InventoryPolicy Decisions

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Inventory Policy Decisions

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Appraisal of Inventories

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FUNCTIONAL CLASSIFICATION OF INVENTORIES

Lot-Size (or Cycle) Inventories

• Lot-size inventories exist whenever one produces (or buys) in larger

quantities than are needed to satisfy immediate requirements.

• The amount of such inventory depends upon the production lot size,

economical shipment quantities, replenishment lead times, price-quantity

discount schedules and inventory carrying cost.

Pipeline (or Transit) Inventories

• Since movement cannot be instantaneous, inventories arise due of

shipment from one point to another.

• The amount of pipeline inventory depend on the time required for

shipment and the nature of the demand

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Safety (or Buffer) Stocks

• Some amount of stock is created as a protection against uncertainties of

demand and the lead time.

• Demand and lead time are variables with probable deviations.

• This may cause unpredictable shortage with a high penalty cost.

• To prevent the losses due to future uncertainty additional stocks have to

be held in addition to the regular stock called as safety stock.

• Level of safety stock is determined by desirable trade-off between

protection against demand and supply uncertainties and the level of

investment in safety stock.

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Seasonal Inventories

• Seasonal inventory is needed for products whose markets exhibit seasonal

patterns of demand and whose production (or supply) is not uniform

• Seasonal inventories are built up on advance to meet the demand.

• The amount of seasonal inventories should be determined by balancing

the holding (or carrying) and expiry (if any) costs of seasonal inventories.

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Inventory Objectives

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Decoupling Inventories

• If various manufacturing process (stages) operates is series, then in the

case of breakdown of one or any disturbance at some stage can affect the

entire system.

• This kind of interdependence is not only costly but also disruptive for the

entire system.

• Thus stocking point of inventory are created between adjacent stages so

as to achieve a certain degree of independence in operating the stages.

• Decoupling inventories can be classified into 4 groups:

Raw Materials and Components Parts : Raw material and

components parts inventory could

Act as a buffer to take care of delays on the part of the supplier (s)

Guard against seasonal variations in the demand of final product

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Work-in –Process Inventory :

• Since it takes time to convert raw material into finished product, work-in-

process inventory is incurred.

• Level of such inventory can be changed by changing the manufacturing

process, lot sizes or production schedules.

Finished Goods Inventory :

• It is the inventory of final products which could be released for the sale to

the customers.

• The size of this inventory depends on the Demand Shelf life Storage Capacity Working Capital constraints etc

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Spare Parts Inventory :

• These are parts typically used for after sales service.

• Size of this inventory depends on breakdown rate, natural life of

components etc.

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ADVANTAGES OF CARRYING INVENTORYInterdependence : • One of the major advantage of keeping inventory is to link various

manufacturing stages within the firm so that down time in one stage does not affect the entire manufacturing process.

• It helps the business going on by acting as a buffer between successive stagesIrregular Supply and Demand : • When the supply or demand for an inventory item is irregular, storing certain

amount of an item in inventory can provide service to customers at various locations by maintaining a adequate supply to meet their immediate and seasonal needs.Quantity Discounts :

• Inventory of items is carried to take advantage of price-quantity discount because many suppliers offer discounts for large orders.

Avoiding Stock-outs : • An important function of inventory is to ensure an adequate and prompt supply

of items to the customers.• Loss of goodwill can be an expensive price to pay for not having the right item

at the right time

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Basic Inventory Models

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FEATURES OF INVENTORY SYSTEM

• Relevant Inventory Costs

• Demand for Inventory items

• Replenishment Lead Time

• Length of Planning period

• Constraint on the inventory system

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RELEVANT INVENTORY COSTS

• The costs that are affected by the firm’s decision to maintain a particular

level of stock are called relevant costs. These costs typically are

Purchase Cost

Carrying (or Holding) Cost

Ordering (or Set-up) Cost

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PURCHASE COST

• This cost consists of the actual price paid for the procurement of items.

