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1. PURCHASE COST.
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2. CAPITAL COST.
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3. ORDERING COST.
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4. INVENTORY CARRING COST.
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5. SHORTAGE COST.
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1. Demand : Number of items required per unit time.
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2. Order Cycle : The time period b/w two successive order.
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3. Lead Time : The time gap b/w placing a order & received the
item.
4. Safety stock : This is the buffer stock for overcome
uncertainties.
5. Re-order level : When the stock level reaches re-order level
new order issued.
6. Re-order quantity : This is the quantity of material to be
ordered in ROL.
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Let, D = Annual demand.
C0 = Order cost.
Ch = Inventory carrying cost.
Cp = Price per unit.
Q = Quantity order.
Q* = Economic order quantity.
N = Number of order placed per year.
Tc = Total cost per annum.
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Annual ordering cost = No. of orders * ordering cost / order.
= Annual demand / order quantity * ordering cost / order.
= D / Q * C0 …………..(i)
Annual inventory carrying cost = Avg. Inventory investment * inventory
carrying cost.
= (Max Inventory – Min Inventory ) / 2 * Inventory carrying cost .
= Q / 2 * Ch..................(ii)
Annual Total Cost = Annual ordering cost + Annual Inventory cost.
= DCo / Q + QCh /2 ………….(iii)
To determine EOQ differentiate Annual Total Cost eq (iii) we got,
dTC / dQ = -d DCo / Q²
So, Q² = 2DCo / Ch
Q* = √ 2DCo / Ch ( Q* = economic order quantity).
If inventory carrying cost is expressed as a % of annual avg. inventory
investment then,
Q* = √ 2DCo / Cp.I
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1. Optimal number of order placed (N*) = D / Q*
2. Optimal time diff b/w two order (T*)
= no. of working days / N*
3. Minimum total yearly inventory cost (Tcm)
= √ 2 D . Co. Ch
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A co. has got a demand for particular part at 10,000 units per year. The cost per unit is
Rs. 2 & it costs Rs. 36 to place an order and to process the delivery. The inventory
carrying cost is estimated at 9% of average inventory investment. Determine
(i) Economic order quantity.
(ii) Optimum no. of orders placed per annum.
(iii) Minimum total cost of inventory per annum.
Sol : (i) EOQ ( Q*)= √ 2DCo / Cp.I
= √ 2 . 10,000 . 36 / 2 . 0.09
= 2000 units.
(ii) Optimum no. of order = D / Q*
= 10,000 / 2000 = 5
(iii) Total annual inventory cost = Ordering cost + Inventory carrying cost
= 2 * Ordering cost ( at EOQ Ordering cost=carrying cost)
= 2 . D / Q* . Co
= 2 . 5 . 36 = 360 .