a project on the economic order quantity

5/25/2018 a project on the economic order quantity

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RESEARCH PROJECT:INVENTORY MODEL FOR A RETAIL

TRADING STORE

Done by

FORTUNE MUSHONGA P0113892H

Applied Mathematics Department


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Abstract

Medicinal drugs have and always will be a necessity for most if not all entities of

this world. The demand for medicinal drugs has always been high and it has

maintained its status regardless of the economic challenges that Zimbabwe has

been facing. A private owned pharmaceutical company in Zimbabwe that

supplies medicinal drugs to Bulawayo citizens. The company operates under

one management, and has been struggling to meet this demand thereby resulting

in a lot of shortages.

The EOQ model was used in this project to help in the solving such shortages. It

was discovered that the procurement manager was not keeping track of the

pharmacys inventory to make sure he orders in time before the medicinal drugs

actually run out hence making it impossible to meet demand. It was also

discovered that the company was sometimes ordering more than enough

medicinal drugs in anticipation of a high demand, thereby losing a lot of moneyin storage fees and transportation charges. The procurement manager was

sometimes ordering less medicinal drugs which were not sufficient to cater for

the demand of the product.

From calculations of the EOQ model, results were established to give the

procurement manager a guideline of how to manage the companys inventory.The results gave the amount of medication that is supposed to be ordered each

time and the level of medication that is supposed to trigger a new order (reorder

point). A conclusion was made that the model would work for this

pharmaceutical company and recommendations were made on how to implement

the results of the EOQ model.


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Acknowledgements

Special thanks Arms Trading Store, Meluleki Sihwede for allowing me to do a

research of the companys products. Great thanks also go to the Records and

Archives Manager Miss Florence Kupeta. Special thanks also go to the staff of

R.J Pharmacy in the Bulawayo, for providing the information necessary for my

project.

I would also like to thank my family members and fellow classmates, for their

help and support during the research process and also for giving me ideas on

how best to present my project. Thanks also goes to my lecturer Mr. P.

Nyamugure for his tireless efforts in teaching the concepts that were required to

be able to come up with this project, his efforts are greatly appreciated. Also I

greatly appreciate Mr. Jason for assisting me in presenting this project.

A last but not least thanks goes to the Lord Almighty for his guidance and

protection throughout the course of my study of the project.


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of units that a company should add to inventory with each order to minimize

the total costs of inventorysuch as holding costs, order costs, and shortage

costs. The EOQ is used as part of a continuous review inventory system, in

which the level of inventory is monitored at all times, and a fixed quantity is

ordered each time the inventory level reaches a specific reorder point. The

EOQ provides a model for calculating the appropriate reorder point and the

optimal reorder quantity to ensure the instantaneous replenishment of

inventory with no shortages. It can be a valuable tool for small business

owners like pharmacies who need to make decisions about how muchinventory to keep on hand, how many items to order each time, and how

often to reorder to incur the lowest possible costs.

The EOQ model assumes that demand is constant, and that inventory is depleted

at a fixed rate until it reaches zero. At that point, a specific number of items

arrive to return the inventory to its beginning level. Since the model assumes

instantaneous replenishment, there are no inventory shortages or associated

costs. Therefore, the cost of inventory under the EOQ model involves a tradeoff

between inventory holding costs (the cost of storage, as well as the cost of tying

up capital in inventory rather than investing it or using it for other purposes) and

order costs (any fees associated with placing orders, such as delivery charges).

Ordering a large amount at one time will increase a small business's holding

costs, while making more frequent orders of fewer items will reduce holding

costs but increase order costs. The EOQ model finds the quantity that minimizes

the sum of these costs.

In business management, holding cost is money spent to keep and maintain a

stock of goods in storage.


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The most obvious holding costs include rent for the required space; equipment,

materials, and labor to operate the space; insurance; security; interest on money

invested in the inventory and space, and other direct expenses. Some stored

goods become obsolete before they are sold, reducing their contribution to

revenue while having no effect on their holding cost. Some goods are damaged

by handling, weather, or other mechanisms. Some goods are lost through

mishandling, poor record keeping, or theft.

