08 Jun 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; ProductCodespecifies 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.
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