory.

In the figure above, the inventory builds first as shown by the sloping line AB, then the consumption is shown as

the drooping line BC. At the point B is the maximum inventory level at any point of time. Line CD represents the

shortages and the stocks are replenished at point D, which build back to E, the point at which the demand ofearlier period is satisfied and the backlog becomes zero.

Formula’s to be used in Model-III are given below:

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Solved problem on the above model

The demand for a company’s product is 24000 units per year and can produce at the rate of 3000 per month. The

cost of one set up is Rs. 500 and the holding cost of one unit per month is 25 Paise. The shortage cost is Rs.20 per

unit per year. Determine the optimum quantity to be produced and the number of shortages that the company

faces. Also determine the manufacturing time and the time between each set ups?

• Model – IV: Quantity Discount Model

In this model the quantity discount in price of the supplies is considered while calculating the EOQ and then

orders are placed depending on the economics of placing orders with or without discount and the quantity being

ordered. However the fact that the materials if brought to the huge quantities may result in heavy build up of

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inventory and hence the inventory carrying cost, which has to be borne by the inventory managers. A decision has

to be taken by the purchaser on whether to stick to the EOQ or raise the order quantity to take advantage of price

discount.

The following procedure is adopted in this decision making process:

Step – 1: calculate EOQ at different price levels

Step – 2: Determine the Economic quantity to be purchased at each price level

Step – 3: Calculate the annual total cost including those of materials for each of the quantities determined by step

– 2

Step – 4: Select an optimal quantity to be purchased which involves the least annual total cost

Formula’s to be used in this model:

Solved Problem for Model-Iv

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A Transmission manufacturer is purchasing 4800 forgings per year. The requirement is known and the demand is

mostly fixed. The supplier offers quantity discount as detailed below:

From the above three price values and the EOQ’s, it is observed that the price of Rs.150 for purchase of 500

forgings has resulted in an EOQ of 447, the least units of purchase. Next come EOQ at price of 140/unit with a

quantity of 462 units and the next being 480 numbers when the unit cost is Rs.130

Step – 2: from the above figures in step-1, it can be concluded that the choice in the descending order for the

manager to order are a) best EOQ of 447 units at Rs.150, or b) the quantity of 500 forgings ordered at Rs.140 or c)

750 forgings at Rs.130 and this decision depends on the actual demand requirements over the particular period of

time.

Step – 3: To calculate the annual total cost including materials for all selected quantities in step-2, we use the

formula

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TAQ – 1: Cu D + Co (D/Q) + Cu x (i) (Q/2) = [{(150x4800)} + {(4800/447) x 750} + {150 x (447x0.02x12)/2}]

= Rs. 748099

Similarly

TAQ – 2 = [(140x4800) + (4800/500) x750 + {140x (500x0.02x12)/2)}] = Rs. 687600

TAQ – 3 = [{(130x4800)} + {(4800/750) x750} + {130 x (750x0.02x12)/2}] = Rs. 640500

While we observed that the EOQ is best at purchase of 447 numbers, the total cost, consisting of materials and the

annual ordering cost plus the inventory carrying cost, out of the above three quantities considered, is least when

the order is placed for 750 numbers in one go. Therefore the price discount could be used for the economy when

the buying quantity is warranted up to 750 numbers at any point of time in the production cycle.

PROBABLISTIC MODEL ASSUMPTIONS

Demand is NOT deterministic but probability distribution is known

Lead time MIGHT NOT BE deterministic

Shortages MAY OCCUR

All ordered units arrive at once

Purchasing cost is independent of the order quantity

SUPPLY CHAIN MANAGEMENTN AND INVENTORY CONTROL

Supply chain management (SCM) is the management of a network of interconnected businesses involved in the

ultimate provision of product and service packages required by end customers. Supply chain management spans

all movement and storage of raw materials, work-in-process inventory, and finished goods from point of origin to

point of consumption .

Another definition is provided by the APICS Dictionary when it defines SCM as the "design, planning

execution, control, and monitoring of supply chain activities with the objective of creating net value, building a

competitive infrastructure, leveraging worldwide logistics, synchronizing supply with demand and measuring

performance globally."

