Soal
Review sistem persediaan
Calculate EOQ
Qeoq =
2DS
=
H
2(Annual Demand)(Order or set-up cost)
Annual Holding Cost
when to place an order.
Reorder point R=DL
D = Avg daily demand (constant)
L = Lead time (constant)
Exercise EOQ and reorder point?
•Annual demand = 2,000 units
•Days/year in average daily demand = 365
•Cost to place an order = £10
•Holding cost /unit p.a. = £2.50
•Lead time = 7 days
•Cost per unit = £15
EOQ Solution
Q eoq =
2DS
=
H
2(1,000 )(10)
2.50
= 89.443 units or 90 units
1,000 units p.a.
d =
= 2.74 units/day
365 days p.a.
Reorder point
D L = 2.74 units/day = 19.18 or 20 for 7 day lead time
EOQ order = 90 units.
When only 20 units left, place next order for 90 units.
EOQ and ROQ example 2
Annual Demand = 10,000 units
Days per year considered in average daily demand = 365
Cost to place an order = £10
Holding cost per unit per year = 10% of cost per unit
Lead time = 10 days
Cost per unit = £15
2DS
Q
=
eoq
H
2(10,000)(10)
=
1.50
D=
= 365.148 (366 units)
10,000 units/year
365 days
= 27.397 units/day
If lead time = 10 days, ROL= 273.97 = 274 units
Place order for 366 units. When 274 left, place next order for 366.
Total variable cost
Avg.stock
Demand
2
x unit cost x Hc% + Oc
Once per year
1200
2
x £3 x 25% = £450 + £10
= £460
Once per week
1200/52 x £3 x 25% = £9 + £510
2
= £519 approx
Find point of minimum TVc
EOQ Table – minimum TVc
Avg.stock x item £ x hc %
Oc + Hc
Item £ 3
Holding cost % =
25%
No. of Quantity Order Average Holding Total
orders Ordered cost
stock
cost
cost
1
1200
10
600
450
2
600
20
300
225
3
400
30
200
150
4
300
40
150
113
6
200
60
100
75
8
150
80
75
56
10
120
100
60
45
12
100
120
50
38
460
245
180
153
135
136
145
158
Minimum point of Total Inventory
Costs
EOQ =
£ Costs
minimum TVc point
Total variable costs
Total Hc
Total Oc
EOQ*
Order Size (Q)
EOQ Example
Cheapo Bags wants to calculate the EOQ for
tapestry cloth used to produce hand bags.
 Last year demand = 10,000 metres (constant
rate).
 Value per metre of tapestry = £6.40
 Oc – each order = £250.
 Hc = £1.20 per metre = 18.75%
What is the EOQ?
2 x 10,000 x £250
£6.40 x 18.75%
= 2042 metres
Price-Break Model
Assumptions similar to as EOQ model
2DS
QOPT =
=
iC
2(Demand p.a.)(Order or Setup-cost)
Holding cost per annum
i = % of unit cost as carrying cost
C = cost per unit
“C” varies for each price-break so apply the formula to each
price-break cost value.
Price-Break Example
Brunel University can reduce ordering costs for
photocopy paper by placing larger quantity orders.
What is the optimal order quantity?
• e-mail order cost = £4
• carrying cost % = 2%
• Demand p.a. = 10,000 units?
Quantity price
breaks
2DS
iC
Order Price/un
Quantity(unit
it(£)
s)
0 to 2,499
£1.20
Solution
Put data into formula for each price-break of “C”.
D = 10,000 units
Order cost (S) = £4
Carrying cost % (i) = 2%
Cost per unit (C) = £1.20, £1.00, £0.98
Are Qopt values feasible for the price breaks?
2DS
=
iC
2(10,000)(4)
= 1,826 units
0.02(1.20)
Qopt 0 - 2499 Feasible
2500-3999 and 4000+ Not feasible
=
2(10,000)(4)
=2,000
0.02(1.00)
=
2(10,000)( 4)
=2,020
0.02(0.98)
U-shaped function
True Qopt values occur at the start of each price-break
interval.The total annual cost function is a “u” shaped function
Total
annual
costs
Price-breaks
0
1826
2500
4000
Order Quantity
Price-Break Solution
Now apply the Qopt values to total annual cost & identify
the total cost for each price-break.
D
Q
TC = DC +
S+
iC
Q
2
TC(0-2499)=
(10000x1.20)+(10000/1826)x4+(1826/2)(0.02x1.20) = £12,043.82
TC(2500 -3999) = £10,041
TC(4000+) = £9,949.20
Least cost Qopt = 4000