Abstract – This paper helps to investigate the application of

inventory control model in Khyber Marble dealers. An Economic Order Quantity

model was used to determine the optimal order quantity in an optimal time for

multiple products. The result of the analysis shows the variations in the

stocks. The orders at different time interval was carefully and regularly updated

and verified because reorder points and EOQ may change. It was noted that

reorder points may often coincides little close together. This EOQ model can help in purchasing decisions in

real world situations more dynamically.

Key Words – Economic Order Quantity, Marble Dealers, optimal

time, inventory, Re-order point.

I.

Introduction

Inventory is a quantitative control

technique meaning a store of goods or a stock consisting of dependent and

independent demands. The function of inventory is to meet foreseen demands, to

smooth production requirements, to decouple operations and to protect against

stock outs. It also take advantage of expected

number of orders. It helps to hedge against price increases. It permit

operations and take advantage of quantity discounts 1.

An inventory problem occurs when there is need to stock

goods or commodities in order to satisfy demand over a specified period of

time. Almost every business must stock goods to ensure smooth and efficient

handlings of its operations. The demand to stock goods may be satisfied by

stocking once for the period of time concerned or by stocking gradually for

every time during the time horizon 2.

The EOQ

model is a basic model which is used to manage inventory levels and ordering. EOQ

model can be used in many different scenarios, but there are assumptions and

conditions that also have to be met. An EOQ model is acceptable when the actual EOQ

value is greater than the standard deviation of annual demand 3.

‘Khyber Marble

Dealers’ is selected to get details about inventory items and other products.

It is a private whole sale dealer which is run by Jahan Khan. It is located on

service road, near Sanghar town chaklala, Rawalpindi. Khyber Wholesale dealers take

the demand from customers, places their orders to the manufacturer Meherban

Khan and provide customers their finished product. Finished products are

shipped to the customer by shipper Hameed Khan. The product categories which

are presented are sunny grey (1″, ½”), sunny white (1″, ½”) and black (1″, ½”)

marble.

Table

I?I

DETAILS

ABOUT MANUFACTURER AND SHIPPER

Manufacturer

Name

Address

Meherban Khan

Near small industries Road,

Mardan

Shipper

Hameed Khan

Service road,

near Sanghar town Chaklala, Rawalpindi

Table

I?II

PRODUCT

CATEGORIES

Product Name

Category Name

Sunny Grey

1″

Sunny Grey

½”

Sunny White

1″

Sunny White

½”

Black

1″

Black

½”

The study is aimed to achieve the

following objectives; to handle details about

inventory and the products, interface to generate sales order for customers and

track down the customer orders. It generate inventory control models.

II.

Literature Review

Inventory model is defined as mathematical equation

or formula that helps an organization in determining the economic order

quantity, and the rate of ordering, to keep stocks, or services which are flowing

to the customers without interruption or delay. Inventory planning and control

is an inclusive exercise which comprises of the policies, procedures, programs

and strategies which an organization uses to regulate the range of items held

in stock, and the amount of replenishment stock required for efficient

operation. An

inventory system monitors inventory levels through inventory policies and controls

identified by the organization. Through the inventory system the

levels of inventory that has to be maintained, when inventory replenishments

should occur and the size of the orders is established. Inventory theory is used by manager

that are established rules that can be used to maintain inventory levels at the

lowest cost possible while meeting customer demand. In an inventory system

there are three types of costs that are subject to control, at least two has to

be controlled at a particular time; 1) Replenishment cost of inventory

( also called setup or order cost), 2) Carrying cost of inventory (also known

as holding cost) 3) Shortage cost 3.

Inventories

cannot be decoupled or separated from other functions such as purchasing

production and marketing. It keeps the stock levels down to make cash available

for other purposes. Inventory control also balances the conflicting goals.

