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A RESEARCH PROJECT ON THE ECONOMIC ORDER QUANTITY OF RETAIL OUTLETS

GITAM INSTITUTE OF INTERNATIONAL BUSINESS, VISAKHAPATNAM

Section – “A”; Trimester - III MBA (IB) 2008-2010

Submitted to : Dr. R.Venkateswarlu & Dr.B.Padma Narayan (Professor: Research Methods and Techniques)

Submitted By: Group-IX Names

Roll No:

•

Mr. Abhishek kumar

1224108101

•

Mr. Avinash Chauhan

1224108113

•

Mr.B.Jayaram Pavan

1224108119

•

Mr.Rajyavardhan

1224108146

1

Contents

1.

Acknowledgement

-01

2.

Executive Summary

-01

3.

Introduction

-02

4.

Objective of study

-03

5.

Research Methodology

-03

6.

Analysis and interpretation of data

-04-15

7.

Conclusion

-16

8.

References

-17

2

ACKNOWLEDGEMENT We are extremely thankful to Prof. R.VENKATESWARLU and

Dr. B.PADMA NARAYAN who gave us an opportunity

to do a project on ECONOMIC ORDER QUANTITY Model and guided us through out in making this project a successful one. We are also thankful to Mr.B.Chandra Shekar (Regional Manager Spencer hyper market), who helped us with various information in completion of this project. We have also received assistance in preparing this project by going through the articles of various writers and internet sources. We would like to express our gratitude to all those who have assisted in completing this project. We thank all

the respondents who have co-operated with us for giving their valuable time to give their most valuable opinions while collection of our data.

EXECUTIVE SUMMARY 3

Inventory management is big issue today, it gives one company competitive edge over other companies. The word inventory refers to any kind of resource having economic value and is maintained to fulfill the present and future needs of an organization. Fred hansman defined inventory as an idle resource of any kind provided such a resource has economic value. Inventory of resources is held to provide desirable service to customers and to achieve sales turnover target. Investment in large inventories adversely affects firms cash flow and working capital as investment in inventory represents substantial portion of total capital investment in any business. It is in therefore essential to balance the advantage of having inventory of resources and the cost of maintain it so as to determine an optimal level of inventory of each resource so that total inventory cost is minimum. Holding of stock is expensive so controls are needed to ensure that stock level remains as low as possible. Stocks should be controlled using rational policies to balance between holding cost and demand. One such policy is ordering ECONOMIC ORDER QUQNTITY for stock replenishment at this point holding cost reduces significantly and total annual inventory cost is lowest. Though maintaining exact EOQ is sometime not possible working in the vicinity of it results in lower total annual inventory cost. Holding cost is straight line that is it directly varies with ordering quantity (according to classic EOQ model) is fairly true if product is non perishable, but in real life situation and specially in the case of perishable item it is a curve, we will see it through data provided by Spenser’s mall through examples and regression analysis. This happens because in case of perishable items holding cost is not constant again threat of spoilage forces companies to adopt mark down policy. We will check through linear regression the relation of holding cost with time and quantity that it is a curve in case of perishable items.

4

Introduction In the era of recession every firm is trying to cut their cost and inventory cost plays a vital role in this. Managing inventory properly is an important means of controlling costs and, thereby, improving the profitability of firm. Since a higher quantity is not best … and a lower quantity is not best … there must be some “Economic order quantity (EOQ)” which minimizes the total variable costs of inventory. Total variable costs are usually computed on an annual basis and include two components, the costs of ordering and holding inventory. Annual ordering cost is the number of orders placed times the marginal or incremental cost incurred per order. This incremental cost includes several components: - The costs of preparing the purchase order, paying the vendor's invoice, and inspecting and handling the material when it arrives. It is difficult to estimate these components precisely but a ball-park figure is good enough. The holding costs used in the EOQ should also be marginal in nature. Holding costs include insurance, taxes, and storage charges, such as depreciation or the cost of leasing a warehouse. Some of the firms also include the interest cost of the money tied up in inventory. In classic EOQ model as the quantity increases holding cost increases proportionally i.e. it remains linear to the function of time but in real life the cumulative holding cost is a convex function of time curve because the handling and holding costs together increases with cumulative increase in cost per day because of wastage, pilferage and obsolescence. This happens in the case of perishable goods, such as milk and produce, sold in small to medium size grocery stores, because these products are perishable, meeting a constant demand over time with an aging product may require markdowns in their prices or removal of spoiled products. The use of either practice can be molded as convex holding costs with time. 5

Objective of study: To develop EOQ model ,calculate EOQ of an item and show that at this point total annual inventory cost is minimum and to show that holding cost is not constant it varies with time in case of perishable items that is it is not straight line but a curve.