Holding cost also includes the opportunity cost of reduced responsiveness to

customers' changing requirements, slowed introduction of improved items, andthe inventory's value and direct expenses, since that money could be used for

other purposes.

Ordering costs include all the costs incurred while placing an order and receivingthe order, it does not include the actual cost of the goods. These costs include

cost of preparing the order or the invoice, the stationery used, salary of the

clerks, telephone costs etc. There is a cost involved in placing each order so

firms try to avoid ordering for items individually so what they do is that they

place the combined order for many items in one order to reduce the costs. Each

order has a fixed costs associated with it and it is independent of the number of

items in the order. If the ordering cost is C, the total demand or the number of

units required is D and the number of items in an order is Q then:

Total Ordering cost = C D/Q


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3. MethodologyMany companies in the world have experienced shortages in the products they

supply due to poor management of inventories. Other companies have suffered

losses due to large unnecessary inventories which are also due to poor

management of inventories. The application of operations research techniques in

the area of inventory management has helped the business world to gain a

competitive edge in the market.

Inventory management involves:

1.

Formulating a mathematical model describing behaviour of the inventorysystem

2. Seeking an optimal inventory policy with respect to the model.3. Use a computerised information processing system to maintain a record of

the current inventory levels

4. Using this record of current inventory levels, apply the optimal inventorypolicy to signal when and how much to replenish inventory.

Economic order quantity (EOQ) Modelis the level of inventory that

minimizes the total inventory holding costs and ordering costs. EOQ determines

the point at which the combination of order costs and inventory carrying costs

are the least. The result is the most cost effective quantity to order. In


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purchasing this is known as the order quantity, in manufacturing it is known as

the production lot size. The EOQ model is applicable where you have repetitive

purchasing or planning of an item, demand for a product is constant over the

year and each new order is delivered in full at one time when the inventory

reaches zero.

The model to be used in this particular project is called The Economic Order

Quantity Model (EOQ). The objectives of this model are to determine:

a) How much to order when the level of inventory dropsb) When to order to avoid shortages

The EOQ involves a continuous review of the following attributes:

1. Demand- This is described as the number of units that will need to bewithdrawn from inventory for some use ( e.g. Sales) during a specific

period

2. Cost of Ordering- this is the cost of ordering a given product, the costcomprises of transportation costs incurred per order. This cost is

regarded constant regardless of the order quantity.

3. Holding Cost- this figure represents all the costs associated with thestorage of the inventory until it is sold.

This project will be dwelling on all the attributes of the EOQ model to help R.JPharmacy determine how much to order to minimise its inventory costs and to

determine the reorder points to avoid shortages.

1.Formulasi. Determining how much to order when inventory level drops at the

same time minimising the total inventory costs


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I =annual holding cost rate

C = unit cost of inventory item

Ch= annual cost of holding one unit in inventory

Ch= I* C

Q= order quantity

D= Demand (constant)

Co= cost of placing one order (constant)

Annual Holding Cost= Q*Ch


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Annual Ordering Cost= (D/Q) Co

Total cost= QCh+ (D/Q) Co

Q*= Amount to order to minimize costs

ii. Determining reorder points to avoid shortagesr = reorder point d= daily demand m= lead time (Time

between inception of order and delivery)

r=d *m

Q*=2DCo/Ch


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4.Data collectionChoice of data to be collected

The main problem here is to determine the demand for different medicinal drugs

namely Antiretroviral (ARVs), Paracetamol, Antibiotics and the amount of

inventory required at the pharmacy in order to meet the established demand.

Therefore the following data is to be collected:

a)Financial accounts are prepared to acquire the opening stock, closing stock,and the damaged stock which cannot be resold or which can be sold at half

the price of the medicinal drugs.

b)Prescription forms that are used by the customers to buy some medicationc)Receipts of purchase of the medicinal drugs from various warehouses namelyDatlabs, Pharmanova and Varichem

d)Sales of the paracetamol, antibiotics and ARV medication.


