# Research Paper Writing-Statistics

Inventory Management

1. Full Court Press, Inc. buys slick paper in 1500 pound rolls for textbook printing. Annual
demand is 1920 rolls. The cost per roll is \$1000, the annual inventory carrying cost factor is
15 percent, and placing an order costs \$250.
(a) How many rolls should Full Court Press order at a time in order to minimize total
annual cost?
(b) What is the associated annual inventory carrying cost? annual ordering cost? total
annual cost?
(c) What is the annual item cost?
(d) How long does an order last?
(e) What is the time between orders?
2. Carol Philips is in charge of pharmaceutical suppliers at City General Hospital (CGH).
During the past year, average forecasted daily demand for JY-25 bandages has been 20 cases.
The forecast error standard deviation is 7.4 cases per day. The average lead time for this
item is 10 days with a standard deviation of lead time of 1.8 days. The item cost is \$140 per
case, associated annual inventory carrying cost is 27% of the item cost, and ordering cost is
\$20. The Hospital has a targeted service level of 90% for these bandages. CGH is open 365
days per year.
(a) What is the reorder point for the JY-25 bandages?
(b) What is the total annual cost associated with Ms. Philip’s current policy of ordering
200 cases?
(c) How much could be saved by ordering the EOQ amount?
3. Demand during a product’s lead time is 218 units with a standard deviation of 40 units. If
the reorder point is 300 units, what is the service level?
4. Suds Company is a regional distributor for Wortman, a local microbrewery. The demand
rate for the beer is 60 cases per day. Wortman makes deliveries to Suds in quantities of 140
cases per day. Suds’ ordering cost and annual carrying cost percentage are \$20 per order and
40 percent, respectively. The cost of the beer is \$18.45 per case with a lead time of 4 days.
The company is open 310 days per year. What is the:
(a) optimal order quantity?
(b) annual inventory holding cost? annual ordering cost? total annual cost?
(c) delivery cycle time?
(d) reorder point?
5. Consider the historical demand for a product which appears in Table 1. Information
pertaining to the demand probability distribution as well as expected excess inventory and
expected shortages for various reorder points are given in the partially completed Table 2.
The inventory carrying cost is computed annually at 35% of the item cost of \$200 per unit.
The annual demand is 5,000 units while the stockout cost is \$10 per unit and the cost of
placing an order is \$75.
(a) Determine the missing demand probabilities in Table 2.
(b) Verify all of the entries in Table 2.
(c) Determine the missing excess inventory and shortage quantities.
(d) For a reorder point (ROP) of 50 units, what is the:
Χ expected excess?
Χ expected carrying cost per year?
Χ expected short per cycle?
Χ expected stockout cost per cycle?
Χ expected stockout cost per year?
Χ expected total cost
(e) What should be the reorder point?
(f) What is the service level for the optimal reorder point?
(g) What is corresponding EOQ?
Table 1: Demand Frequency Distribution
Demand Frequency
40 40
45 270
50 450
55 160
60 80
Table 2: Demand Probability Distribution and Expected Excess Inventory / Shortages
Reorder Point
Demand Probability 40 45 50 55 60
40 0.04 0 0.20 0.40 0.60 0.80
45 1.35 2.70 4.05
50 -4.50 -2.25 0 2.25 4.50
55 0.16 -2.40 -1.60 -0.80 0 0.80
60 0.08 -1.60 -1.20 -0.80 -0.40 0
expected excess, e 0.00 0.20 5.55 10.15
expected carrying cost per
year, E[CC} \$0.00 \$14.00 \$388.50 \$710.50
expected short, g 9.85 5.05 0.40 0.00
stockout cost per cycle, G \$98.50 \$50.50 \$4.00 \$0.00
expected stockout cost per
year, E[SC] \$3,136.94 \$1,884.33 \$188.68 \$0.00
expected total cost \$3,136.94 \$1,898.33 \$577.18 \$710.50
2
6. SOCKS, Inc. uses blank DVDs in producing foreign language courseware. The company’s
purchasing manager is reviewing the current policy of placing orders for 100 cases of DVDs
at a time. Company records indicate that the annual demand is 10,000 cases (each case holds
50 DVDs). Accounting has estimated that it costs \$20 per order. Inventory carrying cost for
this item is \$5.43 per case per year, based on a purchase cost of \$15.50 and an annual
carrying cost of 35%. The lead time is 3 working days. The firm operates 250 days per year.
(a) How many tapes should SOCKS order at a time?
(b) What is the associated:
Χ total annual cost?
Χ duration of a cycle in days?
Χ reorder point?
(c) How much will this save over the current policy of purchasing 100 cases at a time?
7. The supplier of blank DVDs for SOCKS, Inc. has approached management with an offer to
make smaller deliveries in quantities of 80 cases per day. However, to cover the added
shipping costs, the price of DVDs will increase by 2 cents per case. Should the offer be
accepted?
8. The weekly demand for a product is normally distributed with mean and variance of 300 and
81, respectively. Lead time is 9 weeks. For a 99% customer service level, what is the:
(a) mean and variance of demand during lead time?
(b) safety stock?
(c) reorder point?
9. Sharpe Cutter is a small company that produces specialty knives for paper cutting machinery.
The annual demand for a particular type of knife is 10,000 units. The demand is uniform
over the 250 working days per year. Sharpe Cutter produces this type of knife in lots and, on
average, can produce 50 knives per day. The cost to set up a production run is \$200 and the
cost of carrying inventory for one year is \$3.20 per knife. The company is open 50 weeks
each year. Determine the:
(a) order quantity that minimizes the total annual cost.
(b) annual setup cost, annual inventory holding cost, and total annual cost.
(c) production cycle time. 