Purchasing manager may wish to order large batches to get volume discounts. The

production manager similarly wants long production runs to avoid time consuming

setups. He also prefers to have large raw material inventory to avoid stops in

production due to missing materials. The marketing manager would like to have a

high stock of finished goods to be able to provide customers high service level

4.

Another

goal of inventory control model is to determine the optimal quantity of objective

to order for and then to place an order given the certain contingencies and

peculiarities of a particular business scenario.

Further

studies shows that an inventory models has to be developed for the smooth

running process in determining stock control in an organization. In

probabilistic inventory models, Single-period

inventory model is one of those elementary models in which only a single

procurement is being made 5. Application of such model can be seen in production management

systems, for example stocking seasonal items.

An EOQ model is adequate

when the standard deviation of the annual demand is smaller than the value of actual

EOQ. Literature

shows that standard economic order quantity (EOQ) model is based on the

assumption that the dealer’s capitals are unrestricted and must pay for the products

as soon as the products are received. However, this may not be true in every

case. In most of the real cases, the supplier allows up to a certain fixed

credit period to settle the account for stimulating dealer’s demand. During the

credit period before payment must be made, the retailer can sell the items,

accumulate sales revenue and earn interest. Goyal was the first one who developed

an economic order quantity (EOQ) model under the conditions of accepted delay

in payments 6.

In Fixed-Order Economic Order Quantity Model the order

quantity stays constant. The inventory levels are monitored and when the stock

level reaches a specific point an order is placed. The only danger regarding

stock depleting to zero is during lead time. The demand range can be determined

by the analysis of past demand data. Safety stock is dependent of the service

level desired, the safety stock must not be too high as this will incur excess

inventory cost. In the multiproduct EOQ system products of

differ frequency usage are set alongside each other and comparisons regarding

each item’s reorder frequency is made. Reordering cycles of the slower items

are lined up to that of the fast moving items and corresponding order cycles

can be determined.

Combination

of a fixed-order EOQ model and multi-product EOQ

model was most probably considered sufficient. It was also found that reorder

points and EOQ may change. In EOQ models, it was observed that the reorder

points sometimes coincide or occur close together. An EOQ model is acceptable

when the standard deviation of the annual demand is smaller than the actual EOQ

value 3.

Literature

shows multi-product production and inventory model using the net present value.

It was also noted that as long as deterministic demand is used, the two models shows

very little variations, but, while dealing with the probabilistic or stochastic

demand, the differences are major. The EOQ model uses long-run average cost and

is fairly simple as compared to the complexity of using net present value. the

results are also straight forward and robust 2.

Base-stock

policy was used by some researchers in addressing the problem of determining

the optimal production and inventory policy for a multi-product production

inventory system. The problem which arose concerns homogenous products with an

average determined demand for each time period and random demand during the

period over an infinite horizon. To investigate the effect of optimal

production and inventory policy when the products are not homogenous, a

heuristic algorithm had to be generated. This developed into a very complex

algorithm that had to be implemented on each product 7.

EOQ

model is not always considered as adequate for slow and fast moving items in a

system. In general, it can be understood that an EOQ model is fully acceptable

for medium and slow moving items in a system.

III.

Method

The basic EOQ model is used for

determining the optimal order size that minimizes the sum of carrying costs and

ordering costs. The model formula is derived under a set of restrictive

assumptions, as follows:

Demand is known with

certainty and is constant over time.

No shortages are

allowed.

Lead time for the

receipt of orders is constant.

The order quantity is

received all at once.

The two costs i.e. carrying and ordering costs can react

inversely to each other. As the order size increases, less orders are required,

resulting the ordering cost to decline, whereas the average amount of inventory

on hand will increase, resulting in an increase in carrying costs. Thus, the

optimal order quantity represents a cooperation between these two inversely

related holding and setup costs.

Example: The

I-75 Carpet Discount Store in North Georgia stocks carpet in its warehouse and

sells it through an adjoining showroom. The store keeps several brands and

styles of carpet in stock; however, its biggest seller is Super Shag carpet.

