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'''Economic order quantity''' is the order quantity that minimizes total inventory holding costs and ordering costs. It is one of the oldest classical production scheduling models. The framework used to determine this order quantity is also known as  '''Wilson EOQ Model''' or '''Wilson Formula'''. The model was developed by Ford W. Harris in 1913,<ref>{{cite jstor|170962}}</ref> but R. H. Wilson, a consultant who applied it extensively, is given credit for his in-depth analysis.<ref name=Hax1984>{{Citation
| title = Production and Operations Management
| url = http://catalogue.nla.gov.au/Record/772207
| year = 1984
| author = Hax, AC and Candea, D.
| publisher = Prentice-Hall, Englewood Cliffs, NJ
| pages = 135
}}</ref>
 
==Overview==
EOQ applies only when demand for a product is constant over the year and each new order is delivered in full when inventory reaches zero. There is a fixed cost for each order placed, regardless of the number of units ordered. There is also a cost for each unit held in storage, commonly known as [[holding cost]], sometimes expressed as a percentage of the purchase cost of the item.
 
We want to determine the optimal number of units to order so that we minimize the total cost associated with the purchase, delivery and storage of the product.
 
The required parameters to the solution are the total demand for the year, the purchase cost for each item, the fixed cost to place the order and the storage cost for each item per year. Note that the number of times an order is placed will also affect the total cost, though this number can be determined from the other parameters.
 
==Underlying assumptions==
# The ordering cost is constant.
# The rate of demand is known, and spread evenly throughout the year.
# The [[lead time]] is fixed.
# The purchase price of the item is constant i.e. no discount is available
# The replenishment is made instantaneously, the whole batch is delivered at once.
# Only one product is involved.
EOQ is the quantity to order, so that the sum of ordering cost and holding cost is at its minimum. These costs will be equal to one another at the minimized cost point.
 
==Variables==
*<math>c</math> = purchase price, unit production cost
*<math>Q</math> = order quantity
*<math>Q^*</math> = optimal order quantity
*<math>D</math> = annual demand quantity
*<math>K</math> = fixed cost per order, setup cost (''not'' per unit, typically cost of ordering and shipping and handling. This is not the cost of goods)
*<math>h</math> = annual holding cost per unit, also known as carrying cost or storage cost (capital cost, warehouse space, refrigeration, insurance, etc. usually not related to the unit production cost)
 
==The Total Cost function==
The single-item EOQ formula finds the minimum point of the following cost function:
 
Total Cost = purchase cost or production cost + ordering cost + holding cost
 
- Purchase cost: This is the variable cost of goods: purchase unit price &times; annual demand quantity. This is c &times; D
 
- Ordering cost: This is the cost of placing orders: each order has a fixed cost K, and we need to order D/Q times per year. This is K &times; D/Q
 
- Holding cost: the average quantity in stock (between fully replenished and empty) is Q/2, so this cost is h &times; Q/2
 
<math>TC = cD + {\frac{DK}{Q}} + {\frac{hQ}{2}}</math>.
 
To determine the minimum point of the total cost curve, partially differentiate the total cost with respect to Q (assume all other variables are constant) and set to 0:
 
<math>{0} = -{\frac{DK}{Q^2}}+{\frac{h}{2}}</math>
 
Solving for Q gives Q* (the optimal order quantity):
 
<math>Q*^2={\frac{2DK}{h}}</math>
 
Therefore: <math>Q^* = \sqrt{\frac{2DK}{h}} </math>.
 
Q* is independent of c; it is a function of only K, D, h.
 
The optimal value Q* may also be found by recognising that<ref>{{Cite journal | last1 = Grubbström | first1 = Robert W. | doi = 10.1016/0925-5273(95)00109-3 | title = Modelling production opportunities — an historical overview | journal = International Journal of Production Economics| volume = 41| pages = 1–14 | year = 1995}}</ref>
 
 
<math>TC = {\frac{DK}{Q}} + {\frac{hQ}{2}} + cD ={\frac{h}{2Q}}(Q - \sqrt{2DK/h})^2 +  \sqrt{2hDK} +cD,  </math>
where the non-negative quadratic term disappears for <math>Q = \sqrt{2DK/h}, </math> which provides the cost minimum <math>TC_{min} =  \sqrt{2hDK} + cD. </math>
 
==Extensions==
Several extensions can be made to the EOQ model, including backordering costs and multiple items. Additionally, the [[economic order interval]] can be determined from the EOQ and the [[economic production quantity]] model (which determines the optimal production quantity) can be determined in a similar fashion.
 
