### The purpose of this assignment is to develop your

Assignment -

The purpose of this assignment is to develop your capability in applying your skills and knowledge in a hypothetical situation and to build your problem solving and report writing skills which will be used in Assignment.

For this assignment, you are required to work on a linear programming case study.

Note - A Word file to explain your mathematical models, to report your answers, and to write recommendations for decision-makers based on the solutions; and An Excel file to demonstrate how you use Solver to identify the solutions. You must ensure that the file is in a workable condition before the submission.

SCMD Assignment -

The company produces mandarins at three plants, which can be delivered directly to the two customers or it can first be shipped to the two warehouses and then to the customers. Shipments between plants are allowed. This also applies to between warehouses and between customers.

The cost of producing the orange product is the same at each plant; as a result, the company is only concerned with minimising the total shipping cost incurred in meeting customer demands. The production capacity of each plant (in tons per year) and the customer demand are summarised in the table below:

 Plant Capacity Plant 1 350 Plant 2 400 Plant 3 450

 Customer Demand Customer 1 480 Customer 2 460

The cost (in thousands of dollars) of shipping a ton of the product between each pair of locations is listed in the table below where a blank indicates that the company cannot ship on that route:

 From node To node Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2 Plant 1 3 3 6 7 15 15 Plant 2 3 2 5 6 16 16 Plant 3 3 2 7 6 14 15 Warehouse 1 3 6 8 Warehouse 2 3 7 7 Customer 1 4 Customer 2 4

The management has set the maximum flow between nodes (in tons) as shown in the table below:

 From node To node Plant 1 Plant 2 Plant 3 Warehouse 1 Warehouse 2 Customer 1 Customer 2 Plant 1 200 200 250 250 250 200 Plant 2 200 200 250 250 250 200 Plant 3 200 200 250 250 250 200 Warehouse 1 250 250 250 Warehouse 2 250 250 250 Customer 1 200 Customer 2 250

Since sometimes the demands are fluctuated, the company plans to have safety stock of 50 tons at Warehouse 1 and 100 tons at Warehouse 2. The company wants to determine a minimum-cost shipping strategy.

SCMD Assignment Report Structure -

1. Cover page

a. Report's title

b. Names and student IDs

2. Problem formulation (please ensure that all mathematical symbols are correct and consistent)

a. Define decision variables with a measurement unit (e.g. pallets, kg, or km).

b. Provide an objective function and constraints and clearly show how you formulate them with an explanation what each equation means.

c. Ensure that decision variables and each equation are linked back to the data.

3. Problem solving (i.e. process of how you find the solution step-by-step)

a. Explain how you implement the model in the Excel spreadsheet

i. Explain how you implement each equation in the model using what functions in Excel (e.g. SUMPRODUCT) and where you place it on the spreadsheet (e.g. at Cell B2). If constraints are of the same kind and implemented in the same way, you just need to explain the first one and summarise the rest.

b. Explain how you set up Solver in Excel

c. Do not forget to submit the Excel spreadsheet together with the Word report

4. Discussion

a. Discuss the optimal solution based on the results that you find

b. If you conduct sensitivity analysis, the results should be presented here.

5. Recommendations

a. List and discuss what action should be taken based on the discussion.

i. For example, the results may suggest that the optimal solution for the production problem is to make 3 units of X and 4 units of Y. In addition, sensitivity analysis indicates that an increase of each Resource A can increase the profit by \$5, up to the maximum of 100 units of Resource A. Your first recommendation can be to produce 3 units of X and 4 units of Y, and the second recommendation is to procure additional 100 units of Resource A.

6. Presentation

a. Discussion and explanation are succinct

b. There is a link between each section. And when the report is read, the reader should not feel jumpy (i.e. some important information is omitted).

c. Cross-referencing and citations are correct, if any

d. All headings and sections are in place

e. Images or figures are clear