More common and accepted definitions of supply chain management are:

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Supply chain management is the systemic, strategic coordination of the traditional business functions and the

tactics across these business functions within a particular company and across businesses within the supply chain,

for the purposes of improving the long-term performance of the individual companies and the supply chain as a

whole.

Supply Chain Management Decision

Supply chain management has emerged over the past few years as the key to success in the global economy,

regardless of industry or company size. Its premise is simple: operational strategies should be designed and

managed around customer needs. Supply Chain (SC), which involves the configuration, coordination, and

improvement of sequentially related set of operations in establishments, integrates technology and human resource

capacity for optimal management of operations to reduce inventory requirements and provide support to

enterprises in pursuance of a competitive advantage in the marketplace. A coordinated SC integrates procurement,

production, and distribution and links together suppliers, manufacturers, distributors, customers and carriers in a

network system that allows for effective planning, information exchange, transaction execution, and performance

reporting. There are three links in the supply chain--distribution, production, and procurement/materials.

Integrated Supply Chain and Inventory Management

Integrated supply chain require that each segment of the supply chain i.e., procurement, production and

distribution be functionally integrated for optimum result. Today's technology is the key that allows the supply

chain to become integrated and therefore reduces the inventory requirement. Some examples are the electronic

transmission of advance ship notices (ASN) to advise customers of the contents of a shipment and its expected

delivery date. The transmission of purchase orders via electronic data interchange (EDI) can provide more timely

and accurate data to suppliers, allowing for more efficient information in management and production planning

Also, freight tracking systems now are being used in the management of the movement of goods, which provides

flexibility that can be used to react to rapidly changing internal and external needs such as changes in production

schedule or changes in customer product delivery requirements.

It is important that companies develop a supply chain management strategy that is consistent with their overall

business strategy. A key tool to achieving this is to develop a supply chain "diagnostic method" that can be used to

improve operations and reduce inventories . The first consideration here is for the company to examine and

understand their supply and demand planning. This is the key to optimizing resources as well as the timing of

activities associated with procuring raw materials and producing and distributing products. The next step is to

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begin the process of transitioning from a functional organization to a process organization. And finally, as

companies reorganize to be process driven, then the performance measures for the various functional departments

should be changed to support the overall supply chain management goals. Some examples of the measurements

would include perfect order fulfillment, customer satisfaction, product quality, total supply chain cost, inventory

days supply, and cash-to-cash cycle time.

JUST-IN-TIME INVENTORY

JIT, or just in time, inventory is an inventory management strategy that is aimed at monitoring the inventory

process in such a manner as to minimize the costs associated with inventory control and maintenance. To a great

degree, a just-in-time inventory process relies on the efficient monitoring of the usage of materials in the

production of goods and ordering replacement goods that arrive shortly before they are needed. This simple

strategy helps to prevent incurring the costs associated with carrying large inventories of raw materials at any

given point in time.

Another application of a just in time inventory focuses not on raw materials but on finished goods. Again, the idea

is to develop a solid understanding of what is needed to produce goods and schedule them for shipment to

customers within the shortest time frame possible. As with raw materials, shipping finished goods shortly after

producing them leads to minimizing storage costs and any taxes that may be applicable. This dual application of a

just in time inventory strategy can significantly cut the operational expenses of a business in regards to the amoun

of inventory that must be stored at any one time and the amount of taxes that must be paid on larger inventories.

A just in time inventory management process involves understanding how much of a given item is needed to

maintain production while more of the same item is ordered. This involves two key factors. First, it is necessary to

know how long it will take for the item to be shipped from the supplier and arrive at the manufacturing facility.

Second, the anticipated life or usage of the item must be determined. By knowing these two pieces of information,

it is possible to establish procedures that allow the item to be reordered just in time to arrive and replace a worn

item, without having the replacement set in storage for an extended period of time. Many purchasing departments

employ a just in time inventory for such key items as raw materials and machine parts.

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Documents

Materials Management(3)