Management science

Mexician Foods operates a plant in Texco, a Mexican state of Guerro, for manufacturing taco sauce
used in fast­food restaurants. The sauce, which is packaged in plastic containers, is made from a
special recipe that includes tomato concentrate, onions, and chilli peppers that Mexician
purchases from various suppliers. The plant operates 365 days a year and Mexician uses an annual
holding cost rate of 17%.
Tomato Concentrate
Mexician Foods purchases its tomato concentrate from Organic Farms. The company requires
2,540 gallons of concentrate per day to produce this sauce. Organic Farms offers customers the
following all units price discount schedule:
Number of Gallons Ordered Price per Gallon ($)
1­9,999 3.12
10,000 – 49,999 3.08
50,000 – 124,999 3.02
125,000 – 249,999 3.00
250,000 or more 2.96
The shelf life of the concentrate is 80 days and the ordering cost is $760. Orders must be placed in
1200­gallon increments. The lead time for delivery is 10 days. Management wishes to determine the
optimal ordering policy for the concentrate.
In the cooking process, the amount of onion required weekly follows a normal distribution with
mean 16,210 pounds and standard deviation 4,100 pounds. Onions cost $0.15 per pound. If any are
left over at the end of the week, they are unusable and thrown away. If management at Mexician
find themselves running short of onions, they would need to make an emergency purchase from a
local supermarket. They would have to pay the retail cost of onion at $0.95 per pound. Management
wants to determine the optimal order policy for onions.
Chilli Peppers
Mexician also needs an estimated 2,100 pounds of chilli peppers daily. The peppers cost $0.37 per
pound. Order cost, including transportation, is $1,500. Lead time is normally two weeks but may
vary somewhat. Because of this variability, the company estimates that the lead time demand for
chilli peppers follows approximately a normal distribution with mean of 28,100 pounds and a
standard deviation of 4,000 pounds. Management wants to determine the optimal ordering policy
for chilli peppers to meet a desired service level of 99%.
Plastic Containers
Mexician packages the sauce in one­ounce plastic containers it buys from Polymer Plastics
Company at $0.003 per unit. The ordering cost is $130. Mexician is contemplating leasing a
machine to make the containers. The yearly lease cost of the machine is $45,000, and the
production setup cost of the machine is $260. The machine can produce 1.1 million containers
per day at a per unit cost of $0.0027 (excluding leasing, inventory holding and production setup
costs). The company estimates that it requires 453,000 containers per day. Management wants to
determine whether it should continue purchasing containers from Polymer Plastics Company or
begin in­house production and what the optimal policy should be.
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Case 2: Global Travel Agency (50%)
Having run a successful travel agency in Lugano, Switzerland, Sara Bally has decided to open a
branch in Bern, Switzerland. She must decide where to locate her office and which and how many
employees to hire.
Sara has narrowed her choice of office to two locations. The one on Nordweg Road is a large office
with space for virtually any number of employees and customers. Sara estimates that the agency
can attract an average of 13 customers per day at this location. Rent for this office is Swiss Franc
1,200 per month. Utilities, insurance and other expenses should average an additional Swiss Franc
520 per month.
The second choice for an office is on Zeltweg Street, approximately two blocks off Nordweg Road.
This is a much smaller office that can effectively only hold one worker and at most four customers
(including the one being served). It rents for Swiss Franc400 per month. Utilities, insurance, and
other expenses should average an additional Swiss Franc 200 per month. The out­of­the­way
location would reduce the number of potential customers by 20% and any arriving customer finding
the office full will presumably take his or her business to the other travel agency in town.
Sara has decided that if she opens the Nordweg Road office, she will hire one or more local
employees to staff the office. If she opens the Zeltweg Street office, however, she will hire either
Wendy Green, an experienced travel agent form the Bern area, or a local employee to staff the
office. Sara would have to pay Wendy a monthly salary (including benefits) of Swiss Franc 2,100,
whereas she could hire local employees for Swiss Franc 1,200 per month (including benefits).
Because of her experience, Wendy’s average customer service time is approximately 20 minutes,
compared to 48 minutes for local employees.
Sara estimates that each customer served by the Global Travel Agency will result in an average
commission of Swiss Franc 35. She also estimates a goodwill cost to the firm of Swiss Franc 15 per
hour for the time a customer spends waiting in the office for service to begin. In addition, goodwill
costs of Swiss Franc 50 are associated with any customers who find the Zeltweg Street location full
and leave to go to another travel agency.
The travel agency will be open an average of 20 days per month, eight hours each day. Customers
arrive according to a Poisson process, and customer service times follow an exponential distribution.
Determine the most cost effective option for Global Travel Agency.




Sample Solution