Requirements for Project

Requirements for Project.

A company produces three types of switches – S1, S2,
and S3 – and supplies them to a retailer. It is
contractually obligated to meet the demands of the retailer for each
type of switch. Because of limited capacity the company may not have
sufficient machining, assembly, and finishing time available to
satisfy the entire demand in each period through in-house
production alone. Contractual obligation requires the company to make
up the shortfall in production by procuring it from an external
supplier at higher costs. The company aims to meet the retailer’s
demands at minimum cost.

LP Formulation:

Task 1:

Formulate
a linear programming (LP) model that may be solved to identify the
optimal production and procurement plan for the company in each
time period.

Specifically, you must define the decision variables, objective
function, and constraints in your LP model using the following
parameters:

In each time period, for each product :

  • is the demand (number of units required) for product .

  • is the cost (in dollars) for producing each unit of product .

  • is the cost (in dollars) for procuring each unit of product from
    the external supplier.

  • is the machining time (in minutes) required to produce each unit of
    product .

  • is the assembly time (in minutes) required to produce each unit of
    product .

  • is the finishing time (in minutes) required to produce each unit of
    product .

Further, assume that:

  • hours of machining time is available for regular run.

  • hours of assembly time is available for regular run.

  • hours of finishing time is available for regular run.

LP Parameter Estimation:

You must now use available data to estimate the parameters of the LP
formulated in Task 1.

Estimation of , , , and :

The CSV file “production.csv” contains 15,000 records with
6 columns: SerialNo, ProductCode, MachineTime,
AssemblyTime, FinishTime, and Cost. SerialNo
is a unique identifier assigned to each unit produced by the company;
ProductCode specifies the product type; MachineTime,
AssemblyTime, and FinishTime specify the time (in
minutes) taken by each process (machining, assembly, and finishing)
to produce a unit; the last attribute, Cost, specifies the
cost (in dollars) of producing the unit in-house.

Task 2:

Use the data from the “production.csv” file to
estimate the average machining time, assembly time, finishing
time, and cost per unit for each product type as estimates of the
parameters , , , and of the LP model.

Specify your parameter estimates in the table below. Round all
estimates to 1 decimal place.

Estimates
for

Product
type

Parameters

S1

S2

S3

Machine Time
()

Assembly
Time ()

Finish Time
()

Production
Cost ()

Estimation of demand

The CSV file “demand.csv” contains the retailer’s sales
data for the three switches over the last 52 time periods. For
example, the first row shows that 463 units of S1 were sold in
time period 1, and the last row shows that 629 units of S3
were sold in time period 52.

Task 3:

Use
the data from the “demand.csv” file to predict the
demands in time period 53 for each product. Discuss the
prediction method that you chose and justify your choice.

In your report, please present the estimates for time period 53 in
the following format:

 Product
type

S1

S2

S3

Demand () in
period 53

The cost of procuring each product from the external supplier is
specified below:

Product
type

S1

S2

S3

Procurement
Cost ()

$ 185

$230

$300

Optimal LP Solution:

Task 4:

Solve
the LP formulated in Task 1 using the procurement cost specified
above and parameters estimated in Tasks 2 and 3 to determine the
optimal plan for period 53.

Report the minimum cost achievable, number of units of each product
type to be produced in-house, the number of units of each product
type to be procured from the external supplier, and the resources
used during production in the following format:

Minimum cost
attainable:

Number of units
produced

S1

S2

S3

Produced
in-house

Procured from
external supplier

Resources used

Minutes used

MACHINE TIME

ASSEMBLY TIME

FINISH TIME

Sensitivity Analysis:

Task
5
.

Perform
sensitivity analysis by changing one parameter at a time (leaving
all other parameters fixed at the values used in Task 4) and
answer the following questions.

By how much does the total production cost change as the demand
for each product type changes by 1 unit?

At most how much should the company be willing to pay to

Increase the availability of machining time by one hour during
regular run?

Increase the availability of finishing time by one hour during
regular run?

Increase
the availability of assembly time by one hour during regular
run?

Quality Control

The CSV file “quality.csv” contains 5 columns containing
data from quality control tests run on 1500 batches of items
produced. The first column Quality specifies whether a batch
is of good quality or poor quality; the next four
columns Test1, Test2, Test3, and Test4
contain numerical values representing the measurements on four
quality control tests.

Task 6:

Use the data from “quality.csv” to train and test a
Classification Tree that predicts the Quality of a
batch based on values of the features Test1, Test2,
Test3, and Test4. Use 80% of the observations for
training, and the remaining 20% for testing.

Specify the rules that you obtained in Task 6 in the canonical form:

IF …. THEN …

Present the classification accuracy of this set of rules for the
training and test sets set in the form:

Results with training data: Accuracy = ……%

Number of
batches

Actually Poor
Quality

Actually Good
Quality

Predicted Poor
Quality

Predicted Good
Quality

Results with test data: Accuracy = …….%

Number of
batches

Actually Poor
Quality

Actually Good
Quality

Predicted Poor
Quality

Predicted Good
Quality

Optional: You may also try using other classifiers for
this classification task and comment on the results.

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