Inventory homework problems
(Due July 16 (Monday) )
Problem 1(10 points). Harley-Davidson has its engine assembly plant in Milwaukee and its
motorcycle assembly plant in Pennsylvania. Engines are transported between two plants using
trucks, with each trip costing $1,000. The motorcycle plant assembles and sells 438 motorcycles
each day. Each engine costs $500, and Harley incurs a holding cost of 20 percent per year. How
many engine should Harley load onto each truck? What is the cycle inventory of engines at
Harley? (Assume that they work 250 days per year)
Problem 2 (10 points). As part of its initiative to implement JIT manufacturing at the
motorcycle assembly plant in the previous problem, Harley has reduced the number of engines
loaded on each truck to 100. If each truck still costs $1,000, how does the decision impact
annual inventory costs at Harley? What should the cost of each truck be if a load of 100 engines
is to be optimal for Harley?
Problem 3 (10 points). Smith Company purchases components from three suppliers.
Components purchased from Supplier A are priced at $5 each and used at the rate of 20,000 units
per year. Components purchased from Supplier B are priced at $4 each and are used at the rate
of 2,500 units per year. Components purchased from Supplier C are priced at $5 each and used
at the rate of 900 units per year. Smith incurs a holding cost of 20 percent per year. Currently,
Smith purchases a separate truckload from each supplier. As part of JIT drive, Smith has
decided to aggregate purchases from the three suppliers. The trucking company charges a fixed
cost of $400 for the truck with an additional charge of $100 for each stop. Thus, if Smith asks
for a pickup from only one supplier, it charges$500; from two suppliers, it charges $600, and
from three suppliers, it charges $700. Suggest a replenishment strategy for Smith that
minimizes annual cost. Compare the cost of your strategy with Smith’s current strategy of
ordering separately from each supplier. What is the cycle inventory of each component at
Smith?
Problem 4 (10 points). Prefab, a furniture manufacturer, uses 20,000 square feet of plywood per
year. Its trucking company charges Prefab $400 per shipment, independent of the quantity
purchased. The manufacturer offers an all unit quantity discount with a price of $1 per square
foot for orders under 20,000 square feet, $0.98 per square feet, and $0.96 per square foot for
orders larger than40,000 square feet. Prefab incurs a holding cost of 20%. What is the optimal
lot size for Prefab?
Problem 5 (10 points). Weekly demand for Motorola cell phones at a Best Buy store is normally
distributed, with a mean of 300 and a standard deviation of 200. Motorola takes two weeks to
supply a Best Buy order. Best Buy is targeting a CSL of 95% and monitors its inventory
continuously. How much safety inventory of cell phones should Best Buy carry? What should
its ROP be?
Problem 6 (10 points). Reconsider the Best Buy in Previous problem. The store manager has
decided to follow a periodic review policy to manage inventory of cell phones. She plans to
order every three weeks. Given a desired CSL of 95 percent, how much safety inventory should
the store carry?
Problem 7 (30 points). Epson produces printers in its Taiwan factory for sale in Europe.
Printers sold in different countries differ in terms of power supply as well as the language of the
manuals. Currently, Epson assembles and packs printers for sale in individual countries. The
distribution of weekly demand in different countries is normally distributed, with means and
standard deviations as shown in the table below.
Country
France
Germany
Spain
Italy
Portugal
UK
Mean Demand
3,000
4,000
2,000
2,500
1,000
4,000
Standard deviation
2,000
2,200
1,400
1,600
800
2,400
a) Compute safety stock without aggregation given that the base printers are to be
manufactured in Taiwan with a lead time of eight weeks.
b) Now Epson decides to build a central DC in Europe. Assume demand indifferent
counties to be independent, i.e. correlation is zero. Given that lead time from the Taiwan
factory to the central DC is eight weeks, how much safety inventory does Epson require
in Europe if it targets CSL of 95%?
c) Compute safety stock that Epson carries as a result of building a European DC if
correlation is all identically 0.2 given eight weeks of lead time from Taiwan with CSL of
95%
Problem 8 (10 points). Teddy Bower is an outdoor clothing and accessories chain that purchases
a line of parkas at $10 each from its Asian supplier, TeddySports, Unfortunately, at the time of
order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally
distributed with mean of 2,100 and standard deviation of 1,200. Teddy Bower sells these parkas
at $22 each. Assumer unsold parkas have value of $2. Decide an optimal production amount of
Teddy Bower.