**Optimisation and Simulation for Decision Making**

**LOG307 ****Optimisation and Simulation for Decision-Making**

**Question 1**

*Ding Bakery *makes three different tarts from pineapple and flour: Pineapple Tarts, Pineapple Balls, and Nyonya Pineapple Tarts. The demand forecast for next week, percentages of pineapple and flour, and net profit for each product are shown in the following table.

Products | |||

Pineapple Tarts | Pineapple Balls | Nyonya Pineapple Tarts | |

Demand (kg) | At least 550 | No more than 150 | Between 260 and 310 |

Pineapple % | 48 | 43 | 65 |

Flour % | 52 | 57 | 35 |

Net profit ($/kg) | 27 | 18 | 23 |

* **Ding Bakery *has 620 kilograms of pineapple and 510 kilograms of flour for use next week. These products are made using three different machines. The availability of the machines next week is as follows: 35 hrs for Machine I, 32 hrs for Machine II, and 38 hrs for Machine III. The following table summarises the time required by each product on each machine.

Minutes required per kilogram | |||

Machine I | Machine II | Machine III | |

Pineapple Tarts | 1.40 | 2.10 | 1.10 |

Pineapple Balls | 1.20 | 1.30 | 0.80 |

Nyonya Pineapple Tarts | 1.40 | 1.20 | 0.60 |

Assume you have been tasked to find the production plan that maximises the total profit.

**Question 1a**

Formulate an LP model for this problem. (10 marks)

**Question 1b**

Set up a spreadsheet model for this problem.

Determine the optimal solution using the Solver. Comment on your results. (20 marks)

**Question 1c**

If you want to change the production of any product, which one would you recommend and why? (10 marks)

**Question 2**

John is the store manager at *Challenger* in Changi City Point. He is evaluating inventory policies for Samsung TVs for the next two years.

The monthly demand for Samsung TVs follows a triangular distribution with a minimum of 100, a maximum of 500, and a most likely value of 340. Challenger incurs $980 for purchasing these TVs from Samsung and sells them to customers for $1,950. In addition, the holding cost is $20 per TV per month, and the ordering cost is $120.

Consider the following assumptions:

- Beginning inventory is 410 units.
- Current inventory policy is to order 900 TVs whenever the inventory at the end of a month falls below 200 units.
- Orders placed at the end of one month arrive at the beginning of the next month.
- Unmet demand in any month is considered as lost sales.

**Question 2a**

Construct a spreadsheet model to determine the average profit Challenger will earn from Samsung TVs over the next two years. Comment on your findings. (25 marks)

**Question 2b**

Suppose John has the option to place an emergency order when demand exceeds the on-hand inventory. These orders will arrive instantaneously but cost $50 per TV. Analyse whether he should opt for such an option. (15 marks)

**Question 2c**

Suppose John wants to find the best reorder point and order quantity that results in the highest profit over the next two years. The following table illustrates the options available:

Policy Number | Reorder point | Order Quantity |

1 | 150 | 700 |

2 | 200 | 700 |

3 | 200 | 900 |

4 | 300 | 900 |

5 | 300 | 1100 |

6 | 400 | 1100 |

Adjust the spreadsheet model you constructed for Q2b and find the best inventory policy for Samsung TVs for the next two years.

Comment on your findings. (20 marks)