The store wants to determine the optimal order size and total inventory cost for this

brand of carpet given an estimated annual demand of 10,000 yards of carpet, an

annual carrying cost of $0.75 per yard, and an ordering cost of $150. The store

would also like to know the number of orders that will be made annually and the

time between orders (i.e., the order cycle) given that the store is open every

day except Sunday, Thanksgiving Day, and Christmas Day (which is not on a

Sunday).

Solution:

Cc = $0.75 per yard

Co = $150

D = 10,000 yards

The optimal order size is

The total annual inventory cost is determined by substituting Qopt into

the total cost formula:

The number of orders per year

is computed as follows:

Given that the store is open

311 days annually (365 days minus 52 Sundays, Thanksgiving, and Christmas), the

order cycle is

This example clearly explains one of the inventory

control model which is economic order quantity model which calculates the

optimal size in an optimal time. The specific formulas for the application of

economic order quantity EOQ (Q*), total costs (TC), expected number of orders

(N) and expected time between orders (T) were also demonstrated by an example

mentioned above. Further, if reorder point is to be calculated, demand per day

will be multiplied by the lead time in order to calculate product’s ROP. Demand

per day can be calculated when annual demand is divided by the total number of

working days in a year.

In ‘Khyber

Marble Dealers’ three products that is sunny grey, sunny white and black having

two categories (1″ and ½”) respectively are selected for the inventory control

model analysis.

Real time data of

seven customers is collected who placed their orders for marble to be delivered

to their location on time which is shown in Table

III?II. This

real time data is collected to generate the specific optimal model, having no

initial inventory, in order to calculate the optimal order quantity at the

optimal time, taking into consideration the inventory level of items and lead

time by optimizing the frequency of shipment of orders. Table

III?I shows

the details of marble Dealers.

Table III?I

MARBLE

DETAILS

Product Name and category

(Sq. ft.)

Sale price per unit

Purchase price per unit

Setup cost (sq. per ft.)

Holding cost (sq. per ft.)

Sunny Grey ½’

28

24

400

0.2

Sunny Grey 1′

50

43

400

0.3

Sunny White ½’

34

30

400

0.2

Sunny White 1′

62

56

400

0.3

Black ½’

190

160

400

0.2

Black 1′

320

280

400

0.3

Table III?II

CUSTOMERS

DETAILS

Sr. No.

Customers

Address

1

Anayat Ullah

Hs#68,

St#7, Mangral Model Town, Rawalpindi

2

Anwar Ul Haq kiani

Hs#26,

St#1-A, New Mangral Model Town, Rawalpindi

3

Raja Abid

St#18-B,

Sultan Town, Rawalpindi

4

Raja Sami

St#23,

Sabri Street Chaklala, Rawalpindi

5

Zahid Bhatti

Hs#56,

St#13, Shaheen Town, Rawapindi

6

Raja Ghulfam

Near

Leading Public School, Shaheen Town, Rawalpindi

7

Usman Aslam

Jamia

Farooq Masjid, Rawalpindi

Table III?III and Table

III?IV shows

the calculations for inventory control EOQ (Q*) model, total costs, expected

numbers of orders and expected time between orders, holding and ordering costs

when no discount is provided to the customers (that is, sales price per unit). Given

that the store is open 308 days annually (365 days minus 52 Sundays and Islamic

festival Holidays).

Table III?III

CALCULATIONS

FOR EOQ MODEL

Demand

(Sq. ft.)

Annual Holding cost

EOQ (Q*)

Expected No of Orders (N)

Expected time between

orders (T) (days)

13400

5.6

978

14

22

2650

15

266

10

31

9600

6.5

751

13

24

2200

18.6

218

10

30

1540

38

127

12

25

190

96

28

7

46

Table III?IV

CALCULATIONS

FOR EOQ MODEL

Ordering cost

Carrying cost

Total cost (Rp.)

