LOG307 Optimisation and Simulation

LOG307 Optimisation and Simulation

LOG307 Optimisation and Simulation for Decision-Making

This assignment is worth 15% of the final mark for LOG307 Optimisation and Simulation for Decision-Making.

Note to Students:

Please note that you are required to submit only an Excel File for your TMA.

Question 1

Adnan is the production manager at HomePro, a manufacturer of small home appliances in Turkey. The firm produces the following five electric products: kettle, toaster, oven, sandwich maker, and mixer. To ensure these products meet quality specifications, each will go through three different testing machines. The table below illustrates the time needed (in minutes) for each product at each testing machine, and the revenue and cost per unit for each product.

Product Time needed at each testing machine



Per Unit ($)


Cost Per

Unit ($)

Machine 1 Machine


Machine 3
Kettle 1 2 2 135 35
Toaster 2 2 1 95 28
Oven 4 3 4 300 145
Sandwich maker 2 2 3 120 30
Mixer 5 6 4 350 180

Assume that:

  • Test Machines 1 and 3 are available for 95 hours per week, while Test Machines 2 is only available for 85 hours per week.
  • Variable labor costs are $16 per hour for test machine 1, $13 per hour for test machine 2, and $18 per hour for test machine 3.

Adnan is tasked to find the best product mix that maximises HomePro’s profit.

(a) Demonstrate the linear programming (LP) model formulation for this problem. (17 marks)

(b) Create a spreadsheet model for this problem. Determine the optimal solution using the Solver. Comment on your results. (25 marks)

(c) Should HomePro add more test machines to make more time available? If so, on which machines(s) should it be added? (8 marks)

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Question 2

John, a logistics manager at Cargo Global in Malaysia, has been tasked to prepare a loading plan for a freighter destined to Oman. The ship has three cargo holds with the capacity restrictions shown in the below table:

   Cargo Hold
Forward Centre Rear
Weight Capacity (tons) 3,200 5,700 3,700
Volume Capacity (cubic feet) 130,000 180,000 156,000

A commodities dealer intends to transport the products aboard this ship as shown in the table below:

1 2 3
Amount Available (tons) 4,500 3,300 1,700
Volume per Ton (cubic feet) 36 24 60
Profit per Ton ($) 58 45 52

Assume that John only can place one type of commodity into any cargo hold and that he can elect to load any and/or all of the available commodities. However, because of balance considerations, the weight in the forward cargo hold must be within 15% of the weight in the rear cargo hold, and the centre cargo hold must be between 45% to 55% of the total weight on board.

Analyse the problem by formulating the integer linear programming model. (30 marks)

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Important Note: Grading of TMA Submissions

Marks awarded to your assignment are based on the following guidelines:

Component Description Marks
1. Content •     Identifies key points correctly and comprehensively; applies relevant knowledge to solve the problem or address the issue

•     Provides supporting reasons drawn from course materials and other credible sources, wherever relevant

•     Shows a good grasp of the problem/issue with critical insight

•     Provides a mature response with feasible recommendations

2. Quality of


•     Demonstrates highly original writing*

•     Constructs sentences that are grammatically and syntactically correct, and are free from spelling mistakes

•     Uses, wherever relevant, specialised vocabulary and terminology related to the subject matter

•     Provides proper in-text citation and referencing to content drawn from course materials and other credible sources that follow APA formatting and style guidelines**

3. Quality of


•     Presents key points, workings, numerical formulations and results in a clear, logical and succinct manner

•     Presents well-annotated tables and figures, wherever relevant, that follow APA formatting and style guidelines**

•     Provides a reference list at the end of the main report • Includes less relevant details in an Appendix, if necessary • Shows proper formatting that may include:

o a properly formatted cover page and numbered pages o adherence to the specified word count, where applicable o paragraphs with proper spacing and page margins

Total   100


Reports with high Turnitin similarity and/or AI writing percentage, especially when the matching content is not cited and referenced, can attract further penalties.

See https://apastyle.apa.org/index for tutorials and webinars on the APA formatting and style guidelines. See also Purdue University’s Online Writing Lab https://owl.purdue.edu/ for information on APA formatting and style guide.

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