METHODOLOGY We visited Spencer’s mall. We find out economic order quantity by classic EOQ model.EOQ provides information about how much to order, it is the point where trade off between annual holding cost and annual order cost and total inventory cost is minimum. In real life holding cost in not constant as assumed by classic EOQ model where it is a straight line, it is actually a curve. We show through regression analysis the dependability of holding cost on number of days.

6

Elements of Inventory Cost:Many inventory decision rules involve economic criteria.

Thus, it is very

important to understand the cost of inventory, which may be broken down into the following details. Item Cost - This is the cost of buying/producing the individual inventory items. Item cost may be lowered by mass production due to the economies of large scale. Item cost of a bulk purchase is often lowered by a bulk (trade) discount. Cash (settlement) discounts may not be taken into account because an early payment decision is usually not within the inventory management system. Freight cost (also import duties and so on) may be part of the item cost if it varies with the number of items purchased. The item cost can usually be estimated, with good accuracy, directly from historical records. Ordering/Setup cost -The ordering cost is associated with ordering a batch or lot of items. Ordering cost does not depend on the number of items ordered; it is assigned to the entire batch. This cost includes: typing cost and postage of the purchase order, bank charges on letter of credit and bill process, expediting the order, receiving and inspection costs, and so on. Transportation cost and handling charges may be included if they are fixed per order of purchase. Similarly, for a manufacturing concern, setup cost is those costs associated with placing an order of a batch of items to be produced irrespective of the number of items in the batch. It includes: paperwork of the production order, costs required to set up the production machine for a run, chasing the order, and so on. The ordering/setup cost can also be determined from company records. However, difficulties are sometimes encountered in separating fixed and variable cost components. The ordering cost should include only the fixed costs for each order irrespective of its size for decision making purposes.

7

Holding (or Carrying) Cost -The holding cost is associated with keeping items in inventory for a period of time. It is typically charged as a percentage of the item cost per unit time. The holding cost usually consists of three components: (a) Opportunity cost of capital – When items are carried in inventory, the capital invested

is

not

available

for

other

purposes.

(b) Cost of storage – This cost includes variable space cost, insurance, wages, protective

clothing/containers,

and

so

on.

In theory, only variable costs are included because fixed costs remain unchanged for different sizes of reorder quantity when we, say, consider the economic

order

quantity.

(c) Costs of obsolescence, deterioration and loss – Obsolescence costs, including possible rework or scrapping, should be assigned to items which have a high risk of becoming out of fashion. Perishable goods should be charged with deterioration costs which include costs of preventing deterioration. The costs of loss include pilferage and breakage costs associated with holding items in inventory. The holding cost is more difficult to determine accurately. The opportunity cost of capital cannot be directly derived from historical records but may only be estimated on the basis of current financial considerations. Costs of storage, obsolescence and etc can be estimated from company records plus special cost studies; however, it is difficult to separate the fixed and variable components and only to include those variable ones into the holding cost. The effect of price level changes is the most difficult one for estimation. Stockout Cost - It reflects the economic consequences of running out of stock. There are two cases here. First, items are backordered. Second, the sales are lost. In cases, the cost of administration on backorders, the loss of profit from the sales forgone, and the savings on holding less inventory may be calculated. However the loss of goodwill or future business associated with both cases is

8

very difficult to calculate and is often handled indirectly by specifying an acceptable stockout risk level. EOQ MODEL: - The economic order quantity model is a classic independent demand inventory system that provides many useful ordering decision .the basic question the correct order size to minimize total inventory cost . this issue revolves around the trade off between annual holding cost and annual order cost . the EOQ model seeks to determine an optimal order quantity where the sum of annual order cost and the annual inventory holding cost is minimized . Assumptions of the economic order quantity model 1 the demand is known and constant. 2 delivery times is known and constant 3 replenishment is instantaneous 4 prices is constant 5 the holding cost is known as constant 6 ordering cost is known and constant 7 stock outs are not allowed

Derivation of EOQ: The economic order quantity can be can be derived easily from the total annual inventory cost formula using simple calculus the total inventory cost is the sum of the annual purchase cost , the annual holding cost and the annual order cost. The formula can be shown as TAIC =APC+AHC+AOC =(R*C) + (Q/2*h*C) + (R/Q*S) TAIC = total annual inventory cost APC= annual purchase cost AHC = annual holding cost AOC =annual order cost R = annual demand C =purchase cost per unit S = cost of placing one order h = holding cost rate, where annual holding cost per unit = h*c 9

Q= order quantity Q is the only known variable in the TAIC equation. The optimum q can be obtained by taking first derivative of TAIC with respect to Q and then setting it to equal to zero. Ex d(TAIC)/dQ= 0 +(1/2 *h*c) +(-1*R*S*1/Q^2) = hc/2- RS/Q^2 Now setting it equal to zero Hc/2 – RS/Q^2 = 0 Hc/2 = RS/Q^2 Q^2

=2RS/hc

EOQ = (2RS/hc)^1/2 The second derivative of TAIC is Ex

d^2(TAIC)/Dq^2=0-(-2*RS/Q^3) = (2RS/Q^3) IS GREATER THAN OR

EQUAL TO ZERO. Implying TAIC is at its minimum.

