EOQ Problem Solving

13.1. AV City stocks and sells a particular brand of laptop.
It costs the firm $625 each time it places an

order with the manufacturer for the laptops. The cost of carrying one laptop in inventory for a year is
$130. The store manager estimates that total annual demand for the laptops will be 1500 units, with a
constant demand rate throughout the year. Orders are received within minutes after placement from a
local warehouse maintained by the manufacturer. The store pol- icy is never to have stockouts of the
laptops. The store is open for business every day of the year except Christmas Day. Determine the
following:
a. Optimal order quantity per order
= sqrt(2AO/C)
2∗1500∗625
=
√ 130
= 120.076 units
b. Minimum total annual inventory costs
= ordering cost + conveying cost
1500 120.096
= [ 120.096
∗625 +
][2
∗130
]
= $15,612.50
c. The number of orders per year
no. of orders per year = annual demand / EOQ
1500
=
120.096
= 12.5 orders
d. The time between orders (in working days)
frequency = no. of working days/ no. of orders
364
=
12.5
= 29 days
13.5. The Wallace Stationery Company purchases paper from the Seaboard Paper Company. Wallace
produces stationery that requires 1,415,000 sq. yards of paper per year. The cost per order for the
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company is $2200; the cost of holding one yard of paper in inventory is $0.08 per year. Determine
the following:
a. Economic order quantity
EOQ = sqrt((2 * Demand * cost per order) / holding cost)
( 2 ( 1,415,000 ) ( 2,200 ) )
=
√ 0.08
= 278,971 sq. yards
b. Minimum total annual cost
min. cost = EOQ * holding cost per unit
= 27,971 * 0.08
= $22,317.71
c. Optimal number of orders per year
orders per year = annual demand / EOQ
1,415,000
=
278,971
= 6 orders
d. Optimal time between orders
time between orders = working days/number of orders per year
365
=
6
= 60.83 days
13.29. The bookstore at Tech purchases jackets emblazoned with the school name and logo from a
vendor. The vendor sells the jackets to the store for $38 apiece. The cost to the bookstore for placing
an order is $120, and the annual carrying cost is 25% of the cost of a jacket. The bookstore manager
estimates that 1700 jackets will be sold during the year. The vendor has offered the bookstore the
following volume discount schedule:
Order Discou
Size nt
1–299 0%
300–499 2%
500–799 4%
800+ 5%
What is the bookstore’s optimal order quantity, given this quantity discount information?
EOQ = sqrt (2*1700*120/9.5)
≈ 207 units
Annual inventory cost = ((25% of 38) * 207.3)/ 2
= 984.34
Total cost of operation = D*P + D*S/Q + H*Q/2
At the EOQ,
Total cost of operation = 1700*38 + 1700*120/207.23 + 9.5*207.23/2 = 66568.75
At 300 units,
Total cost of operation (1) = 1700*(38*0.98) + 1700*120/300 + (0.98*38*0.25)*300/2 =

65384.5
At 500 units,

64704
At 800 units,
65235
Best quantity is at 500 units.
1. What are the assumptions of the basic EOQ model and to what extent do they limit the usefulness of
the model?
Some of the assumptions that are made under EOQ are demand is uniform for an item
under consideration, due to storage capacity, there is no limit on the size of an order, the same
quantity is ordered every time an order is placed, and another assumption made is that the cost of
placing an order is independent of the order’s size.
The usefulness of the model is limited because lead times in real life vary, and they can’t
be assumed as constant, limiting the usability of the model.
2. Explain in general terms how a safety stock level is determined using customer service levels.
Customer service levels are used to balance inventory costs vs. the cost of stock out.
When determining the safety stock level, the average daily use for a product is multiplied by its
lead time and subtracted from the maximum everyday use. The increasing customer service level
can also determine safety stock. Therefore, an increase in safety stock means that there is an
increase in customer service level.
3. What are the objectives of an MRP system?
The objectives of the MRP system are; Ensuring raw materials are available for
production, maintaining the lowest possible material and product levels, and that products are
available for delivery to customers.
4. How does MRP II differ from MRP?
MRP is widely used for producing planning and scheduling in industries, while MRP II
provides information needed in all functional areas and encourages cross-functional interactions.
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13.1. AV City stocks and sells a particular brand of laptop.

It costs the firm $625 each time it places an

a. Optimal order quantity per order

b. Minimum total annual inventory costs

= ordering cost + conveying cost

c. The number of orders per year

no. of orders per year = annual demand / EOQ

d. The time between orders (in working days)

frequency = no. of working days/ no. of orders

a. Economic order quantity

EOQ = sqrt((2 * Demand * cost per order) / holding cost)

= 278,971 sq. yards

b. Minimum total annual cost

min. cost = EOQ * holding cost per unit

c. Optimal number of orders per year

orders per year = annual demand / EOQ

d. Optimal time between orders

time between orders = working days/number of orders per year

EOQ = sqrt (2*1700*120/9.5)

Annual inventory cost = ((25% of 38) * 207.3)/ 2

Total cost of operation = D*P + D*S/Q + H*Q/2

Total cost of operation = 1700*38 + 1700*120/207.23 + 9.5*207.23/2 = 66568.75

Total cost of operation (1) = 1700*(38*0.98) + 1700*120/300 + (0.98*38*0.25)*300/2 =

Total cost of operation (2) = 1700*(38*0.96) + 1700*120/500 + (0.96*38*0.25)*500/2 =

Best quantity is at 500 units.

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EOQ = sqrt (21700120/9.5)

Total cost of operation = DP + DS/Q + H*Q/2

Total cost of operation = 170038 + 1700120/207.23 + 9.5*207.23/2 = 66568.75

Total cost of operation (1) = 1700(380.98) + 1700120/300 + (0.98380.25)300/2 =

Total cost of operation (2) = 1700(380.96) + 1700120/500 + (0.96380.25)500/2 =