RDK has just developed a state of the art wearable technology device and wants t
ID: 3296602 • Letter: R
Question
RDK has just developed a state of the art wearable technology device and wants to determine a production level for the next three years. (Note: Once set, the production level will remain the same for all three years.)
RDK’s marketing department has estimated the device has a 25% chance of selling for $120, a 50% chance of selling for $160, and a 25% chance of selling for $200. The selling price is random, but once it is set, the price applies to all devices sold.
Variable production cost per device is assumed to be normally distributed with a mean of $100 and a standard deviation of $20 for the first year. After the first year, the cost is expected to reduce by 5% per year for each of the next two years (HINT: only the first year is a random variable).
The annual demand for the device during first year is believed to be normally distributed with mean 50,000 and standard deviation 5,000. For year two, the demand is normally distributed with the mean being the demand from year one. For year three, the demand is normally distributed with the mean being the demand from year two. For all three years, the standard deviation is 5000.
RDK assumes that unmet demand will result in the loss of a customer, as they will likely buy a device from a competitor. As such, for each unit of unmet demand, RDK assumes a cost of $50. This will be considered a Cost of Lost Profit.
RDK is considering the following production levels: 30,000, 40,000, 50,000, 60,000 and 70,000.
Build a Monte Carlo simulation model to calculate the total profit after three years. Use a two-variable data table to simulate each of the production levels under consideration. For each production level, calculate the mean, standard deviation, min, and max of the distribution of Total Profit.
Price Per Unit Inputs Number Line 120 160 200 25% 50% 25% 0 Cost of Lost Profits (per unit 0.25 $ 0.75 50 Year 1 Cost per Unit Inputs Production Levels to Consider Mean StDev 100 20 30,000 40,000 50,000 60,000 70,000 Year 1 Demand Inputs Mean StDev 50,000 5,000Explanation / Answer
Problem 1: Optimization Modeling
Cost per unit
Factory A
Factory B Time per unit
Factory A
Factory B Product 1 Product 2 Product 3 $ 15.00 $
4.00 $ 10.00
$ 22.00 $ 40.00 $ 11.00
Product 1 Product 2 Product 3 7
8 7.5
9 8
7.5 A company manu
required for prod
The time and cos
tables in this wor
Demand for prod
There are a total
Additionally, at le
at least 40% of o
Create a linear p
production plan t
Note: The cost is A company manufactures 3 products in 2 different factories. The cost of production and time
required for production for each product varies depending on which factory produces it.
The time and cost required for production of each product in each factory is provided in the
tables in this worksheet.
Demand for products 1, 2 and 3 are 200, 240 and 100 units, respectively.
There are a total of 3000 hours available in each factory.
Additionally, at least 60% of the total units of Product 1 must be produced in Factory A, and
at least 40% of of the total units of Product 2 must be produced in Factory B.
Create a linear programming model and use the Solver add-in to determine the optimal
production plan that will minimize total cost.
Note: The cost is per unit not per hour. All demand must be met. and time
es it.
ed in the y A, and timal 8/19/2017 5:18 Problem 2: Simulation Modeling
$
$
$ Price Per Unit Inputs
120
25%
160
50%
200
25% Year 1 Cost per Unit Inputs
$ 100
Mean
$
20
StDev Year 1 Demand Inputs
50,000
Mean
5,000
StDev Cost of Lost Profits (per unit)
$
50 Production Levels to Consider
30,000
40,000
50,000
60,000
70,000 RDK has just developed a state of the art wearable technology device and wants to determine
a production level for the next three years. (Note: Once set, the production level will remain
the same for all three years.)
RDK’s marketing department has estimated the device has a 25% chance of selling for $120, a
50% chance of selling for $160, and a 25% chance of selling for $200. The selling price is
random, but once it is set, the price applies to all devices sold.
Variable production cost per device is assumed to be normally distributed with a mean of
$100 and a standard deviation of $20 for the first year. After the first year, the cost is expected
to reduce by 5% per year for each of the next two years (HINT: only the first year is a random
variable). The annual demand for the device during first year is believed to be normally distributed with
mean 50,000 and standard deviation 5,000. For year two, the demand is normally distributed
with the mean being the demand from year one. For year three, the demand is normally
distributed with the mean being the demand from year two. For all three years, the standard
deviation is 5000.
RDK assumes that unmet demand will result in the loss of a customer, as they will likely buy a
device from a competitor. As such, for each unit of unmet demand, RDK assumes a cost of
$50. This will be considered a Cost of Lost Profit.
RDK is considering the following production levels: 30,000, 40,000, 50,000, 60,000 and
70,000.
Build a Monte Carlo simulation model to calculate the total profit after three years. Use a
two-variable data table to simulate each of the production levels under consideration. For
each production level, calculate the mean, standard deviation, min, and max of the
distribution of Total Profit. ants to determine
level will remain elling for $120, a
lling price is th a mean of
e cost is expected
year is a random y distributed with
rmally distributed
d is normally
ars, the standard y will likely buy a
mes a cost of 60,000 and e years.
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