10

LET us take a hypothetical example Annual requirement(R) =7200 units

Order cost (s) =100 per order Annual holding rate (h) =20%=.2 Unit purchase cost (c) =20 Rs per unit Lead time (lt)

=6 days

EOQ = (2 R S/hc)^1/2=600 unit Annual purchase cost =R * c = 144000 RS The annual holding cost =Q/2 *h *c = 1200 RS The annual order cost = R/Q *s =1200 Total annual inventory cost = 144000 + 1200 +1200 =146400 For lead time of 6 days, reorder point would be =118.35 UNIT=118 Number of order per year = 12 Time between orders =365/12 = 30.41 =30 days (approximately) We can see that at EOQ annual total cost is lowest, as we reduce order quantity annul holding cost reduces but annual ordering cost increases as a result annual total cost increases. When we increase order quantity annual holding cost increases and annual order cost decreases but annual cost increases, the trade off point is EOQ order where total annual cost is minimum. The graph shows that 11

we should work in the vicinity of EOQ. . Graph shows that holding cost is a straight line but in real life where many products are perishable or out fashioned behavior of holding cost changes because it is no longer constant it grows commutatively .that we will show in next example.

T o ta l Co st In ve n to ry Co st

C o s t

S e tu p Co st Q ua n tity

12

We consider a variation of the economic order quantity (EOQ) model where cumulative holding cost is a nonlinear function of time. we here show how it is an approximation of the optimal order quantity for perishable goods, such as milk, and produce, where there are delivery surcharges due to infrequent ordering, and managers frequently utilize markdowns to stabilize demand as the product’s expiration date nears. We show how the holding cost curve parameters can be estimated via a regression approach from the product’s usual holding cost (storage plus capital costs), lifetime, and markdown policy. The model is a variation of the economic order quantity (EOQ) model where cumulative holding cost is a convex function of time; this is in contrast with the classic EOQ model where holding cost is a linear function of time. More specifically, the cumulative holding cost for one unit that has been stored during t units of time is H (t) =ht^y, where h andγ≥1 are constants; if γ=1 then the problem reduces to the classic EOQ mode with h being the cost to hold one unit for one time period. This problem is an approximation of the optimal order quantity for perishable goods, such as milk and produce, sold in grocery stores such as Spencer’s . . Product demand and cost are fairly constant over time, however, the cost to stock the product increases over time, as we discuss below. Because products are perishable, meeting a constant demand over time with an aging product may require markdowns in their prices or removal of spoiled product. The use of either practice can be modeled as convex holding costs with time, as we show through two examples. The first markdown occurs at roughly half the product’s sellable lifetime and is typically 10–50% of the product’s original price. The second markdown occurs at 75% of product’s sellable lifetime and is typically 25–75% of the original price. A second contributor to convex holding cost is spoilage, or variable expected shelf life. Within a product category, the percentage of individual units that spoil each day increases as the product ages. spoilage can be approximated by a 13

convex holding cost curve even in the absence of markdown pricing. In that case, however, the order quantity in the model must be adjusted upwards to account for spoilage. Most papers on perishable inventory models with deterministic demand consider that inventory spoils (decays) with time, at different patterns, and that demand depends on the level of inventory. our application assumes a constant demand rate due to a markdown policy.

We provide a simple

methodology to estimate the holding cost curve parameters given a product’s lifetime, regular holding (storage + cost of capital) cost, and markdown policy or spoilage curve.

Model Consider a product facing a constant demand rate d. Fixed ordering cost is s replenishment lead-time is constant, and holding cost per unit increases with the time t that the product has been in stock according to H(t)= ht^y, where h and γ≥ 1 are constants. The firm’s objective is to choose

an order quantity that

minimizes average combined ordering and holding costs over an infinite horizon. With an order quantity of Q, and constant demand rate d, the length of an order cycle is Q/d . During the first cycle, the inventory level varies with time I(t) =Q – dt Thus, the average holding cost during the cycle (0, Q/d) is: H =h Q^y/(y +1)d^y-1 And EOQ is Q= ((1+1/y) sd^y/h)^1/ y+1 Equation agrees with the classical EOQ model when y =1

Estimating Holding Cost Parameters In this section, we give two examples that show how the parameters and h and y can be estimated, using linear least squares regression, from the product holding cost h, the product’s lifetime T, and a given markdown policy or spoilage curve.

