inventory models - new

8/13/2019 Inventory Models - New

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INVENTORY MODELS


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One of the basic functions of management is

to employ capital efficiently so as to yield the

maximum returns. This is known as Return on

Capital Employed(ROIC).

This can be done in either of two ways or by

both, i.e.

Increasing fixed asset productivity

Increasing current asset productivity


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The importance of materials management /inventory control arises from the fact that

materials account for 60 to 65 percent of thesales value of a product, that is to say, fromevery rupee of the sales revenue, 65 paisa arespent on materials.

Hence, small change in material costs canresult in large sums of money saved or lost.

Inventory controlshould, therefore, be

considered as a function of prime importancefor our industrial economy.


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65%

15%

20%

Sales Revenue Spent

Materials

Wages & Salaries

Overheads

By careful financial analysis, it is shown that a 5%

reduction in material costs will result in increased

profits equivalent to a 36% increase in sales.Inventory control provides tools and techniques, to

reduce/control the materials cost substantially.


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Inventory of resources is held to providedesirable services to customersand to achieve

sales turnover target. Investment in large inventories adversely affects

the organizations cash flow and working capitalas investment in inventory represents substantial

portion of total capital investment in anybusiness.

It is therefore essential to balancethe advantageof having inventory of resources and the costofmaintaining it so as to determine an optimal levelof inventoryof each resources so that the totalinventory cost is minimum.


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DEFINITION OF INVENTORY

The word inventory means a physicalstock of

material or goods or commodities or other

economic resources that are stored or

reserved or kept in stock or in hand for

smooth and efficient running of future affairsof an organization at the minimum cost of

funds or capital blocked in the form of

materials or goods (Inventories).


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Forms of Inventory

Type of

organization

Types of inventories held

Manufacturer Raw materials; semi-finished

goods; finished goods; spare parts

etc.Hospital Number of beds; stock of drugs;

specialized personnel etc.

Bank Cash reserves; tellers etc.

Airline company Seating capacity; spare parts;

specialized maintenance crew etc.


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DEFINITION INVENTORY CONTROL

Inventory control systems appear complicated,

however, there are only a few basic questions to

answer for an efficient control of inventory and the

most important of these are:

1. What items should be stocked?

Criticality

Availability

Movement

2. Whenshould an order be placed to replenish inventory?

Periodic review system

Fixed order quantity system

Optional replenishment system


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DEFINITION INVENTORY CONTROL

Inventory control systems appear complicated,

however, there are only a few basic questions to

answer for an efficient control of inventory and

the most important of these are:

3. How much should be ordered in eachreplenishment?

Demand pattern

Price of an item, discount option, total budget, warehouse space

Lead time


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Classification of Inventories

Inventories which play direct role duringmanufacture (or which can be identified on

the product) is labelled as direct inventories

Inventories which are needed for

manufacturing, but not as a part of production

(or cannot be identified on the product) are

labelled as indirect inventories.


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Direct Inventories

1. Raw material inventories Bulk purchase of materials to save the investment,

To meet the changes in production rate,

To plan for buffer stock or safety stock to serve against the

delay in delivery of inventory against orders placed and also

against seasonal fluctuations.

2. Work-in -process inventories Provide economical lot production,

Cater to the variety of products,

Replacement of wastages,

To maintain uniform production even if sales varies.


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3. Finished goods inventories To ensure the adequate supply to the customers

To allow stabilization of the production level and

To help sales promotion programme

4. Spare parts inventories To provide after sales service to the customer

To utilize the product fully and economically by the

customer.

5. Scrap or waste inventory


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Indirect Inventories

Anticipation (Seasonal) inventory When there is an indication that the demand for companys

product is going to be increased in the coming season, a large

stock of material is stored in anticipation.

Examples: Fashion items, agricultural products, childrens toys,

etc.

Lot size inventory or Cycle inventories It is the inventory necessary to meet the average demand

during the successive replenishments. The amount of such

inventory depends upon production lot size, economicalshipment quantities, warehouse space available, replenishment

lead time, price-quantity discounts, inventory-carrying cost


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Decoupling inventories If various manufacturing processes (stages) operate

successively, then in the event of the breakdown of one, thewhole system could get affected. Thus stocking points of

inventory could act as buffer to take care of such eventualities.