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Data Analysis

RETAIL

PRODUCTS

COSTS (US$) Salt Dlite BabyCereal

Diapers

Purchase cost 0.20 7.00 0.16

Transportation cost 0.05 1.20 0.01

Total/Ordering cost 0.25 8.20 0.17

The cost of each retail product is per unit sold in Arms Trading Store


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The demand for Salt, Dlite Baby Cereal and Diapers in the 1stquarter of the year

2013 was 2503, 1058 and 645


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Calculations

Annual holding cost rate of each 1kg packet of Salt is at 10%

Annual holding cost rate of each 1kg packet of Dlite Baby Cerealis at 22%

Annual holding cost rate of each Diaper is at 8%

Unit cost per packet (C): Salt - $0.20

Dlite Baby Cereal - $7.00

Diaper - $0.16

Annual holding cost per unit cost: Ch IC

Salt: $0.20 * 0.1 =

$0.02 Dlite Baby

Cereal: $7.00 * 0.22

= $1.54

Diapers:

$0.16 * 0.08 = $0.0128

Quarter Annual demand (D)

Salt: 2503

Dlite Baby Cereal: 1058

Diapers: 645

Quarter annual Ordering cost per unit

Salt: 0.25

Dlite Baby Cereal: 8.20

Diaper: 0.17


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How much to order decision

Salt:

Q

=62575

=250.14996

=250

Dlite Baby Cereal:

Q

=26720.848

=163.46513

=163

Diapers:

Q

= 41.39180

= 41

Q*= 2DCo/Ch


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Quarter annual holding cost = Salt

QCh 0.02

= 2.5014996

= 2.50

Dlite Baby Cereal

QCh

= 125.8681501

= 125.87

Diapers

QCh =

= 0.26490752

= 0.26

Annual Ordering Cost= Co

Salt

= 2.50

Dlite Baby Cereal

= 53.07

QCh


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Diapers

= 2.65

Total Cost= QCh* Co

Salt

T.C = 2.50 + 2.50

= 5

Dlite Baby Cereal

T.C = 125.87 + 53.07

= 178.94

Diapers

T.C = 0.26 + 2.65

= 2.91

Determining reorder points to avoid shortages Re-order

point: r=dm

r = 14annual demand * daily lead time

Salt

The lead time to order salt from Fortwell Wholesalers is 2 days were 1 day is

for placing the order and the other day for processing the order and getting it

ready for collection.

r = 2503 * (2/120)

= 42

Dlite Baby Cereal


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The lead time to order antibiotics from the National Foods Harare branch which

is 4days were 1 day is for placing the order and the other 2 days for processing

the order and getting it ready for collection and the last day is for collection.

r = 1058 *(4/120)

= 35

Diapers

The lead time to order diapers from Fortwell Wholesalers is 2days were 1 day is

for placing the order and the other day for processing the order and getting it

ready for collection.

r = 645 *(2/120)

= 11

Results

From the calculations done above, the results can be shown in the followingtable:

Entity Salt Dlite Baby Cereal Diapers

Q* 250 163 41

r 42 35 11

Total Cost 5 178.94 2.91

Q*- This is the minimum order quantity, meaning that this is the amount of

medicinal drugs per packet of 20 tablets or 50millilitres that the procurement

manager needs to order each time an order for more medicinal drugs is made in

order to minimize costs incurred by the company.

r - This is the reorder point, meaning that each time the stock levels of

medicinal drugs get to this point in the pharmacy, the pharmacist is supposed to

inform the procurement manager to start ordering more medicinal drugs.


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Total CostThis is the total of those costs associated with maintaining or

carrying a given level of inventory which depend on the size of the inventory

and the costs associated with ordering the retail products.

With the results shown above it can be seen that Meluleki Sihwede is ordering

little salt than the quantity required to satisfy the demand for the salt. Also there

must be some problem with his sales person that he is not informing the him

(Meluleki Sihwede) well in time to reorder the salt when the stock levels get to

42 packets.