14

Example 1: mark down policy Consider 500 ML of heritage whole milk, with T = 12 days (expiration date), h = 0.01/day, and a markdown policy that decreases the product’s price by RS 0.50 on days 5 and 10. the cumulative holding cost curve per unit H(t) is given as a function of time in Table 1. Notice that at day 5, the cumulative holding cost jumps from 0.04 to 0.55 (0.01 + 0.50), which is a result to the product being marked down; similarly at day 10. We use convex approximation H(t) = ht^y to the data in table 1 taking log on both side yields Log H(t) =log h + y log t Table 1 DAY

COMMULATIVE HOLDING COST

1

0.01

2

0.02

3

0.03

4

0.04

5

0.55

6

0.56

7

0.57

8

0.58

9

0.59

10

1.10

11

1.11

12

1.12

Using a linear regression where the independent variable is t, and the dependent variable is 15

H(t), plot shows the cumulative holding cost and its convex approximation curve Analysis Y = holding cost X= no of days Regression equation Y = bo +b1 X Since R^2 =0.890971=90 This implies that 90% of variability in holding cost is explained by the number of days. We take null hypothesis Ho= holding cost is not dependent on no of days Alternative hypothesis Ha = holding cost is depends on no of days Now level of significance alpha=.05 From regression table p value is =1.26 *10^-5 When we compare p value with alpha, pvalue is less than alpha, therefore null hypothesis is rejected. We select alternative hypothesis that is holding cost depends on no of days. When we calculate holding cost it is increasing. We can see in the plot that holding cost is a curve rather than a straight line as assumed by classic EOQ model.

16

Example 2: Spoilage Consider Amul cheese. Pack of 100 gm With T = 5 days (expected lifetime), h = 0.01/day, and a cost of 2RS /unit. Average spoilage, based on historical observations, is 5%, 7.5%, 10%, and 22.5% of the remaining stock of cheese after the second, third, fourth and fifth days respectively. Thus, cumulative spoilage cost per unit is (0.05)2RS= RS0.10 for the second day; (0.05 + 0.075)2RS = RS0.25 for the third day, and so forth. Adding the regular storage cost of RS0.01 per unit per day, we obtain the cumulative holding cost, shown in Table 2. Notice that at day 6, all cheese will be spoiled. Running a linear regression between H (T) AND t the plot is a curve. Day

%spoilage

csc

c st c

H (t)

0.01

0.01

1

0

2

5

.10

0.02

0.12

3

7.5

.25

0.03

0.28

4

10

.45

0.04

0.49

5

22.5

.90

0.05

0.95

6

55

2.0

0.06

2.06

Through linear regression y can be calculated and EOQ can be calculated. R^ 2shows significant relationship. Hence we can see that in case of perishable items holding cost is not constant. We can compute y and by using EOQ formula we can calculate how much to order to reduce total annual inventory cost.

17

Analysis Y =commutative holding cost X= no of days Regression equation is Yo = bo +b1X Since R^2 is .849 =.85 This implies that 85% of variability in holding cost is explained by the number of days due to spoilage. We take hypothesis Ho= c holding cost does not depend on no of days due to spoilage Ha= c holding cost depends on no of days due to spoilage Now alpha = 0.5 P value

= 0.02

When we compare null hypothesis by alternative hypothesis p value is less than alpha therefore we select alternative hypothesis that is holding cost depend on no of days due to spoilage. When we calculate holding cost we can see that it is increasing with no of days.

18

Findings The tradeoff between annual holding cost and order cost occur at EOQ order. If we order more holding cost will increase though annual order cost decreases but the overall impact is total annual inventory cost increases.

If we order less

holding cost will decrease but order cost increases effect is same total annual inventory cost increases. At EOQ total inventory cost is minimum. again we find that holding cost is not constant in case of perishable items it is not a straight line as assumed by classic EOQ model but curve.

CONCLUSION: Every store wants to minimize its inventory cost .inventory is necessary to provide expected level of customer service ,lack of inventory can will result in lost sale which will reduce profit. But inventory blocks working capital at the same time perishable item will be spoiled and causes loss. If inventory is high it blocks cash flow and working capital. inventory cost has three components material cost ,holding cost and order cost, high inventory results in higher holding cost (specially in case of perishable materials) and lower order cost, if inventory is low it reduces holding cost and increases ordering cost ,ramification is increased total inventory cost. ECONOMIC ORDER QUANTITY is that point at which trade off between inventory holding cost and annual order cost occur and total annual inventory cost is minimum. In this report we have shown that how EOQ gives minimum inventory cost (for a non perishable item). Classic economic order quantity theory assumes constant holding cost but in a real life holding cost is not constant for perishable goods it increases commutatively and we have shown that its plot is a curve due to its nature through linear regression y and other factors can be calculated and economic order quantity can be found which results in lower total annual inventory cost. 19

Reference: 1 QUANTITATIVE TECHNIQUES

J K SHARMA

2 SUPPLY CHAIN MANAGEMENT

SUNIL CHOPRA

3

JOEL D WISNER

SUPPLY CHAIN MANAGEMENT A BALANCED APPROACH

20

21

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GITAM INSTITUTE OF INTERNATIONAL BUSINESS, VISAKHAPATNAM

Section – “A”; Trimester - III MBA (IB) 2008-2010

Submitted to : Dr. R.Venkateswarlu & Dr.B.Padma Narayan (Professor: Research Methods and Techniques)

Submitted By: Group-IX Names

Roll No:

•

Mr. Abhishek kumar

1224108101

•

Mr. Avinash Chauhan

1224108113

•

Mr.B.Jayaram Pavan

1224108119

•

Mr.Rajyavardhan

1224108146

1

Contents

1.