Decoupling inventories could classified into four groups:

1. Raw materials and components

2. Work-in-process inventory

3. Finished goods inventory

4. Spare parts inventory

Supplier Manuf. Stage 1 Manuf. Stage 2 Distributor

Decouple 1(RM Store) Decouple 2

Decouple 3(FG Store)


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Safety inventory A specific level of extra inventory is maintained for protection against

uncertainties of demand and supply (lead time). The demand and leadtime both are random variables with known probability distribution.

The level of buffer stock is determined by trade-off between

protection against demand and supply uncertainties and the level of

investment in additional stock.

Transportation Inventories

Since movement of inventory cannot be instantaneous, optimal

inventory level is required for shipment of inventory to distribution

centres and customers from production centres. Such an inventory is

calledprocess inventory, as it consists of materials actually being

worked on or moving between work centres. Hence for satisfyingdemand without delay, it is essential to keep extra stock of inventory

at various work places to meet the demand while the supply is in

transit. The amount of pipeline inventory depends on the time

required for shipment and the nature of the demand.


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Factors Involved in Inventory Problem Analysis

A number of factors must be considered in the

analysis of inventory problems:

1. Relevant inventory costs

2. Demand for inventory items

3. Replenishment lead time4. Length of the planning period

5. Constraints on the inventory system


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Decisions regarding the size and timing of

replenishment orders are influenced by four

factors:

1. The forecast of demand for the item

2. Replenishment lead time

3. Inventory related costs

4. Management policy


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Factors affecting the inventory level

Inventory models can be classified according to the

following factors:

1. Inventory related costs

Inventory related costs are classified as

a) Purchase(or production) cost

It is the cost at which an item is purchased, or if

an item is produced, it is the direct manufacturing

cost.


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c) Carrying(or holding) cost(Ch)

The cost associated with maintaining the

inventory level is known as Holding Cost.It is directly proportional to the quantityto be

kept in stock and the timefor which an item is

held in stock. It includes the cost of money,

handling cost, maintenance cost, depreciation,

insurance, warehouse rent, taxes, etc.

This cost may be expressed either as cost per unit

of item held per unit of timeor as a percentage of

average rupee value of inventory held.


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Shortage(or stock out) cost(Cs)

It is the cost, which arises due to running outof stock (i.e., when an item can not be

supplied on the customer's demand).

It includes the cost of production stoppage,

loss of goodwill, loss of profitability, specialorders at higher price, overtime/idle time

payments, expediting, loss of opportunity to

sell, etc.


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Total Inventory Cost

Total Inventory cost = Purchase cost +Ordering cost + Carrying cost + Shortagecost

Demand

The size of demand is referred to the number ofthe item required in each period (cycle or

season). The demand pattern may be either deterministic

or probabilistic.


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3. Ordering cycle

An ordering cycle is defined as the time period

between two successive placement of orders. The

order may be placed on the basis of following two

types of inventory review systems:

a) Continuous review:

In this case, record of the inventory level is

updated continuously until a specified

point (known as reorder point) is reached,

at this point a new order is placed.

Sometimes, this is referred to as the two-

bin system.


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Periodic review :

In this case, the orders are placed at equally

spaced intervals of time. The quantity ordered

each time depends on the available inventory

level at the time of review.


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4. Lead time or delivery lag

The time gap between the moment of placing an

orderand actually receiving the materialis

referred to as lead time.

The lead time can be deterministic, constant orvariable, or probabilistic.


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5. Buffer (or safety) stock

Normally, demand and lead time are uncertain and

cannot be predetermined completely. So to absorb the

variation in demand and supply, some extra stock is kept.

This extra stock is known as buffer stock.

6. Available space

Generally, an inventory system involves more than one

commodity. The number of items held in inventory affect

the situation when these items compete for limited floor

space or limited total capital.


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Inventory Control Models without

Shortages (Deterministic)

In this model demandis assumed to occur atconstantrate.

The objective is to select an inventory policy, i.e. to

choose an economic order quantity Q* (EOQ) and

ordering frequency (time when the order must be

placed) in such a way that the total yearly inventory

cost is minimized.


