Numerical Problem on Economic Order Quantity (EOQ)

A manufacturing company consumes 12,000 units of a specific component annually. The cost per unit is $50. The ordering cost is $100 per order, and the annual carrying cost is estimated at 12% of the average inventory value. 

Task: Calculate the EOQ and the Total Variable Cost (excluding material cost).

Solution:

Given,

Annual Demand (D)		= 12000 Units
Ordering cost (S) 		= $100
Unit cost (C) 			= $50
Holding Cost (H) : 12% of Average Inventory Value ( Cost per unit)
				= 0.12 * 50 = $6 per unit/year

EOQ CALCULATIONS

EOQ = √((2✕D✕S)/H) = √((2✕12000✕100/6) = √(400,000) ≍ 632.46 units


TOTAL VARIABLE COST (TVC)

TVC =((D/EOQ))✕S) +((Q/2)✕H) = ((12000/632.46)✕100) +( (632.46/2)✕6)) ≍  1897.37+1897.38 
≍ $3794.75

A retailer currently orders 2,500 units of a product four times a year. The annual demand is 10,000 units. The cost to place an order is $100, and the holding cost is $5 per unit per year. 

Task: Determine how much the retailer could save annually by switching to the EOQ model.

Solution:

Given,

Annual Demand (D)		= 10000 Units
Ordering cost (S) 		= $100
Holding cost (H) 		= $5

Current Order Policy (Q)	= 2500 units

Total Variable Cost at Q 

=((D/Q))✕S) +(Q/2)✕H
= ((10000/2500)✕100) +((2500/2)✕5) 
=  400+6250
= $ 6,650

EOQ Calculation

EOQ 	=√((2✕D✕S)/H) = √((2✕10000✕100/5) = √(400,000)
	= 632.46 units

Total Variable Cost at EOQ 

=((D/EOQ)✕S) +((EOQ/2)✕H)
= ((10000/632.46)✕100) +( 632.46/2✕5) 
=  1581.14+1581.14
= $ 3162.28

Annual Savings = $ 6650-3162.28 = $ 3487.72

If D = 5,000 units/year, S = $49, i = 20%. Find the best order quantity:

1. 0 – 999 units: $5.00
2. 1,000 – 1,999 units: $4.80
3. 2,000 units and above: $4.75

Solution:

Calculating EOQ at Cost per unit @ $4.75

Holding Cost 		= 20% of Cost per unit
			= 0.20* $4.75
			= 0.95

EOQ = √((2✕D✕S)/H) = √((2✕5000✕49/0.95) ≍ 718.18 Units

Since 718 < 2,000, we must check the price break at Q = 2,000

Calculating EOQ at Cost per unit @ $4.80

Holding Cost 		= 20% of Cost per unit
			= 0.20* $4.80
			= 0.96

EOQ = √((2✕D✕S)/H) = √((2✕5000✕49/0.96) ≍ 714.43 Units

Since 714 < 1,000, we must check the price break at Q = 1000

Now, Calculating Total Cost at Q= 1000 units

Total Cost 	=(D/Q✕S) +(Q/2)✕H +D✕Cost per unit
		=(50001000✕49) +(1000/2)✕0.96+5000✕4.8
		= 245 +480 + 24000
		= $ 24,725

Now, Calculating Total Cost at Q= 2000 units

Total Cost 	=(D/Q)✕S) +(Q/2)✕H +D ✕ Cost per unit
		=((5000/2000))✕49) +(2000/2)✕0.95+5000✕4.75
		= 122.5+950 + 23750
		= $ 24,822.50

Since the Total Cost @ 2000 units is more, the optimal order quantity is 1000 units.

A factory produces its own parts. Annual demand is 10,000 units. The machine produces 20,000 units per year. Setup cost is $200 and holding cost is $2/unit/year. Task: Calculate the EBQ (EPQ) and the maximum inventory level.

Solution

Given,


Annual Demand (D)	= 10,000 Units
Ordering cost (S) 		= $200
Holding cost (H) 		= $2
Production Rate (P)		= 20,000 units

For EBQ,

EBQ =√(2✕D✕S)/(H✕(1-D/P)) =√((2✕10000✕200)/(2✕(1-10000/20000)) = √((400000/(2✕0.5)) = 2,000 units

For, Max Inventory Level,

I(max) = EBQ ✕ (1-D/P) 
	= 2000 ✕ (1-0.5)
	= 1000 units