• If the unit price ‘C’ of an item is independent of the size of the quantity

ordered or purchased, the purchase cost is given by:

Purchase Cost = (Price per Unit) * (Demand per unit time)

= C * D

• When price-break or quantity discounts are available for bulk purchase

above a specified quantity, the unit price becomes smaller as size of order,

Q exceeds a specified quantity level. In such cases the purchase cost

becomes variable and depends on the size of the order. In this case,

purchase cost is given by:

Purchase Cost = (Price per unit when order size is Q) * (Demand

per unit time)

= C(Q) * D

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CARRYING (OR HOLDING) COST

• The carrying cost is associated with carrying (or holding) inventory.• This cost arises due to many factors which include:

Storage cost incurred for providing warehouse space to store the products

Handling cost incurred for payment of salaries to employees to handle inventory

Insurance cost against possible loss from fire or other form of damage

Interest paid on investment of capital Obsolescence and deterioration costs incurred when a portion of

inventory become either obsolete or is lost or pilfered.• Carrying cost can be determined by two different ways:

1. Carrying Cost = (Cost of Carrying one unit of an item in the inventory for a given length of time) * (Average number of units of an item carried in the inventory for a given length of time)

2. Carrying Cost = (Cost to carry one rupee’s worth of inventory per time period) * (Rupee value of units carried)

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CARRYING (OR HOLDING) COST

• If ‘r’ is the carrying cost expressed in rupees per year per rupee of inventory investment and ‘C’ is the unit cost of the item in rupees, then the annual carrying cost for the item in rupees per year per unit is ‘rC’.

• r can also be expressed as the percentage of the unit cost of an item to be charged as inventory carrying cost

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ORDERING (OR SET-UP) COST• Ordering cost is associated with the cost of placing orders for procuring

items from outside suppliers or producing the items setting up of machinery.

• Cost per order generally includes Requisition cost of handling of purchase orders, invoices, stationery,

payments etc, Cost of services include cost of mailing, telephone calls and other

follow up actions Material handling cost incurred in receiving, inspecting and storing the

items included in the order.• For practical purposes, ordering (set-up) cost is independent of the size of

the order, rather it varies with the number of orders placed during a given period of time.

• Thus if a large number of orders are placed, more money will be required for procuring the items.

• Ordering cost is calculated as: Ordering Cost = (Cost per order or per set-up) * (Number of

orders or set-ups in the inventory planning period)

• When items are produced internally, a set-up cost is incurred and has the same meaning as the ordering cost.

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Total Inventory Cost

• If unit price of an item depends on the quantity of purchase (if price

discount is available), then we should formulate an inventory policy which

takes into consideration the purchase costs of the items held in stock

also.

• The total inventory cost (TC) is then given by:

Total Inventory Cost = Purchase cost + Ordering Cost+

Carrying Cost+ Shortage CostTotal Variable Inventory Cost

• When price discounts are not offered, the purchase cost remains constant

and is independent of the quantity purchased. The Total Variable cost

(TVC) is given by:.

Total Variable Inventory Cost = Ordering Cost+ Carrying

Cost+ Shortage Cost

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Demand for Inventory Items

• The understanding of the nature of demand (i.e. its rate, size and pattern)

for the inventory items is essential to determine an optimal inventory

policy.

• Size of demand is referred to the number of items required in each period.

• The size of demand may be either deterministic or probabilistic.

• In the deterministic case, the quantities needed over a period of time are

known with certainty. This can be fixed (Static) or can vary (dynamic)

from period to period.

• In the probabilistic case, the quantities needed over a period of time are

not known with certainty but the nature of such requirement can be

described by a known probability distribution.

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Order Cycle

• An ordering cycle is the time period between two successive placement of

orders.

• The ordering cycle may be determined in one of the two ways:

Continuous Review: In this case the level of inventory is updated

continuously as current level is reached at which point (also called

reorder point) a new order is placed. This is also referred to as the

two-bin system, fixed order size system, Q-system or (Q,R) system

Periodic Review: In this case the orders are placed at equal interval

of time, but the size of the order may vary with the variations in

demand. This is also referred to as fixed order interval system, P-

system, (S,t) system.

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Lead Time or Delivery Lag

• When an order is placed, it may require some time before delivery is

reached. The time between the placement of an order and its receipt is

called delivery lag or lead time.