The same applies to Dlite Baby CerealMeluleki has been ordering a constantsupply of 80 packets which is approximately half the required amount to caterfor the demand of 163

Meluleki is ordering too many packets of the diapers. The demand is at 41

packets yet he is ordering 150 packets each month hence creating unnecessary

holding costs of storing the unsold diaper packets


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Conclusion

The conclusion thereby stands to say that R.J Pharmacy was using a poor

inventory management system resulting in some financial losses. The

procurement manager should therefore use the results in the previous chapter to

make decisions on how much to order and when to order more medicinal drugs.

This model will ensure that the pharmacy never runs out of medicinal drugs,

meaning there will always be medicinal drugs at all times for clients who want

to purchase the different types of medicinal drugs. This will increase the

companys efficiency resulting in increased customer faith and a greater

competitive edge.

The model also ensures that the costs of storing the medicinal drugs decrease.

Hence increasing the companys profits, since the costs are reduced the amount

of revenue increases.


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Recommendations

The procurement manager needs to continuously monitor the demand for

medicinal drugs because although this model is for a constant demand, it is

recommended that any changes in the demand be catered for in order to avoid

further losses. The demand is likely to increase because of the increased

customer faith resulting from better efficiency of the company, so the model

will have to be recalculated using the new figures.

The pharmacist will need to be vigilant in keeping up to date with their balances

of medicinal drugs to make sure they do not order before medicinal drugs is

needed as it may resulting in demurrage costs. Keeping up to date with their

balances of medicinal drugs will also ensure that they do not order after there isno more medicinal drugs. They should The procurement officer will also need

to be ready at all times to order more medicinal drugs so as to minimise any

delays in delivery which may cause run outs at the stations because the lead

time will have been tempered with.

R.J Pharmacy can also invest in a medicinal drugs management system that willmanage the inventory of the company. This will help the pharmacist to keep

track of how many medicinal drugs are left and be able to keep track of the

reorder point.

A manual with the results of this project must then be drafted and released in the

procurement department and the stations so that even when new employees are


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contracted by the company, they will know how to manage the inventory to

avoid losses

Appendix

Salt

DliteBabyCereal Diapers

Date

1/1/2013 4 100 32 72 38 80 6 112 42 150 20 172

1/2/2013 72 - 36 36 112 - 8 104 172 - 5 1671/3/2013 36 - 34 2 104 - 15 89 167 - 11 156

1/4/2013 2 2 0 89 - 11 78 156 - 8 148

1/5/2013 0 100 38 62 78 - 13 65 148 - 8 140

1/6/2013 62 - 35 27 65 - 10 55 140 - 10 130

1/7/2013 27 - 27 0 55 - 2 53 130 - 7 1231/8/2013 0 - 0 0 53 - 2 51 123 - 9 114

1/9/2013 0 - 0 0 51 - 1 50 114 - 6 108

1/10/2013 0 100 28 72 50 - 3 47 108 - 17 91

1/11/2013 72 - 30 42 47 80 5 122 91 - 23 68

1/12/2013 42 - 25 17 122 - 10 112 68 - 5 63

1/13/2013 17 - 14 3 112 - 8 104 63 - 4 59

1/14/2013 3 - 0 3 104 - 13 101 59 - 5 54

1/15/2013 3 100 30 73 101 - 17 84 54 - 3 51

1/16/2013 73 - 21 52 84 - 20 64 51 - 6 45

1/17/2013 52 - 0 52 64 - 9 55 45 - 3 42

1/18/2013 52 - 0 52 55 - 11 44 42 - 0 42

1/19/2013 52 - 42 10 44 - 5 39 42 - 0 42

1/20/2013 10 100 33 77 39 - 4 35 42 - 0 421/21/2013 77 - 25 52 35 80 8 107 42 - 0 42

1/22/2013 52 - 27 25 107 - 12 105 42 - 1 41

1/23/2013 25 - 0 25 105 - 34 71 41 - 0 41

1/24/2013 25 - 15 10 71 - 3 68 41 - 0 41

1/25/2013 10 100 0 110 68 - 4 64 41 - 0 41


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1/26/2013 110 - 17 93 64 - 10 54 41 - 2 39