Acknowledgement

-01

2.

Executive Summary

-01

3.

Introduction

-02

4.

Objective of study

-03

5.

Research Methodology

-03

6.

Analysis and interpretation of data

-04-15

7.

Conclusion

-16

8.

References

-17

2

ACKNOWLEDGEMENT We are extremely thankful to Prof. R.VENKATESWARLU and

Dr. B.PADMA NARAYAN who gave us an opportunity

to do a project on ECONOMIC ORDER QUANTITY Model and guided us through out in making this project a successful one. We are also thankful to Mr.B.Chandra Shekar (Regional Manager Spencer hyper market), who helped us with various information in completion of this project. We have also received assistance in preparing this project by going through the articles of various writers and internet sources. We would like to express our gratitude to all those who have assisted in completing this project. We thank all

the respondents who have co-operated with us for giving their valuable time to give their most valuable opinions while collection of our data.

EXECUTIVE SUMMARY 3

Inventory management is big issue today, it gives one company competitive edge over other companies. The word inventory refers to any kind of resource having economic value and is maintained to fulfill the present and future needs of an organization. Fred hansman defined inventory as an idle resource of any kind provided such a resource has economic value. Inventory of resources is held to provide desirable service to customers and to achieve sales turnover target. Investment in large inventories adversely affects firms cash flow and working capital as investment in inventory represents substantial portion of total capital investment in any business. It is in therefore essential to balance the advantage of having inventory of resources and the cost of maintain it so as to determine an optimal level of inventory of each resource so that total inventory cost is minimum. Holding of stock is expensive so controls are needed to ensure that stock level remains as low as possible. Stocks should be controlled using rational policies to balance between holding cost and demand. One such policy is ordering ECONOMIC ORDER QUQNTITY for stock replenishment at this point holding cost reduces significantly and total annual inventory cost is lowest. Though maintaining exact EOQ is sometime not possible working in the vicinity of it results in lower total annual inventory cost. Holding cost is straight line that is it directly varies with ordering quantity (according to classic EOQ model) is fairly true if product is non perishable, but in real life situation and specially in the case of perishable item it is a curve, we will see it through data provided by Spenser’s mall through examples and regression analysis. This happens because in case of perishable items holding cost is not constant again threat of spoilage forces companies to adopt mark down policy. We will check through linear regression the relation of holding cost with time and quantity that it is a curve in case of perishable items.

4

Introduction In the era of recession every firm is trying to cut their cost and inventory cost plays a vital role in this. Managing inventory properly is an important means of controlling costs and, thereby, improving the profitability of firm. Since a higher quantity is not best … and a lower quantity is not best … there must be some “Economic order quantity (EOQ)” which minimizes the total variable costs of inventory. Total variable costs are usually computed on an annual basis and include two components, the costs of ordering and holding inventory. Annual ordering cost is the number of orders placed times the marginal or incremental cost incurred per order. This incremental cost includes several components: - The costs of preparing the purchase order, paying the vendor's invoice, and inspecting and handling the material when it arrives. It is difficult to estimate these components precisely but a ball-park figure is good enough. The holding costs used in the EOQ should also be marginal in nature. Holding costs include insurance, taxes, and storage charges, such as depreciation or the cost of leasing a warehouse. Some of the firms also include the interest cost of the money tied up in inventory. In classic EOQ model as the quantity increases holding cost increases proportionally i.e. it remains linear to the function of time but in real life the cumulative holding cost is a convex function of time curve because the handling and holding costs together increases with cumulative increase in cost per day because of wastage, pilferage and obsolescence. This happens in the case of perishable goods, such as milk and produce, sold in small to medium size grocery stores, because these products are perishable, meeting a constant demand over time with an aging product may require markdowns in their prices or removal of spoiled products. The use of either practice can be molded as convex holding costs with time. 5

Objective of study: To develop EOQ model ,calculate EOQ of an item and show that at this point total annual inventory cost is minimum and to show that holding cost is not constant it varies with time in case of perishable items that is it is not straight line but a curve.