• Lead time may be deterministic or probabilistic

Planning Horizon (Period)

• Planning horizon defines the period over which a particular inventory level

will be maintained.Constraints in the inventory system

• This could be:

• Warehouse space constraints

• Investment constraints

• Production capacity constraints

• Transportation capacity constraints

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INVENTORY MODEL BUILDING

• An inventory control problem can be solved by using several methods

starting from trial-and-error methods to mathematical and simulation

models.

• Steps to build a suitable inventory model are:

Collect the data regarding the pattern of demand, replenishment

policy, planning horizon, relevant inventory costs etc.

Build up a mathematical model

Derive an optimal inventory policy (i.e. economic order quantity) by

using an appropriate solution procedure as to balance among

inventory costs

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LIST OF SYMBOLS

• C = Purchase (or manufacturing) cost per unit (Rs / Unit)

• Cp= Ordering (or set-up) cost per order (Rs / Order)

• Ch= Cost of carrying one unit in the inventory for a given length of time

(Rs/Unit time)

• r = Cost of carrying one rupee’s worth of inventory per time period

(usually expressed in terms of percent of rupee value of inventory)

• Cs= Shortage cost per unit per time (Rs / Unit-Time)

• D = Demand Rate, Units per time (Unit / Time). Also denoted by d

• Q = Order Quantity i.e. number of units ordered per order (units)

• ROL = Reorder Level i.e. the level of inventory at which an order is placed

(units)

• LT = Replenishment Lead Time.

• n = number of orders per time period (orders / time)

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LIST OF SYMBOLS

• t = reorder cycle time i.e the time interval between successive orders to

replenish (time)

• tp= Production period (time)

• p = Production rate i.e the rate at which quantity Q is added to inventory

(quantity / time)

• TC = Total Inventory Cost (Rs)

• TVC = Total Variable Inventory Cost (Rs)

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MODEL I (a) – ECONOMIC LOT SIZE MODEL WITH CONSTANT DEMAND

• The inventory control system in this case can be described in terms of the

following assumption:

Demand (D) rate is constant and known throughout the reorder cycle

time.

Production rate (rp) is infinite (the entire order quantity Q is received

at one time as soon as the order is placed)

Lead Time (LT) is constant and known with certainty (No shortage of

inventory)

Purchase price (or Cost, C) per unit of the given item is constant i.e

quantity discount is not available

Unit costs of carrying inventory (Ch) and ordering (Cp) are known and

constant

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1. Q (EOQ) = 2 D CpCh

= 2 X Annual Demand X Ordering

CostCarrying Cost

2. Optimal length of inventory replenishment cycle time (t) i.e optimal interval between 2 successive orders• Q = Annual Demand x Reorder Cycle time = D X t• t = Q /D• t = 1/D x 2 D Cp

Ch

= 2 Cp

D Ch

2 x Ordering Cost

Annual Demand x Carrying Cost

=

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3. Optimal number of orders (N) to be placed in the given time period (assumed as one year)• N = Annual Demand /Optimal Order Quantity

= D/Q

=

2 x Cp

D x Ch

Annual Demand x Carrying Cost

2 x Ordering Cost=

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4. Optimal (minimum ) Total Variable Cost (TVC)

=

2 x Annual Demand x Ordering Cost x Carrying Cost=

2 D CpCh

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Problem:

The production department for a company requires 3,600 kg of raw material for

manufacturing a particular item per year. It has been estimated that the cost of

placing an order is Rs. 36 and the cost of carrying inventory is 25% of the

investment in the inventories. The price is Rs. 10 per kg. The purchase

manager

wishes to determine an ordering policy for raw material. Calculate :

1. Optimal Lot Size

2. Optimal Order Cycle Time

3. Minimum yearly variable Inventory Cost

4. Minimum yearly total cost or Total Inventory Cost

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Given Data:

• D = 3,600 kg per year

• Cp= Rs. 36 per order

• Ch= 25 percent of the investment in inventories

= Rs. 10 x 0.25 = Rs. 2.5 per kg /year

Calculation of Optimal Lot Size:

= 2 X Annual Demand X Ordering

CostCarrying Cost

EOQ, Q

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= 2 X 3,600 X 36

2.5

Q

= 322 kg per order

2. Optimal Order Cycle Time:

• t = Q/D = 322/3600 = 0.0894 year = 32.6 days

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3. Minimum Yearly Variable Inventory Cost:

