Management 3: Quantitative Methods in Business
Session 8 – Assignment (20 points total)
Q1. R&W is a manufacturer of janitorial supplies; the company produces a line of industrial cleaning solutions
which it sells in bulk, primarily to medium and large businesses. R&W produces the solutions at its warehouse
in Denver, Colorado, and acquires the various chemicals used to produce its solutions from a network of
chemical suppliers located throughout the United States and Canada. One of the most common chemicals
the company purchases is ammonium hydroxide (NH4OH), which it purchases in 55-gallon drums at a cost of
$1,150 per drum. The company operates 250 days a year and has a highly consistent rate of production,
processing an average of 900 drums’ worth of NH4OH annually. The bulk of R&W’s NH4OH supply is primarily
purchased from a single supplier, who charges a fixed cost of $550 per order to cover the cost of
transportation and insurance and quotes a lead time of 14 working days to fulfill new orders. Between on-site
storage and allowance for waste, the company attributes holding costs as 12% of the cost of capital.
Solve the following metrics that describe R&W’s optimal inventory ordering strategy:
a. The economic order quantity. (3 pts)
b. Optimal number of orders per year (1 pt)
c. Reorder point (2 pts)
d. Cycle time (1 pt)
e. Total annual cost of inventory (including cost of goods) (2 pts)
Q2. The San Diego County Fair takes place annually from the first week of June through July 4. Every year, the
fair hosts nearly a hundred stands that sell various food and drink items, and provides dozens of areas
throughout the fairgrounds specifically designated for eating. As the fairgrounds are situated very close to the
ocean, evenings at the fair can be quite chilly. After years of fielding complaints from guests about the dining
areas being too cold in the later hours of the day, management has decided to place heat lamps throughout
each dining area. The lamps will be powered by reusable propane tanks which are to be provided by a local
propane supplier. As this is the first year lamps will be provided, management is still refining its plan for
propane delivery. The supplier has suggested a delivery process in which it would deliver a certain number of
filled tanks every day over a fixed number of days. At the end of this production run, the supplier would collect
all empty tanks and return them to its warehouse to be refilled. The fair would then deplete its supply of
propane until the next production run, at which point the supplier will deliver the refilled tanks and again
collect the empty ones for refilling. This cycle would repeat through the duration of the fair, which runs every
day for 5 weeks (35 days total). Management has negotiated to buy the filled tanks at $12 per tank, and the
supplier has negotiated a fixed delivery rate of $100 per production run. The supplier has the capacity to
deliver up to 300 tanks per day. As the lamps are to be lit on a consistent daily schedule, management
estimates that propane will be consumed at a near constant rate of 90 tanks each day. Management also
assumes that the holding costs for filled propane tanks total approximately $2.50 per tank. (As empty tanks do
not require careful storage, management has decided to attribute holding costs only to any filled tanks on the
premises.)
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a. What is the optimal number of tanks that should be delivered in each complete production run in order to
minimize the total cost of managing inventory? Note that any ‘annual’ estimates used in your calculations
should only reflect the duration of the fair. (3 pts)
b. Using the optimal lot size, how long will each production run last? (1 pt)
c. Although the fair plans to accommodate a supply of both filled and empty tanks at any given moment, the
filled tanks require special care, as they are both pressurized and highly flammable, and must be stored
in a safe environment until ready for use. In order to plan for storage accordingly, management would like
to know the following: using the recommended order quantity as determined in the part A, what is the
maximum number of filled propane tanks that will be on the premises at any given moment? (1 pt)
d. How many production runs will occur over the length of the fair? (1 pt)
e. What is the total cost of managing inventory, including cost of goods? (2 pts)
Q3. Miradello’s is chocolatier based in the Bay-Area. Every year, the company looks forward to its largest annual
sales event: Valentine’s Day. Miradello’s is well-known for its signature Valentine’s Day chocolate roses,
which are made out of fine chocolate shavings carefully arranged on a chocolate base to resemble blooming
rose petals. Although Miradello’s products are made from premium ingredients, it enjoys quite healthy
contribution margins: Each “rose” costs $2 to manufacture and retails for $15. The roses typically go on sale
two weeks before Valentine’s Day, and the remaining supply of roses not sold by the end of day on February
14 is discarded. Forecasted sales for roses for the next Valentine’s Day are shown to be normally distributed
with a mean of 8,000 roses and a standard deviation of 500 roses.
a. What is the recommended order quantity? (2 pts)
b. By how many units in safety inventory should management pad the average expected demand quantity
such that they can guarantee a 99.9% service rate? (1 pt)