METHODOLOGY We visited Spencer’s mall. We find out economic order quantity by classic EOQ model.EOQ provides information about how much to order, it is the point where trade off between annual holding cost and annual order cost and total inventory cost is minimum. In real life holding cost in not constant as assumed by classic EOQ model where it is a straight line, it is actually a curve. We show through regression analysis the dependability of holding cost on number of days.

6

Elements of Inventory Cost:Many inventory decision rules involve economic criteria.

Thus, it is very

important to understand the cost of inventory, which may be broken down into the following details. Item Cost - This is the cost of buying/producing the individual inventory items. Item cost may be lowered by mass production due to the economies of large scale. Item cost of a bulk purchase is often lowered by a bulk (trade) discount. Cash (settlement) discounts may not be taken into account because an early payment decision is usually not within the inventory management system. Freight cost (also import duties and so on) may be part of the item cost if it varies with the number of items purchased. The item cost can usually be estimated, with good accuracy, directly from historical records. Ordering/Setup cost -The ordering cost is associated with ordering a batch or lot of items. Ordering cost does not depend on the number of items ordered; it is assigned to the entire batch. This cost includes: typing cost and postage of the purchase order, bank charges on letter of credit and bill process, expediting the order, receiving and inspection costs, and so on. Transportation cost and handling charges may be included if they are fixed per order of purchase. Similarly, for a manufacturing concern, setup cost is those costs associated with placing an order of a batch of items to be produced irrespective of the number of items in the batch. It includes: paperwork of the production order, costs required to set up the production machine for a run, chasing the order, and so on. The ordering/setup cost can also be determined from company records. However, difficulties are sometimes encountered in separating fixed and variable cost components. The ordering cost should include only the fixed costs for each order irrespective of its size for decision making purposes.

7

Holding (or Carrying) Cost -The holding cost is associated with keeping items in inventory for a period of time. It is typically charged as a percentage of the item cost per unit time. The holding cost usually consists of three components: (a) Opportunity cost of capital – When items are carried in inventory, the capital invested

is

not

available

for

other

purposes.

(b) Cost of storage – This cost includes variable space cost, insurance, wages, protective

clothing/containers,

and

so

on.

In theory, only variable costs are included because fixed costs remain unchanged for different sizes of reorder quantity when we, say, consider the economic

order

quantity.

(c) Costs of obsolescence, deterioration and loss – Obsolescence costs, including possible rework or scrapping, should be assigned to items which have a high risk of becoming out of fashion. Perishable goods should be charged with deterioration costs which include costs of preventing deterioration. The costs of loss include pilferage and breakage costs associated with holding items in inventory. The holding cost is more difficult to determine accurately. The opportunity cost of capital cannot be directly derived from historical records but may only be estimated on the basis of current financial considerations. Costs of storage, obsolescence and etc can be estimated from company records plus special cost studies; however, it is difficult to separate the fixed and variable components and only to include those variable ones into the holding cost. The effect of price level changes is the most difficult one for estimation. Stockout Cost - It reflects the economic consequences of running out of stock. There are two cases here. First, items are backordered. Second, the sales are lost. In cases, the cost of administration on backorders, the loss of profit from the sales forgone, and the savings on holding less inventory may be calculated. However the loss of goodwill or future business associated with both cases is

8

very difficult to calculate and is often handled indirectly by specifying an acceptable stockout risk level. EOQ MODEL: - The economic order quantity model is a classic independent demand inventory system that provides many useful ordering decision .the basic question the correct order size to minimize total inventory cost . this issue revolves around the trade off between annual holding cost and annual order cost . the EOQ model seeks to determine an optimal order quantity where the sum of annual order cost and the annual inventory holding cost is minimized . Assumptions of the economic order quantity model 1 the demand is known and constant. 2 delivery times is known and constant 3 replenishment is instantaneous 4 prices is constant 5 the holding cost is known as constant 6 ordering cost is known and constant 7 stock outs are not allowed

Derivation of EOQ: The economic order quantity can be can be derived easily from the total annual inventory cost formula using simple calculus the total inventory cost is the sum of the annual purchase cost , the annual holding cost and the annual order cost. The formula can be shown as TAIC =APC+AHC+AOC =(R*C) + (Q/2*h*C) + (R/Q*S) TAIC = total annual inventory cost APC= annual purchase cost AHC = annual holding cost AOC =annual order cost R = annual demand C =purchase cost per unit S = cost of placing one order h = holding cost rate, where annual holding cost per unit = h*c 9

Q= order quantity Q is the only known variable in the TAIC equation. The optimum q can be obtained by taking first derivative of TAIC with respect to Q and then setting it to equal to zero. Ex d(TAIC)/dQ= 0 +(1/2 *h*c) +(-1*R*S*1/Q^2) = hc/2- RS/Q^2 Now setting it equal to zero Hc/2 – RS/Q^2 = 0 Hc/2 = RS/Q^2 Q^2

=2RS/hc

EOQ = (2RS/hc)^1/2 The second derivative of TAIC is Ex

d^2(TAIC)/Dq^2=0-(-2*RS/Q^3) = (2RS/Q^3) IS GREATER THAN OR

EQUAL TO ZERO. Implying TAIC is at its minimum.

