COMPARISON OF EOQ AND JIT PURCHASING

POLICIES

SHIBIN KT

CLASS NO: 423

S7 INDUSTRIAL

Guided by:Guided by:Regi KumarRegi KumarLecturerLecturer

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OBJECTIVE OF STUDY

Ultimate aim of this study is to expand on two concepts namely the annual holding capacity of an inventory facility, and the break-even point between the annual holding capacity of an inventory facility and the EOQ-JIT cost indifference point, where price discount is available for EOQ system.

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INTRODUCTION• Successful implementation of JIT

purchasing policy in various industries has promoted many companies that still use EOQ purchasing system to ponder whether they should switch to JIT purchasing policy.

• An EOQ-JIT cost indifference point (ie, the level of demand at which the total cost were same) existed between EOQ & JIT systems.

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INTRODUCTION…

• JIT purchasing system is more convenient than EOQ.JIT has the advantage of physical plant square meter reduction.

• So, is it possible for an EOQ system to be more cost effective than a JIT system??

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INTRODUCTION…

Schniedersans and Cao considered “Physical Plant Space” factor in their studies. They suggested JIT is preferable than EOQ at any level of demand. They failed to empirically ascertain the capability of an inventory facility.

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INTRODUCTION…

EOQ price discount model can be categorized into two scenarios where the optimal order quantity is above or below Qmax, the maximum quantity that can be purchased and still receive a quantity discount rate ∏E.

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EOQ with price discount model

TCE= KD + Qh + (PẾ - ∏E Q) D θ 2

Total ordering cost

Total holding cost

Cost of actual purchased unit

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TCE= KD + Qh + (PẾ - ∏E Q) D θ 2

• PẾ = Purchase price / unit

• θ = Fixed order quantity

• K = Cost of planning an order

• D = Demand

• h = Holding cost of one unit for one year

• Qmax = Maximum quantity that can be purchased and still receive a quantity discount

with rate ∏E.

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TCE= KD + Qh + PẾmin D θ 2 for Q›Qmax

PẾmin = Minimum constant purchase price

Optimum order quantity Q* = √2KD/h-2∏ED

when Q*‹ Qmax

When Q*›Qmax, Q** = √2KD/h

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Ultimate EOQ-JIT Cost Indifference

Point The annual demand at which the

inventory can be accommodated by the existing inventory facility and at which the total annual cost under the EOQ system equals the total cost under the JIT system.

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Modify Schniederjans & Cao EOQ-JIT cost indifference point.

Derivation of the function of the annual holding capacity of an inventory facility

Derivation of the break-even point between the annual holding capacity of an inventory facility

and the EOQ-JIT cost indifference point

Derivation of ultimate EOQ-JIT cost indifference point.

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MODIFIY SCHNIEDERJANS & CAO EOQ-JIT COST INDIFFERENCE

POINT.

TCE = kD √h-2∏ED/2KD +

h/2 √2KD/h-2∏ED +

(PẾ - ∏E √2KD/h-2∏ED )K = Cost of placing an order

Substituted Q* instead of Q

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TCJ = PJD-FN• PJ = Unit price under JIT system

• D = Annual Demand

• F = the annual cost to own and maintain a square meter of physical plant space.

• N = Number of square meters of physical plant space saved by adopting a JIT system.

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REVISED COST INDIFFERENCE POINT

• For comparison,

• Z=Total optimal annual cost under

EOQ system - Total cost under JIT system

• Root of the above equation gives the revised cost indifference point as:-

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Dinds= FN(PJ-PẾ) + Kh +

√k²h² + 2Kh(PJ-PẾ)FN-

4∏EKF²N² (PJ-PẾ)² + 4∏EK

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N= NE-NJ

NE = Square meter of an inventory facility under EOQ system

NJ = Square meter of an inventory facility under JIT system.

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Dinds= FNE(PJ-PẾ) + Kh +

√k²h² + 2Kh(PJ-PẾ)FNE-

4∏EKF²NE² (PJ-PẾ)² + 4∏EK

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ANNUAL HOLDING CAPACITY OF AN INVENTORY FACILITY• The number of inventory that can be

held by the inventory facility at a specified time.

