eoq gaurang

8/3/2019 eoq gaurang

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Abstract- Economic order quantity is the level of inventory that minimizes total inventory

holding costs and ordering costs. It is one of the oldest classical productionscheduling models. The framework used to determine this order quantity is alsoknown as Wilson EOQ Modelor Wilson Formula. The model was developed by FordW. Harris in 1913.

EOQ applies only when demand for a product is constant over the year and eachnew order is delivered in full when inventory reaches zero. There is a fixed cost foreach order placed, regardless of the number of units ordered. There is also a costfor each unit held in storage, sometimes expressed as a percentage of thepurchase cost of the item.

We want to determine the optimal number of units to order so that we minimizethe 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, thepurchase cost for each item, the fixed cost to place the order and the storage costfor each item per year. Note that the number of times an order is placed will alsoaffect the total cost, though this number can be determined from the otherparameters.


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Economic Order QuantityDefinition of EOQ

AssumptionHow to use the EOQ model in a business

organization

How the EOQ model works

Real world example


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EOQ or Economic Order Quantity, isdefined as the optimal quantity oforders that minimizes total variablecosts required to order and holdinventory.


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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 orderingcost + carrying cost finds its minimum. (Acommon misunderstanding is that the formulatries to find when these are equal.)


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How much inventoryshould we order each month? The EOQ tool can be usedto model the amount ofinventory that we shouldorder each month.


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Profile of Inventory Level Over TimeQuantityon hand

Q

ReceiveorderPlaceorder Receiveorder Placeorder Receiveorder

LEAD TIME

Reorderpoint

Usagerate

Time


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The Principles Behind EOQ:Holding costsHow EOQ Works

Keeping inventory on hand

Interest

Insurance

Taxes

TheftObsolescence


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The Principles Behind EOQ: The Holding CostsHow EOQ Works

Interest

Obsolescence

Storage


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The Principles Behind EOQ:Procurement costsHow EOQ Works

Primarily the labor costsassociated with processingthe order:Ordering

A portion of the freight ifthe amounts vary according

to the size of the order

Receiving, inspecting,stocking


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Total Cost = Purchase Cost + Order Cost + Holding Cost


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This represents theunchanging fixed costsP = Purchase cost per unitR = Forecasted monthly usage


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This represents thevariable order costsP = Purchase cost per unitR = Forecasted monthly usageC = Cost per order event (not per unit)Q = The number of units ordered


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This represents thevariable holding costsP = Purchase cost per unitR = Forecasted monthly usageC = Cost per order event (not per unit)Q = The number of units orderedF = Holding cost factor


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Taking the derivative of both sides of the equation and setting

equal to zero to find the minimum value of the function, one

obtains.


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The result of differentiation

The Economic Order Quantity


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Review and Summary of the EOQ Formula

P = Purchase cost per unitR = Forecasted monthly usageC = Cost per order event (not per unit)F = Holding cost factor


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eoq gaurang

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