1/27/2013 93 - 20 73 54 - 7 47 39 - 1 38

1/28/2013 73 - 29 44 47 - 9 38 38 - 1 37

1/29/2013 44 - 36 8 38 - 0 38 37 - 0 37

1/30/2013 8 100 34 74 38 - 5 33 37 - 0 371/31/2013 74 - 30 44 33 80 7 106 37 - 1 36

2/1/2013 44 - 26 18 106 - 5 101 36 150 25 186

2/2/2013 18 - 0 18 101 - 9 92 186 - 21 165

2/3/2013 18 100 20 98 92 - 7 85 165 - 18 147

2/4/2013 98 - 18 80 85 - 5 80 147 - 11 136

2/5/2013 80 - 26 54 80 - 10 70 136 - 4 1322/6/2013 54 - 34 20 70 - 10 60 132 - 6 1262/7/2013 20 - 17 3 60 - 4 56 126 - 7 1192/8/2013 3 100 20 83 56 - 5 51 119 - 17 1022/9/2013 83 - 23 60 51 - 9 42 102 - 15 87

2/10/2013 60 - 24 36 42 - 11 31 87 - 10 77

2/11/2013 36 - 20 16 31 80 11 110 77 - 8 69

2/12/2013 16 - 11 5 110 - 8 102 69 - 7 62

2/13/2013 5 100 15 90 102 - 9 93 62 - 3 59

2/14/2013 90 - 20 70 93 - 7 86 59 - 2 57

2/15/2013 70 - 25 45 86 - 6 80 57 - 3 54

2/16/2013 45 - 23 22 80 - 5 75 54 - 1 53

2/17/2013 22 - 22 0 75 - 10 65 53 - 1 52

2/18/2013 0 100 20 80 65 - 8 57 52 - 2 50

2/19/2013 80 - 24 56 57 - 7 50 50 - 1 492/20/2013 56 - 22 34 50 - 5 45 49 - 3 46

2/21/2013 34 - 17 17 45 80 6 119 46 - 1 45

2/22/2013 17 - 17 0 119 - 16 113 45 - 0 45

2/23/2013 0 100 19 81 113 - 7 106 45 - 1 44

2/24/2013 81 - 21 60 106 - 9 97 44 - 3 41

2/25/2013 60 - 20 40 97 - 10 87 41 - 1 40

2/26/2013 40 - 17 23 87 - 15 72 40 - 4 36

2/27/2013 23 - 15 8 72 - 3 69 36 - 0 362/28/2013 8 100 18 90 69 - 7 62 36 150 30 1563/1/2013 90 - 20 70 62 - 7 55 156 - 25 131

3/2/2013 70 - 23 47 55 - 15 40 131 - 33 983/3/2013 47 37 10 40 - 20 20 98 - 17 81

3/4/2013 10 100 26 84 20 80 22 78 81 - 29 52

3/5/2013 84 - 24 60 78 - 12 66 52 - 10 42

3/6/2013 60 - 21 39 66 - 14 62 42 - 7 353/7/2013 39 - 16 23 62 - 8 54 35 - 5 30

3/8/2013 23 - 13 10 54 - 11 43 30 - 0 30


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3/9/2013 10 100 10 100 43 - 9 34 30 - 0 30

3/10/2013 100 - 12 88 34 - 7 27 30 - 0 30

3/11/2013 88 - 14 74 27 - 5 22 30 - 0 30

3/12/2013 74 - 19 55 22 - 6 16 30 - 0 30

3/13/2013 55 - 29 26 16 - 0 16 30 - 0 303/14/2013 26 100 26 100 16 80 7 89 30 - 0 30

3/15/2013 100 - 21 79 89 - 9 80 30 - 1 29

3/16/2013 79 - 23 56 80 - 5 75 29 - 0 293/17/2013 56 - 20 36 75 - 6 69 29 - 0 293/18/2013 36 - 17 19 69 - 7 62 29 - 2 273/19/2013 19 100 21 98 62 - 5 57 27 - 0 27