• Qh=NE/α• NE=Number of square meters of an

inventory facility• α=square meters occupied by unit

inventory

• It is assumed that size of inventory facility is b times the size which holds the optimal order quantity:-

Qh=bQ*• So, NE=ɑbQ*

• Since Q*<Qmax• NE should be limited up to

ɑbQmax:-

NE<ɑbQmax19

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By substituting the value of NE in annual demand function; we will get

Dh safe = bNE²

2Kb²α² + 2∏ENE²

Di ≤ Dh Safe

Di= Cost indifference point

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BREAK EVEN POINT1. The break even point between the

annual holding capacity of an inventory facility & EOQ-JIT cost indifference point is (Neq, Deq)

2. Y = Annual holding capacity of an inventory facility - EOQ-JIT cost indifference point.ie;Dh safe-Dind

3. Setting Y = 0. The root of the eqn will be the break even point represented by square meter of an inventory facility.

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4. Neq= The break-even point represented by the square meter of an inventory facility for order quantity below Qmax.

5. By substituting the value of Neq, value of Deq can be foundout.

6. Deq= Break even point represented by the annual demand of an inventory for order quantity below Qmax.

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Ultimate EOQ-JIT Cost indifference point for order quantity below Qmax

• NE ‹ αb Qmax

• NE ≥ Neq

• Dui = [(PJ-PẾ) FNE + Kh] +

√k²h² + 2 (PJ-PẾ) FNEKh-

4∏EKF²NE² (PJ-PẾ)² + 4∏EK

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Order quantity above Qmax

1. Minimum purchase price PEmin will remain constant.

2. ∏E, discount rate = 0.

3.NE › αb Qmax. Since Q* › Qmax

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EOQ-JIT cost indifference point when Q*>Qmax

NE ≥ Neq** = 2 αb (⍺bF+h)

(PJ – PEmin)hDui** = [(PJ-PEmin) FNE + Kh] +

√2(PJ-PEmin) FNEKh+ K²h²

(PJ-PEmin)²

• Survey showed that among all the RMC suppliers surveyed ; approximately 60% of them purchased cement using the JIT system.

• Because their demand volume was too low , ordering cost were high.

• 40% of the users were engaged in cement business. so their demand volume was high.

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SURVEY

CASE STUDY DATAS

• Q max= 10000 tones• Order quantity = 40000 tones/order• Q**= 35829 tones• NE= 5600 meter square

• Neq= 5016meter square• Deq= 476930 tones• Dui**= 480646 tones

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1. Since,NE>Neq;

Dui**>Deq

EOQ IS PREFFERED

2. Routine order quantity = 40000 tons/order.

Capacity of carrier in JIT System = 1500 tons.

EOQ IS PREFFERED

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Conclusion of CASE STUDY & SURVEY

• The selling price of a product will usually drop during an economic slump , thus causing the JIT companies into liquidation.

• EOQ companies can still make profit from selling raw materials.

• EOQ companies can supply raw materials to the small and medium sized JIT companies and can control the market price to some extent.

• It is better for larger companies whose inventory ordering sizes can’t be economically split to adapt EOQ system of smaller and medium size companies to adapt JIT system.

• By adopting JIT system smaller companies can operate faster, eliminate waste, maintenance of large storage facilities.

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CONCLUSION• Analysis showed that, if the order quantity is

below Qmax, it is possible for an EOQ system to be more cost effective than a JIT system, if the break even point Neq is less than αbQmax.

• If the ordering quantity is above Qmax, EOQ system is more cost effective, when the annual demand reaches the demand at break even point.

• So EOQ can be more cost effective than JIT system.

REFERENCES• Wu Min, “EOQ, JIT and fixed costs in the ready-

mixed concrete industry”, Int. J. Production Economics, Vol 2, No. 4, 2006, pp. 167–180.

• Cao, Q., Schniederjans, M.J., 2004. “A revised EMQ/JIT production-run model: An examination of inventory and production costs”. International Journal of Production Economics 87 (1), 83–95.

• Marc J. Schniederjans, “A note on JIT purchasing vs. EOQ with a price discount: An expansion of inventory costs.

• www.sciencedirect.com• www.google.in

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