• TVC = 2DCpCh

2 x 3,600 x 36 x 2.5=

= Rs. 805 per year

4. Minimum Yearly Variable Inventory Cost:

• TC = TVC + (D*C)

= Rs. 805 + (3,600 kg) (Rs. 10 / kg) = Rs. 36,805

per year

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MODEL I (c) – ECONOMIC LOT SIZE MODEL FINITE REPLENISHMENT (SUPPLY RATE)

This modes is also based on the assumptions in model I (a) except that of

instantaneous replenishment. This is because of the fact that in many

situations, the amount ordered is not delivered all at once, but available at a

finite rate per unit of time.

Q (EOQ)

Economic Order Quantity

= 2DCp

Ch

pp-d

TVC

Total Minimum Inventory Variable Cost

= 2DCpCh 1 – d/p

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t

Optimal Order Cycle Time

= Q/D

= 2Cp

DCh

pP-d

Optimal number of production runs per year

N = D/Q= DCh

2 Cp

p-dp

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Problem

A contractor has to supply 10,000 bearings per day to an automobile

manufacturer. He

finds that, when he starts production run, he can product 25,000 bearings per

day. The cost

of holding a bearing in stock for a year is Rs. 2 and the set up cost of a

production run is Rs.

1800. Assuming 300 working days in a year, calculate

• Economic Order Quantity

• Order Cycle Time

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Solution

Given Data:

Cp = Rs. 1800 per production run

Ch=Rs. 2 per year per bearing

p = 25,000 bearings per day

d = 10,000 bearings per day

D = 10,000 * 300 = 30,00,000 units / year

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Solution

Q (EOQ) = 2DCp

Ch

pP-d

2 X30,00,000 x 1800

2X

25,000

25,000 – 10,000

= 94,868 bearings

=

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SolutionFrequency of Production runs is given by

t = Q/D = 94, 868 /30,00,000 = 0.031 year = 9.486 days

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MODEL I V(a) – EOQ Model with All Units Discounts Available

Suppose the following price discount schedule is quoted by a supplier in which a price break (Quantity discount) occurs at quantity b1. This means:

Quantity Price per unit

0 < Q1 < b1 C1

b1<=Q2 < b2 C2 (< C1)

• First, calculate EOQ, Q2 using both C2, the lowest price.• If Q2 lies in the range b1<=Q2 < b2, the Q2 is the Economic Order Quantity. • The optimal cost TC associated with Q2 is calculated as:

TC = DC2 + (D/b2 ) * (Cp) + (b2/2) (C2 X r) ( r is the annual inventory holding cost)

Step 1

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• If, Q2 <b1, then taking quantity discount is not viable. Calculate EOQ with price C1 and the corresponding minimum total cost, TC1.

Step 2

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The annual demand of a product is 10,000 units. Each unit costs Rs. 100 if

orders placed in quantities below 200 units but for orders of 200 or above the

price is Rs. 95. The annual inventory holding costs is 10% of the value of the

item and the ordering cost is Rs. 5 per order. Find the economic lot size.

Problem

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• D = 10,000 units / year

•Cp = Rs. 5 per order

•R = 10 percent of price of an item = Rs. 0.10

•The unit cost for the range of quantities is given by:

Solution

Given Data

Quantity Price per unit

0 < Q1 < 200 100

200 <=Q2 95

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• The optimum order quantity based on price C2 = Rs 95 is given by:

Q = 2 X 10,000 X 5

Solution

Given Data

95 x 0.10

= 103 units

Since 103 < 200, the given discount will not minimize the Total Variable Inventory Cost.

• The correct optimum order quantity based on price C2 = Rs 95 is given by:

Q = 2 X 10,000 X 5

100 x 0.10= 100 units

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Classification of Inventory Management

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Reason for Selective Inventory Control

• When a firm is dealing with large number of items, all items cannot and need

not be controlled with equal attention.

• All items are not of equal importance to the firm in such terms as sales,

profits, availability etc.

• One way of exercising proper degree of control is to classify them into groups

on the basis of extent and nature of control required in respect of each of

them.

