The slight difference in relevant ordering costs ($8,272) and relevant carrying costs ($8,268) is
because of rounding down the number of packages from 1,378.4 in the EOQ formula to 1,378.
3.
As summarized below, the new Mona Lisa web-based ordering system, by lowering the
EOQ to 1,378 packages, will lower the carrying and ordering costs by $6,260. Soothing Meadow
will spend $2,150 to train its purchasing assistants on the new system. Overall, Soothing
Meadow will still save $4,110 in the first year alone.
Total relevant costs at EOQ (from Requirement 2)
$16,540
Annual cost benefit over old system ($22,800 – $16,540)
$
6,260
Training costs
2,150
Net benefit in first year alone
$
4,110
20-13

20-27
(30 min.)
EOQ, uncertainty, safety stock, reorder point
.
1.
2 DP
2
120,000
$250
EOQ
C
$2.40
= 5,000 pairs of shoes
2.
Weekly demand
= Monthly demand ÷ 4
= 10,000 ÷ 4 = 2,500 pairs of shoes per week
Purchasing lead time = 1 week
Reorder point = 2,500 pairs of shoes per week × 1 week = 2,500 pairs of shoes
3.
Solution Exhibit 20-27 presents the safety stock computations for Warehouse OR2 when
the reorder point excluding safety stock is 2,500 pairs of shoes. The exhibit shows that annual
relevant total stockout and carrying costs are the lowest ($1,080) when a safety stock of 250
pairs of shoes is maintained. Therefore, Warehouse OR2 should hold a safety stock of 250 pairs.
As a result, Reorder point with safety stock = 2,500 pairs + 250 pairs = 2,750 pairs. Reorder
quantity is unaffected by the holding of safety stock and remains the same as calculated in
requirement 1.
Reorder quantity = 5,000 pairs
Warehouse OR2 should order 5,000 pairs of shoes each time its inventory of shoes falls to 2,750
pairs.
SOLUTION EXHIBIT 20-27
Computation of Safety Stock for Warehouse OR2 When Reorder Point is 2,500 Units
Safety
Stock
Level
in Units
(1)
Demand
Levels
Resulting
in
Stockouts
(2)
Stockout
in Units
a
(3)=
(2)–2,500–(1)
Probability
of
Stockouts
(4)
Relevant
Stockout
Costs
b
(5)=(3)×$2
Number
of
Orders
per Year
c
(6)
Expected
Stockout
Costs
d
(7)-
(4)×(5)×(6)
Relevant
Carrying
Costs
e
(8)=
(1)×$2.40
Relevant
Total
Costs
(9)=(7)+(8)
0
2,750
250
0.20
$
500
24
$2,400
3,000
500
0.04
1,000
24
960
$3,360
$
0
$3,360
250
3,000
250
0.04
500
24
$
480
$
600
$1,080
500
--
--
--
--
--
$
0
f
$1,200
$1,200
a
Demand level resulting in stockouts – Inventory available during lead time (excluding safety stock), 2,500 units –
Safety stock.
b
Stockout in units × Relevant stockout costs of $2.00 per unit.
c
Annual demand, 120,000 ÷ 5,000 EOQ = 24 orders per year.
d
Probability of stockout × Relevant stockout costs × Number of orders per year.
e
Safety stock × Annual relevant carrying costs of $2.40 per unit (assumes that safety stock is on hand at all times and
that there is no overstocking caused by decreases in expected usage).
f
At a safety stock level of 500 units, no stockout will occur and, hence, expected stockout costs = $0.
20-14

20.28
(25 min.)
MRP,
EOQ, and JIT.
1.
Under a MRP system:
Annual cost of producing and carrying J-Pods in inventory
= Variable production cost + Setup cost + Carrying cost
= $54 × 48,000 + ($10,000 × 12 months) + [$17 × (4,000 ÷ 2)]
= $2,592,000 + $120,000 + $34,000 = $2,746,000
2.
Using an EOQ model to determine batch size:
2
48,000
$10,000
2 DP
EOQ
C
$17
= 7,515 J-Pods per batch
Production of 48,000 per year divided by a batch size of 7,515 would imply J-Pods would
be produced in 6.4 batches per year. Rounding this up to the nearest whole number yields
7 batches per year, which means a production size of 48,000 ÷ 7 or 6,857 J-Pods per
batch.