Lowery
HW Sarah #2
5.
a) What is Dot Coms optimal order quantity? EOQ = = = 400 books
b) What is the optimal number of orders per year? (32,000)/400 = 800 orders
c) What is the optimal interval (in working days) between orders? 300/80 = 3.75 days
d) What is demand during the lead time? =dL = (5days)(32,000/300) = 533 books
e) What is the reorder point? =dL + SS = 533 + 0 = 533 books
7.
a) What is the EOQ? What would be the average time between orders (in weeks)?
d = 90/week
D = 4,680
S = $54
Price = $11.70
H = 27% (11.70) = $3.159
EOQ = = = = 400 bags
Time between orders, in weeks:
= = 0.08547 years = 4.44 weeks
b) What should R be?
Reorder point, R = demand during protection interval + safety stock
R = dL = 90*3 = 270 bags
SS = 0.84 * 26 = 21.82 or about 22 bags
R= 270 + 22 = 292
c) An inventory withdrawal of 10 bags was just made. Is it time to reorder?
Initial inventory position = OH + SR BO = 320 + 0 0
320 10 = 310. Inventory position remains above 292, so it is not time to place an
order
yet.
d) The store currently uses a lot size of 500 bags (i.e., Q = 500). What is the annual
holding
cost of this policy? Annual ordering cost? Without calculating the EOQ, how
can you conclude
from these two calculations that the current lot size is too large?
Annual holding cost:
Annual ordering cost:
At the economic ordering quantity, the two costs are the same. When Q is 500
though,
the annual holding cost is much larger than the ordering cost. This
means that Q is far
too large. Total costs are now $1,295.19.
e) What would be the annual cost saved by shifting from the 500-bag lot size to the
EOQ?
Annual holding cost:
Annual ordering cost:
quantity of
Total costs are now $1, 263.60, which is $31.59 less than the previous order
500 bags.
1. (EOQ model) You (the buyer) manage the inventory of an item. Your forecast for the
next years demand is 1,000 units for the whole You year. pay the supplier $20 for each
unit. It costs $5 ordering cost to place an order, and the annual inventory holding cost for
a unit is 20% of its purchase cost.
a) Under the current policy, your order size is Q=100. What are the total (sum of)
ordering (setup) costs and inventory holding costs over the next year?
D = 1,000 /yr.
c = $20 /unit
s = $5 ordering cost to place order
i = 20%
H = (.20)(20) = 4
Q = 100 units
Annual setup/ordering costs =
Annual holding costs =
b) If you use EOQ model to manage inventory. What is the EOQ? What is the
corresponding total cost (including ordering and inventory holding costs) for the
whole year?
EOQ =
Corresponding total costs (ordering and inventory holding costs) for the year:
Annual ordering costs + Annual holding costs:
+=
2. (Continuous review system, with safety stock) A factory produces a part to supply its
customers. The factory faces a random demand from its customers. The weekly demand
has a normal distribution, with the expectation (mean) of 300 units and the standard
deviation of 90 units. The production lead time is 4 weeks (thats it takes 4 weeks to
finish a production run). The production manager uses the continuous review system to
plan production.
a) What is the safety stock necessary to achieve the service level of 98%? What is the
corresponding reorder point?
dbar = 300 units
S.D. = 90 units
L = 4 weeks
*Uses continuous review system
SS = Z
ROP = (dbar)(L) + SS = (300)(4) +370 = 1,570 units
b) Suppose the production manager must reduce the safety stock in the above question
by 50%, by lowering the service level (while all other model parameters are
unchanged). What will be the new service level (i.e., the probability of no stockout)
that attains the reduced safety stock?
SS = Z (90)(2) = (370/2)
= 180Z = 185
Z=1.027
New service level needs to be 84% in order to reduce the safety stock by 50%.