5478.69

2739.34

8218.03

3987.48

1993.74

5981.22

5109.99

2555.00

7664.99

4045.74

2022.87

6068.61

4838.18

2419.09

7257.27

2701.11

1350.56

4051.67

The

EOQ will sometimes change when there is a quantity discounts offered by some

suppliers as an incentive to customers who places larger orders. Table

III?V shows

the calculations of model when discount is given to the customer. When holding

cost is expressed to be 10% for ½’ marble and 15% for 1′ marble, Total cost is then

reduced when this discount is given to the customers.

Table III?V

CALCULATIONS FOR EOQ MODEL WHEN DISCOUNT IS GIVEN

Product Name and category

(Sq. ft.)

Annual holding cost

EOQ (Q*)

No of Orders (N)

T days

Total Cost (Rp.)

Sunny Grey ½’

2.8

1384

10

32

5811.02

Sunny Grey 1′

7.5

376

7

44

4229.36

Sunny White ½’

3.4

1063

9

34

5419.96

Sunny White 1′

9.3

308

7

43

4291.15

Black ½’

19

180

9

36

5131.67

Black 1′

48

40

5

65

2864.96

Table III?VI shows the calculations for Reorder point. Demand per

day (d) is the slope which is the ratio of demand to number of working days in

a year.

Table III?VI

CALCULATIONS

FOR REORDER POINT (ROP)

Product Name and category

(Sq. ft.)

d (demand per day)

Lead Time (days)

ROP

Sunny Grey ½”

43.5

3

130.5

Sunny Grey 1″

8.6

3

25.8

Sunny White ½”

31.2

3

93.5

Sunny White 1″

7.1

4

28.6

Black ½”

5.0

5

25.0

Black 1″

0.6

5

3.1

IV.

Results/Discussions

It was noticed

that Khyber marble dealers does not have a proper inventory management which

leads them to sometimes under stocking. The decision was made to develop a

Multi-product Economic Order Quantity model to determine the optimal order

quantities, numbers of cycles and order times which were calculated to be as

follows (Table IV?I). The rate at

which different products like sunny grey, sunny white and black marble can be

ordered were determined.

When holding

cost is reduced to 15% and 10% for 1′ and ½’ respectively, total cost is

reduced and gives a maximum change in an EOQ model, expected time and number of

orders. This change is illustrated in Table IV?II.

Table IV?I

OPTIMAL MODEL

EOQ (Q*)

Expected No of Orders (N)

Expected time between

orders (T) (days)

Total cost (Rp.)

978

14

22

8218.03

266

10

31

5981.22

751

13

24

7664.99

218

10

30

6068.61

127

12

25

7257.27

28

7

46

4051.67

Table IV?II

OPTIMAL

MODEL WITH GIVEN DISCOUNT

EOQ

(Q*)

No of

Orders (N)

T (days)

Total

Cost (Rp.)

1384

10

32

5811.02

376

7

44

4229.36

1063

9

34

5419.96

308

7

43

4291.15

180

9

36

5131.67

40

5

65

2864.96

V.

Conclusion

Inventory or stock control is a quantitative control

technique with strong financial implication. An Economic Order Quantity model for

multiple products were used to determine the optimal order times. The orders at

different time interval were constantly updated and verified because reorder

points and EOQ may change. To determine whether it makes sense to take the advantage of a quantity

discount an owner of any business must compute the EOQ and compute the total

cost of inventory for the EOQ and then select the order quantity that delivers

the minimum total cost.

Further, Inventory management was the main issue which Khyber marble dealers

were facing, for that reason Economic order quantity was applied in order to

meet the timely delivery of the products to the customers. By the implication

of this model, Understocking of products were reduced. The flow of process

becomes good. Total costs were reduced resulting an increase in Profit. EOQ

concept when applied to the real world situations help in purchasing decisions

more dynamically.