R Soft LP Formulation

QUESTION

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 S3were 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.
(a) By
how much does the total production cost change as the demand for each product
type changes by 1 unit?
(b) At
most how much should the company be willing to pay to

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

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

(iii)
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.

Specify the rules that you obtained
in Task 10 in the canonical form:
IF …. THEN
…
Present the classification accuracy
of this set of rules in the form:

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.

ANSWER:

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