10

LET us take a hypothetical example Annual requirement(R) =7200 units

Order cost (s) =100 per order Annual holding rate (h) =20%=.2 Unit purchase cost (c) =20 Rs per unit Lead time (lt)

=6 days

EOQ = (2 R S/hc)^1/2=600 unit Annual purchase cost =R * c = 144000 RS The annual holding cost =Q/2 *h *c = 1200 RS The annual order cost = R/Q *s =1200 Total annual inventory cost = 144000 + 1200 +1200 =146400 For lead time of 6 days, reorder point would be =118.35 UNIT=118 Number of order per year = 12 Time between orders =365/12 = 30.41 =30 days (approximately) We can see that at EOQ annual total cost is lowest, as we reduce order quantity annul holding cost reduces but annual ordering cost increases as a result annual total cost increases. When we increase order quantity annual holding cost increases and annual order cost decreases but annual cost increases, the trade off point is EOQ order where total annual cost is minimum. The graph shows that 11

we should work in the vicinity of EOQ. . Graph shows that holding cost is a straight line but in real life where many products are perishable or out fashioned behavior of holding cost changes because it is no longer constant it grows commutatively .that we will show in next example.

T o ta l Co st In ve n to ry Co st

C o s t

S e tu p Co st Q ua n tity

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We consider a variation of the economic order quantity (EOQ) model where cumulative holding cost is a nonlinear function of time. we here show how it is an approximation of the optimal order quantity for perishable goods, such as milk, and produce, where there are delivery surcharges due to infrequent ordering, and managers frequently utilize markdowns to stabilize demand as the product’s expiration date nears. We show how the holding cost curve parameters can be estimated via a regression approach from the product’s usual holding cost (storage plus capital costs), lifetime, and markdown policy. The model is a variation of the economic order quantity (EOQ) model where cumulative holding cost is a convex function of time; this is in contrast with the classic EOQ model where holding cost is a linear function of time. More specifically, the cumulative holding cost for one unit that has been stored during t units of time is H (t) =ht^y, where h andγ≥1 are constants; if γ=1 then the problem reduces to the classic EOQ mode with h being the cost to hold one unit for one time period. This problem is an approximation of the optimal order quantity for perishable goods, such as milk and produce, sold in grocery stores such as Spencer’s . . Product demand and cost are fairly constant over time, however, the cost to stock the product increases over time, as we discuss below. Because products are perishable, meeting a constant demand over time with an aging product may require markdowns in their prices or removal of spoiled product. The use of either practice can be modeled as convex holding costs with time, as we show through two examples. The first markdown occurs at roughly half the product’s sellable lifetime and is typically 10–50% of the product’s original price. The second markdown occurs at 75% of product’s sellable lifetime and is typically 25–75% of the original price. A second contributor to convex holding cost is spoilage, or variable expected shelf life. Within a product category, the percentage of individual units that spoil each day increases as the product ages. spoilage can be approximated by a 13

convex holding cost curve even in the absence of markdown pricing. In that case, however, the order quantity in the model must be adjusted upwards to account for spoilage. Most papers on perishable inventory models with deterministic demand consider that inventory spoils (decays) with time, at different patterns, and that demand depends on the level of inventory. our application assumes a constant demand rate due to a markdown policy.

We provide a simple

methodology to estimate the holding cost curve parameters given a product’s lifetime, regular holding (storage + cost of capital) cost, and markdown policy or spoilage curve.

Model Consider a product facing a constant demand rate d. Fixed ordering cost is s replenishment lead-time is constant, and holding cost per unit increases with the time t that the product has been in stock according to H(t)= ht^y, where h and γ≥ 1 are constants. The firm’s objective is to choose

an order quantity that

minimizes average combined ordering and holding costs over an infinite horizon. With an order quantity of Q, and constant demand rate d, the length of an order cycle is Q/d . During the first cycle, the inventory level varies with time I(t) =Q – dt Thus, the average holding cost during the cycle (0, Q/d) is: H =h Q^y/(y +1)d^y-1 And EOQ is Q= ((1+1/y) sd^y/h)^1/ y+1 Equation agrees with the classical EOQ model when y =1

Estimating Holding Cost Parameters In this section, we give two examples that show how the parameters and h and y can be estimated, using linear least squares regression, from the product holding cost h, the product’s lifetime T, and a given markdown policy or spoilage curve.