3/20/2013 98 - 23 75 57 - 5 52 27 - 0 27

3/21/2013 75 - 25 50 52 - 6 46 27 - 0 27

3/22/2013 50 - 22 28 46 - 4 42 27 - 0 27

3/23/2013 28 - 17 11 42 - 5 37 27 - 0 27

3/24/2013 11 100 15 95 37 80 0 117 27 - 0 27

3/25/2013 95 - 17 78 117 - 7 110 27 - 0 273/26/2013 78 - 20 58 110 - 3 107 27 - 0 27

3/27/2013 58 - 21 37 107 - 4 103 27 - 0 27

3/28/2013 37 - 28 9 103 - 5 98 27 - 0 27

3/29/2013 9 100 25 84 98 - 7 91 27 - 0 27

3/30/2013 84 - 30 54 91 - 4 87 27 150 23 154

3/31/2013 54 - 23 31 87 - 5 82 154 - 30 124

4/1/2013 31 - 24 7 82 - 3 79 124 - 34 90

4/2/2013 7 100 21 86 79 - 5 74 90 - 11 794/3/2013 86 - 23 63 74 80 10 144 79 - 13 664/4/2013 63 - 26 37 144 - 10 134 66 - 6 60

4/5/2013 37 - 22 15 134 - 7 127 60 - 3 57

4/6/2013 15 - 15 0 127 - 5 122 57 - 1 56

4/7/2013 0 100 20 80 122 - 8 114 56 - 2 54

4/8/2013 80 - 17 63 114 - 5 109 54 - 1 53

4/9/2013 63 - 21 42 109 - 4 105 53 - 0 53

4/10/2013 42 - 17 25 105 - 7 98 53 - 0 534/11/2013 25 - 19 6 98 - 6 92 53 - 2 514/12/2013 6 100 21 85 92 - 12 80 51 - 0 514/13/2013 85 - 22 63 80 - 14 66 51 - 0 51

4/14/2013 63 - 21 42 66 80 10 136 51 - 0 51

4/15/2013 42 - 20 22 136 - 14 132 51 - 1 50

4/16/2013 22 - 17 5 132 - 6 126 50 - 3 47

4/17/2013 5 100 15 90 126 - 8 118 47 - 4 424/18/2013 90 - 18 72 118 - 7 111 42 - 3 394/19/2013 72 - 20 52 111 - 20 91 39 - 2 37


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4/20/2013 52 - 19 33 91 - 25 66 37 - 1 36

4/21/2013 33 - 26 7 66 - 32 34 36 - 4 32

4/22/2013 7 100 34 73 34 - 30 4 32 - 1 31

4/23/2013 73 - 30 43 4 - 4 0 31 - 0 31

4/24/2013 43 - 33 10 0 80 28 52 31 - 2 294/25/2013 10 - 10 0 52 - 34 18 29 - 3 26

4/26/2013 0 - 0 0 18 - 18 0 26 - 1 25

4/27/2013 0 100 36 64 0 - 0 0 25 - 1 24

4/28/2013 64 - 38 26 0 - 0 0 24 - 1 23

4/29/2013 26 - 26 0 0 - 0 0 23 - 1 224/30/2013 0 - 0 0 0 - 0 0 22 150 1 172

References

David Piasecki,Inventory Management Explained, March 2009

James H. Greene, American Production and Inventory Control Society,Production and Inventory Control Handbook, McGraw-Hill, January 1996

Richard J, Tersine, Principles of Inventory and Materials Management, PTRPrentice Hall, August 1993
http://inventoryexplained.com/http://inventoryexplained.com/http://inventoryexplained.com/http://www.amazon.com/exec/obidos/ASIN/0070244286/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0070244286/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0070244286/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0134578880/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0070244286/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0070244286/inventoryopsc-20http://www.amazon.com/exec/obidos/ASIN/0070244286/inventoryopsc-20http://inventoryexplained.com/http://inventoryexplained.com/http://inventoryexplained.com/

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