Prescriptive Analytics: From Data to Decision – QBUS 6820
Semester 1, 2025
Assignment 1
Issued: 21 March 2025
Submit date: Friday 4 April 2025 at 11:59pm
All problems to be submitted for assessment (20%)
Assignments must be typed. Handwritten assignments will not be accepted.
Submission of assignments is strictly through Canvas
For all questions you are required to provide your Python Code (this can be done in an
appendix).
Question 1 (10 marks):
You are a Management Scientist hired to advise a shipping company with an existing contract
to transport 280,000 products per month for Australia Post. The company has already
committed to a fixed price and taken the following actions:
• Hired 35 drivers under long-term contracts with fixed salaries.
• Signed a binding agreement to purchase 50,000 litres of petrol each month at a fixed
price.
• Entered into a binding agreement with a local workshop for up to 400 hours of truck
maintenance per month, at a fixed price.
The contract with Australia Post stipulates that the company must deliver all 280,000
products, either directly or by subcontracting part of the workload to other shipping
companies. After negotiations, the subcontracting rates are as follows:
• $1 per product for the first 25,000 products.
• $1.30 per product for the next 25,000 products.
• $1.60 per product for any additional products beyond 50,000.
To address a potential driver shortage, you have engaged a recruitment firm that can supply
up to 10 additional drivers at a cost of $8,000 per driver per month.
The company has also addressed fuel uncertainty by contracting a fuel supplier, allowing it to
purchase up to 10,000 additional litres at $1.50 per litre, or sell up to 10,000 litres of excess
fuel at $1.10 per litre.
However, the company has not resolved the uncertainty regarding maintenance availability.
The maximum of 400 hours per month cannot be exceeded, and any unused hours are
forfeited.
The company can deploy four types of trucks (models A, B, C, and D), each with different
resource requirements and capacities as shown below:
TRUCK
MODEL
DRIVERS
REQUIRED
DELIVERY
CAPACITY
(products/month)
MAINTENANCE
REQUIRED
(hours/month)
FUEL
CONSUMPTION
(litres/month)
A 2 11,000 20 2,000
B 2 9,000 14 1,700
C 1 7,000 12 1,200
D 1 6,000 10 1,100
Your tasks are as follows:
1. Formulate a Mixed-Integer Linear Programming (MILP) model to determine:
o The number of trucks of each model to operate.
o The optimal use of available and additional resources.
o The optimal subcontracting strategy.
2. Solve the MILP model using Python and provide your code.
3. Based on your solution, what is the optimal purchasing and subcontracting policy, and
what is the corresponding cost (excluding sunk costs such as existing driver contracts
and fixed resource commitments)? Provide a detailed discussion on the company’s
resource utilization and the factors influencing the chosen policy.
Question 2 (10 marks):
A company manufactures and sells three products: A, B, and C. The Operations Manager is
responsible for planning the production levels over the next four months. It is assumed that
all units produced can be sold, with the following per-unit profits (which vary due to
seasonality):
PRODUCT A PRODUCT B PRODUCT C
Month 1 $140 $155 $210
Month 2 $140 $140 $220
Month 3 $150 $150 $230
Month 4 $150 $155 $230
Each product requires two types of resources: labour hours and raw materials. The resource
requirements per unit produced are as follows:
PRODUCT A PRODUCT B PRODUCT C
Labour (hours) 2 3 4
Raw material (kg) 4 3 5
The company has pre-ordered raw materials for each of the next four months, and these
orders cannot be changed. Any unused raw materials from one month can be carried over to
the following months without incurring any holding costs. For example, if 100 kg of raw
material is received in Month 1 and only 90 kg is used, the remaining 10 kg will be available
in Month 2.
The available labour hours for each month have been planned in advance, taking into account
scheduled employee leave. Additionally, the company has surveyed its workforce and
identified how many overtime hours could be made available each month. The company may
choose how many of these overtime hours to use (up to the maximum available), but unused
labour, regular or overtime, cannot be carried forward to future months. The cost of overtime
varies between months due to differing employee wages.
The following table summarizes resource availability and overtime costs:
RAW
MATERIAL
ORDERED
(KG)
REGULAR
LABOUR
AVAILABLE
(HOURS)
OVERTIME
AVAILABLE
(HOURS)
OVERTIME
COST PER
HOUR
Month
1
120 100 30 $25.0
Month
2
140 80 20 $25.0
Month
3
150 90 30 $28.0
Month
4
110 100 10 $30.0
The objective is to determine the production plan that maximizes the company’s total profit
over the 4-month horizon.
Your tasks are as follows:
1. Formulate this as a Linear Programming (LP) model.
2. Implement and solve your model using Python.
3. Based on your results, present a detailed production and resource allocation policy to
the CEO, highlighting key insights and recommendations.
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