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Example 1: mark down policy Consider 500 ML of heritage whole milk, with T = 12 days (expiration date), h = 0.01/day, and a markdown policy that decreases the product’s price by RS 0.50 on days 5 and 10. the cumulative holding cost curve per unit H(t) is given as a function of time in Table 1. Notice that at day 5, the cumulative holding cost jumps from 0.04 to 0.55 (0.01 + 0.50), which is a result to the product being marked down; similarly at day 10. We use convex approximation H(t) = ht^y to the data in table 1 taking log on both side yields Log H(t) =log h + y log t Table 1 DAY

COMMULATIVE HOLDING COST

1

0.01

2

0.02

3

0.03

4

0.04

5

0.55

6

0.56

7

0.57

8

0.58

9

0.59

10

1.10

11

1.11

12

1.12

Using a linear regression where the independent variable is t, and the dependent variable is 15

H(t), plot shows the cumulative holding cost and its convex approximation curve Analysis Y = holding cost X= no of days Regression equation Y = bo +b1 X Since R^2 =0.890971=90 This implies that 90% of variability in holding cost is explained by the number of days. We take null hypothesis Ho= holding cost is not dependent on no of days Alternative hypothesis Ha = holding cost is depends on no of days Now level of significance alpha=.05 From regression table p value is =1.26 *10^-5 When we compare p value with alpha, pvalue is less than alpha, therefore null hypothesis is rejected. We select alternative hypothesis that is holding cost depends on no of days. When we calculate holding cost it is increasing. We can see in the plot that holding cost is a curve rather than a straight line as assumed by classic EOQ model.

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Example 2: Spoilage Consider Amul cheese. Pack of 100 gm With T = 5 days (expected lifetime), h = 0.01/day, and a cost of 2RS /unit. Average spoilage, based on historical observations, is 5%, 7.5%, 10%, and 22.5% of the remaining stock of cheese after the second, third, fourth and fifth days respectively. Thus, cumulative spoilage cost per unit is (0.05)2RS= RS0.10 for the second day; (0.05 + 0.075)2RS = RS0.25 for the third day, and so forth. Adding the regular storage cost of RS0.01 per unit per day, we obtain the cumulative holding cost, shown in Table 2. Notice that at day 6, all cheese will be spoiled. Running a linear regression between H (T) AND t the plot is a curve. Day

%spoilage

csc

c st c

H (t)

0.01

0.01

1

0

2

5

.10

0.02

0.12

3

7.5

.25

0.03

0.28

4

10

.45

0.04

0.49

5

22.5

.90

0.05

0.95

6

55

2.0

0.06

2.06

Through linear regression y can be calculated and EOQ can be calculated. R^ 2shows significant relationship. Hence we can see that in case of perishable items holding cost is not constant. We can compute y and by using EOQ formula we can calculate how much to order to reduce total annual inventory cost.

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Analysis Y =commutative holding cost X= no of days Regression equation is Yo = bo +b1X Since R^2 is .849 =.85 This implies that 85% of variability in holding cost is explained by the number of days due to spoilage. We take hypothesis Ho= c holding cost does not depend on no of days due to spoilage Ha= c holding cost depends on no of days due to spoilage Now alpha = 0.5 P value

= 0.02

When we compare null hypothesis by alternative hypothesis p value is less than alpha therefore we select alternative hypothesis that is holding cost depend on no of days due to spoilage. When we calculate holding cost we can see that it is increasing with no of days.

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Findings The tradeoff between annual holding cost and order cost occur at EOQ order. If we order more holding cost will increase though annual order cost decreases but the overall impact is total annual inventory cost increases.

If we order less

holding cost will decrease but order cost increases effect is same total annual inventory cost increases. At EOQ total inventory cost is minimum. again we find that holding cost is not constant in case of perishable items it is not a straight line as assumed by classic EOQ model but curve.

CONCLUSION: Every store wants to minimize its inventory cost .inventory is necessary to provide expected level of customer service ,lack of inventory can will result in lost sale which will reduce profit. But inventory blocks working capital at the same time perishable item will be spoiled and causes loss. If inventory is high it blocks cash flow and working capital. inventory cost has three components material cost ,holding cost and order cost, high inventory results in higher holding cost (specially in case of perishable materials) and lower order cost, if inventory is low it reduces holding cost and increases ordering cost ,ramification is increased total inventory cost. ECONOMIC ORDER QUANTITY is that point at which trade off between inventory holding cost and annual order cost occur and total annual inventory cost is minimum. In this report we have shown that how EOQ gives minimum inventory cost (for a non perishable item). Classic economic order quantity theory assumes constant holding cost but in a real life holding cost is not constant for perishable goods it increases commutatively and we have shown that its plot is a curve due to its nature through linear regression y and other factors can be calculated and economic order quantity can be found which results in lower total annual inventory cost. 19

Reference: 1 QUANTITATIVE TECHNIQUES

J K SHARMA

2 SUPPLY CHAIN MANAGEMENT

SUNIL CHOPRA

3

JOEL D WISNER

SUPPLY CHAIN MANAGEMENT A BALANCED APPROACH

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