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Assumptions1. The inventory system involves one type of item.

2. The demandis knownand constantand is resuppliedinstantaneously.

3. The inventory is replenished in single delivery for eachorder ( One order, one delivery)

4. The Lead Time (LT) is constantand known.5. Shortages are not allowed.

6. Purchase price and reorder cost do not vary with quantityordered.

7. Carrying cost per year and ordering cost are knownandconstant.

8. One order, One type of item.


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The figure shows the behavior of an inventory systemwhich operates on the assumptions listed .

At the beginning of the inventory cycle time we startwith a maximum amount of inventory equal to theorder quantity D.

As this amount is consumed, the level of inventory

drops at a constant rate equal to the demand rate D. When the level reaches a specific level called the

reorder level (ROL), enough inventory is available tocover expected demand during the lead time LT.

At this point, an order is placed equal to Q whicharrives at the end of the lead time, when theinventory level reaches zero.


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This quantity arrived is placed in stock all at once and

the inventory level goes up to its maximum value.

Obviously, during the reorder cycle, the amount of

order quantity received and consumed are equal as

the stock level at the start and finish of the order

cycle is zero. That is, Order quantity replenished in one inventory cycle =

= Annual demand consumed in one inventory cycle


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In order to determine optimal order size (Q), we

need to calculate the total variable inventory costfor

each order cycle.

Total variable cost = Annual carrying cost + Annual

ordering cost

= {Average inventory level x Carrying cost/unit/year) +{Number of orders placed per year x Ordering cost/order}

= {(Imax+ Imin)/2}Ch+ (D/Q)Co


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Other Important Formulae

Optimal interval between successive orders (t*) =

= (Q*/Demand per day) days

Optimal number of orders (N*) to be placed in the

given period =

= (Annual demand / Optimal Order quantity)= (D/Q*)

Optimal total variable inventory cost (TVC) =

= (D/Q*)Co+ (Q* /2)ChOptimal total inventory cost = Variable cost + Fixed

cost = TC = (D x C) + TVC


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Problem

Company XYZ needs 5,400 units/year of abought-out component which will be

used in its main product. The ordering

cost is Rs.250 per order and the carryingcost per unit per year is Rs.30. Find: the

economic order quantity (EOQ), the

number of orders per year and the timebetween successive orders.


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Solution

D = 5400 units per year

Co= Rs.250/order

Cc= Rs.30/unit/year

EOQ (Q*) = Q* = 2CoD = 2 x 250 x 5400 = 300 unitsCh 30

Number of orders per year = (D/Q*) = 5400/300 = 18

The time between successive orders = (Q*/D) x 360 = 20 days


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Problem

Alpha industry needs 15,000 units per yearof a bought-out component which will be

used in its main product. The ordering cost is

Rs.125 per order and the carrying cost per

unit per year is 20% of the purchase price

per unit. The purchase price per unit is Rs.75.

Find: economic order quantity, number of

orders per year and the time betweensuccessive orders.


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Solution

D = 15,000 units per year

Co= Rs.125/order

Purchase price per unit = Rs.75

Cc= Rs.75 x 20% = Rs.15/unit/year


Number of orders per year = (D/Q*) = 15000/500 = 30

The time between successive orders = (Q*/D) x 360 = 12 days


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Problem

XYZ Company buys in lots of 500 boxeswhich is a 3 month supply. The cost perbox is Rs.125 and the ordering cost isRs.150. The inventory carrying cost is

estimated at 20% of unit value. What isthe total annual cost of the existinginventory? How much money could be

saved by employing the economioc orderquantity?


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Solution

D = 500 x 4 = 2000 units per year

Co= Rs.150/order

Q = Number of units per order = 500

Purchase price per box= Rs.125

Cc= Rs.125 x 20% = Rs.25/box/year

Total annual cost of existing inventory policy

TIC = (D/Q) Co + (Q/2) Ch = (2000/500)*150 + (500/2)*25 = Rs.6850


TIC* = (D/Q*) Co + (Q*/2) Ch = (2000/155)*150 + (155/2)*25 =

= Rs.3872.98

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