A version of the model, the [[Baumol-Tobin]] model, has also been used to determine the [[Money_demand#Inventory_models|money demand]] function, where a person's holdings of money balances can be seen in a way parallel to a firm's holdings of inventory.<ref name=jep>Andrew Caplin and John Leahy, "Economic Theory and the World of Practice: A Celebration of the (S,s) Model", ''[[Journal of Economic Perspectives]]'', Winter 2010, V 24, N 1</ref>
 
==Example==
 
*Suppose annual requirement quantity (D) = 10000 units
*Cost per order (K) = $2
*Cost per unit (c)= $8
*Carrying cost percentage (h/c)(percentage of c) = 0.02
*Annual carrying cost per unit (h) = $0.16
 
Economic order quantity = <math> \sqrt{\frac{2D*K}{h}} </math> <math> = \sqrt{\frac{2*10000*2}{8*0.02}} </math> = 500 units
 
Number of orders per year (based on EOQ) <math> = {\frac{10000}{500}} = 20 </math>
 
Total cost <math> = c*D + K (D/EOQ) + h (EOQ/2) </math>
 
Total cost <math> = 8*10000 + 2 (10000/500) + 0.16 (500/2) = $80080 </math>
 
If we check the total cost for any order quantity other than 500(=EOQ), we will see that the cost is higher.  For instance, supposing 600 units per order, then
 
Total cost <math> = 8*10000 + 2 (10000/600) + 0.16 (600/2) = $80081 </math>
 
Similarly, if we choose 300 for the order quantity then
 
Total cost <math> = 8*10000 + 2 (10000/300) + 0.16 (300/2) = $80091</math>
 
This illustrates that the Economic Order Quantity is always in the best interests of the entity.
 
==See also==
* Demand is random: Classical [[Newsvendor model]]
* Demand varies over time: [[Dynamic lot size model]]
* Several products produced on the same machine: [[Economic Lot Scheduling Problem]]
* [[Reorder point]]
 
==References==
<references/>
 
==Further reading==
* Harris, Ford W. ''Operations Cost'' (Factory Management Series), Chicago:  Shaw (1915).
* Wilson, R. H. "A Scientific Routine for Stock Control" Harvard Business Review, 13, 116-128 (1934).
 
==External links==
*[http://www.logisitik.com/learning-center/inventory-management/item/466-economic-order-quantity-eoq-model.html The EOQ Model]
* http://www.inventoryops.com/economic_order_quantity.htm
* [https://play.google.com/store/apps/details?id=com.matterofbiz.simple.eoq.calculator Simple EOQ Calculator for Android devices]
 
{{DEFAULTSORT:Economic Order Quantity}}
[[Category:Management]]
[[Category:Production and manufacturing]]
[[Category:Supply chain management]]
[[Category:Operations research]]
[[Category:Production economics]]
 
[[de:Klassische Losformel]]

Latest revision as of 16:21, 11 December 2014

If you are having difficulties getting pregnant and are considering seeking help getting pregnant, most experts believe you should wait one year before doing so unless you are 35 years or older. Do we require to keep on obtaining possibly a lot more, or less, ordinary sex. penis enters the woman's vagina and ejaculation of sperm occurs. This will assist you time your fertile period far better to ensure that it is possible to boost your chances of conceiving naturally. If you've searched for them in i - Tunes then you know what I'm talking about.

He can also look in the vagina to determine if you'll find any problems. This is your best time if youre trying to get pregnant. While toxoplasmosis is generally mild to the mother, it can cause serious complications in the fetus. One of the foods you can eliminate from your diet right now to immediately give a boost to your fertility levels are peas. There is just no way to tell for sure when it is safe to have sex without protection throughout the month.

So it's vital to know what to consume, and what not to consume. Herbal treatments are most effective for enhancing your Qi balance, with more than 150 herbs used in treatments for fertility issues. The ones who decide to give their child up for adoption, are able to help a family who can't have a child of their own and still have their adolescence years. Many couples think that in order to get pregnant, all that has to be done is to merely stop the pill or any other form of contraception. There are also numerous herbs that are mentioned to enhance fertility for males and females.

The folic acid (vitamin Bc) should be taken by any future mother. It is caused by not enough estrogen to stimulate the production of cervical mucus which are friendly to sperm invasion. Failing to conceive after so many attempts at ferility treatment can takes its toll physically and emotionally. I hope that you have found these tips on getting pregnant:now. Sexual Relations Position: - Position sex suggested these may increase the likelihood of pregnancy occurring.

The third and doubtless most correct technique to know when you will ovulate is to make use of an ovulation predictor kit. Specialists exclaim that it's innocent for women to have up to 12 ounces of low mercury fish per week. The reproductive organs of our bodies are in best shape when we are young. Some natural solutions can also help you to enhance your fertility in a natural manner without causing any harmful side effects on the patient's body. Since every female is different from one another, this includes her hormone balance which in turn affects her period cycles, there is no exact science saying when a woman is fertile and when one is not.

Should you have any kind of issues relating to exactly where along with the best way to employ what to take to get pregnant fast, you possibly can call us on our own page.