Reference no: EM131413229

Requirements for Business Intelligence Capstone Project.

A company produces four types of alarm systems -S1, S2, S3, and S4 - and supplies them to a retailer. It is contractually obligated to meet the demands of the retailer for each alarm system. Because of limited capacity the company may not have sufficient machining, assembly, andfinishingtime available to satisfy the entire demand in each period through its regular production runs. Contractual obligation requires the companyto make up the shortfall in production through special production runs 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 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 i ∈ (1, 2, 3, 4):

- D_i is the demand (number of units required) for product i.
- C_i^R is the cost (in dollars) for producing each unit of product i in a regular run.
- C_i^S is the cost (in dollars) for producing each unit of product i in a special run.
- t_i^m is the machining time (in minutes) required to produce each unit of product i.
- t_i^a is the assembly time (in minutes) required to produce each unit of product i.
- t_i^f is the finishing time (in minutes) required to produce each unit of product i.

Further, assume that:

220 hours of machining time is available for regular run.

140 hours of assembly time is available for regular run.

100 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 t_i^m, t_i^a, t_i^f, and C_i^R:

The text file "production.csv" contains 7 columns: serialno, batchno, productcode, machinetime, assemblytime, finishtime, and cost. Using any DBMS of your choice, create a table PRODUCTION with serialno as its primary key and the 6 other columns as attributes and insert the 24,000 records from production.csvinto the table. Serialnois a unique identifier assigned to each unit produced by the company; productcode specifies the product type; batchno identifies the batch in which an item is produced (items are produced in batches of 10 units of a product type); machinetime, assemblytime, and finishtimespecify 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 a regular run.

Task 2:

Formulate an SQL query to obtain the average machining time, assembly time, finishing time, and cost per unit for each product type as estimates of the parameters t_i^m, t_i^a, t_i^f, and C_i^R of the LP model.

In your report, you must:

1. Specify your SQL query to obtain the estimates.

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

Estimates	S1	S2	S3	S4
MachineTime (tm )
AssemblyTime (tia )
FinishTime (tif)
Regular Cost (CiR )

Estimation of special run cost C_i^S:

It is known that the regular production cost C_i^R is a linear function of the machining, assembly, and finishing times for each product type. That is, C_i^R = β_i⁰ + β_i^m t_i^m + β_i^a t_i^a + β_i^f t_i^f, where β_i⁰ is the fixed cost incurred to produce each unit of i, and β_i^m, β_i^a, and β_i^f are respectively the costs per minute for machining, assembly, and finishing each unit of product i during regular run.

Task 3:

Run regressions to estimate the coefficients β_i⁰, β_i^m, β_i^a, and β_i^f for each product i.

In your report, please explain how you obtained the data for the 4 regressions to estimate the coefficients. Then present yourcoeffient estimates in the table below. Round all estimates to 1 decimal place.

Coefficient estimates	S1	S2	S3	S4
Intercept (βi0)
MACHINETIME (βim)
ASSEMBLYTIME (βiα)
FINISHTIME (βif)

The fixed costs β_i⁰ associated with the production of each unit of i is the same under the regular and the special run, but the special run costs per minute for machining, assembly, and finishing are double the regular run costs.

Task 4:

Use the above relationship to estimate that the cost for producing each unit of product i in a special run as C_i^S = β_i⁰ + 2(β_i^m t_i^m + β_i^a t_i^a + β_i^f t_i^f ).

Present the estimates in the following format:

Estimation of demand D_i

The text file "demand.csv" contains the retailer's sales data by region (Region1 and Region 2) for the four alarm systems over the last 40 time periods. For example, the first row shows that 334 units of S1 were sold in the Region1 in time period 1, and the last row shows that 264 units of S4were sold in Region2 in time period 40.

Create a table called DEMAND with a composite primary key made up of the attributes period, productcode, and region.Salesis the fourth attribute in theDEMANDtable. Insert all 320 records from demand.csv into the DEMAND table.

Task 5:
Extract the data needed for predicting demand for S1 by formulating an SQL query that lists the Period and the sum of the total sales for S1 from both regions in each of the 40time periods as S1demand. Similarly, formulate three more SQL queries to obtain the 40 records for S2demand, S3demand, and S4demand.

Specify the SQL queries to obtain S1demand, S2demand, S3demand, and S4demand.

Task 6:

Use the results returned by the queries formulated in Task 5 in forecasting models to predict the demands D_i in time period 41 for each product.

You should consider various prediction and forecasting methods that you are familiar with. Use the methodthat you think is most accurate in estimating demands. In your report, please present the estimates for time period 41 in the following format:

Optimal LP Solution:

Task 7:

Solve the LP formulated in Task 1 using the parameters estimated in Tasks 2, 4, and 6 to determine the optimal production plan for period 41.

Report the minimum production cost achievable, number of units of each product type to be produced under the regular and special production runs, and the resources used during regular run in the following format:

Sensitivity Analysis:

Task 8.

Perform sensitivity analysis by changing one parameter at a time (leaving all other parameters fixed at the values used in Task 7) 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 text file "defective.csv" contains 2 columns. The first column defectiveid is an identifier, and the second column serialno specifies the serial number of a defective product. Create a table DEFECTIVE with defectiveid as its primary key and insert all 1639 records from defective.csvinto the table. Note that serialno in the DEFECTIVEtable is a foreign key that references the primary key in the PRODUCTION table.

The text file "quality.csv" contains 5 columns containing data from quality control tests run on 2400 batches of items produced. Create a table QUALITY with BatchNo as its primary key and test1, test2, test3, and test4 as its other 4 attributes. Insert all 2400 records from quality.csv into the table. Note that batchno in the PRODUCTION table is a foreign key that references the primary key batchno in the Quality table.

Any batch that containsmore than one defective items is deemed to be ofpoor quality; a batch with at most one defective item is considered to be of good quality.

Task 9:

Formulate an SQL query that lists all 5 columns from the QUALITY table and adds a derived column batchquality that contains "Poor" if the batch is of poor quality (contains at least 2 defective items) and "Good" otherwise.

In your report, include:
1. The SQL query for task 9
2. The results of the query in a file qualityInput.csv.

Task 10:

Partition the data obtained from Task 9 to train and test a Classification Tree that predicts batchquality based on values of the featurestest1, test2, test3, and test4. Use 80% of the observations for training and the remaining 20% for testing.

In your report:
1. Specify the number of training and test examples that you used.
2. Specify the rules that you obtained in Task 10 in the canonical form:
IF .... THEN ...
3. Present the classification accuracy of this set of rules for the training set and the test set by specifying confusion matrices of the form:

Note that there should be one confusion matrix for the training data and one for the test data.
If you wish, you may also use other prediction and classification methods (such as Logistic Regression, Neural Nets, and Discriminant Analysis) to classify batchquality based on values of the featurestest1, test2, test3, and test4, and comment on the classification accuracy of these methods.

Attachment:- Suggestions.rar