• Some common methods are: ABC VED HML FSN XYZ SOS SDE

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ABC Analysis:

• An ABC (Always Better Control) analysis consists of separating the inventory items into 3 groups – A,B,C, according to their annual cost volume consumption (unit cost * annual consumption).

• Although the breakpoints between these groups vary according to individual business conditions, a common breakdown might be as follows:

Category

% of items % of Total Value

A 10-20 70-85

B 20-30 10-25

C 60-70 5-15

20 50 100

70

90

100

A B C

ABC Distribution Curve% of items

% of Annual Usage Value

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VED ANALYSIS:

V- Vital,

E- Essential,

D- Desirable.

V class item is the item, if not issued, then the production may stop.

Essential Class of items- If these items are not available then stock-out cost

is very high.

Desirable Class of items- If these items are not available then there is not

going to be immediate production loss; stock out cost is very less.

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HML ANALYSIS:

• Based on the unit price of items, the HML classification separate inventory

items, as High price, Medium price and Low price.

• This analysis is helpful to control purchase of various items for inventory.

•Procurement department is more concerned with prices of materials so this analysis helps them to take them the decisions such as, who will procure what based on the hierarchy and price of material .

•When the objective is to keep control over consumption at the department level then authorization to draw materials from the stores will be given to senior staff for H item, next lower level in seniority for M class item and junior level staff for L class items.

•Cycle counting can also be planned based on HML analysis. H class items shall be counted very frequently, M class shall be counted at lesser frequency and L class shall be counted at least frequency as compared to H & M class.

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FSN ANALYSIS:

• F-Fast moving, S-Slow Moving and N- Non moving.

• Sometimes items are also classified as FNSD – Fast Moving, Normal-Moving,

Slow- moving and Dead (or Non-moving)

• This classification is based on the movement (or consumption pattern) and

therefore helps in controlling obsolescence of various items by determining

the distribution and handling patterns.

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XYZ ANALYSIS:

• This classification is based on the closing value of items in storage.

• Items whose inventory values are high and moderate are classified as X-items

and Y-items respectively, while items with low inventory value are termed as

Z items•XYZ analysis is calculated by dividing an item's current stock value by the total

stock value of the stores.

•The items are first sorted on descending order of their current stock value.

•The values are then accumulated till values reach say 60% of the total stock

value. These items are grouped as 'X'.

•Similarly, other items are grouped as 'Y' and 'Z' items based on their

accumulated value reaching another 30% & 10% respectively.

•The XYZ analysis gives, you an immediate view of which items are expensive

to hold. Through this analysis, you can reduce your money locked up by keeping

as little as possible of these expensive items.

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S-OS ANALYSIS:

S- For seasonal MaterialsOS - For non-seasonal Materials

Purchase planning has to be done if the material is seasonal as material shall be available for a particular time period of the year.

For example; Leechee is seasonal fruit which is available only for one month in year. If any Juice and pulp company wants to buy this fruit then the procurement department shall have to plan in advance the requirement and procurement job becomes concentrated only for one month. Other than this issue, shelf life and storage is also a big problem as the plan is consume is throughout the year while the buying time available is only one month.

Non-seasonal materials are available throughout the year without any significant price variation.

Non seasonal items can be Plastics, Metals etc. The prices of these materials are independent of the season

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SDE ANALYSIS:

S Class MaterialsThese materials are always in shortage and difficult in procurement. These materials sometimes require government approvals, procurement through government agencies. Normally one has to make the payment in advance for sourcing these materials. Purchase policies are very liberal for such materials

D Class Materials: These materials though not easy to procure but are available at a longer lead times and source of supply may be very far from the consumption. Procurement of these materials requires planning and scheduling in advance. Particular OEM spares of the machinery may fall under this category as that OEM may be very far from the ordering or consumption location.

E Class MaterialsThese materials are normally standard items and easily available in the market and can be purchased anytime

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GOLF Analysis:

Government, Ordinary, Local, and Foreign Report help you to do material

analysis based on location and type of organization.

G -Government suppliers

O- Ordinary or non government suppliers

L - Local suppliers

F - Foreign suppliers

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InventoryPolicy Decisions