This piece of work will count for 30% of the overall mark for MATH6002. It is intended
that you carry out the analysis using the Xpress-IVE modeling and optimisation
Completed work should be handed in to the Student Office Building 58 (Room 2127)
by Wednesday, January 10th, 2015, at 2:00PM. An Assignment Hand In Cover
must be completed and stapled to the front of your work prior to submission. Make
sure that you are given a receipt when you submit your coursework.
You should make sure that you are given a receipt. The Student Office is open to
students between 9.00 a.m. and 3.00 p.m. Students will not be able to submit coursework
outside these hours.
The deadline is strict.
Please refer to the MSc OR [and Finance] Blue [Pink] book for the penalties applied
to late assignments.
Your report should be word processed. Ensure that you take frequent and multiple
backups of your work, since excuses concerning lost or corrupted files will not be treated
As a very rough guide, I would like about six to ten A4 sides of description, with
any extra material (e.g., diagrams, tables or computer output) attached at the end.
Your report should include:
• an introduction;
• the formulation of your model with a statement of any assumptions made;
• a brief description of how you solved it;
• a presentation of the results;
• a summary of recommended policies that should be followed (and possible suggestions
for further investigations);
• printouts of the XPress-IVE model(s) and corresponding output in one or more
It should be written from the point of view of you, the OR analyst, describing
some work that you have done to an OR manager (who will know the mathematical
Marks will be awarded on the basis of
1• quality of the analysis;
• clarity of the presentation;
Your work must be written up independently. The model and report
must be your own work. You are reminded of the University policy on
plagiarism. Your report must acknowledge clearly all people with whom you
have discussed any part of the coursework, as well as any references you
might have used.
You are expected to complete the coursework without help from staff.
Limited assistance will be available from a postgraduate tutor (you will be told when
the tutor is available). No other assistance will be provided.
Orange Juice Production Planning
You have been assigned to provide Operational Research experience to the company
TropiJuice. TropiJuice is a major producer of frozen concentrated orange juice in
Brazil. Three orange varieties are used: Hamlin, Pera, and Valencia. The company buys
the production from selected orange plantations, picks the fruits, processes it into juices,
and blends them into two products called Standard and Dairy. The Standard juice is
primarily used by beverage industries all over the world. The slightly more expensive
Dairy has to satisfy certain conditions on flavour, acidity, and colour, among others.
The planning horizon is three months. The forecasted demand (in tonnes) over the
planning horizon is as follows:
product Demand in month selling price
1 2 3 (£/tonne)
Standard 1500 1500 700 1000
Dairy 200 100 100 1100
One tonne equals 1000kg. There is no penalty for unfulfilled demand.
The different orange varieties have different maturation periods. The expected availabilities
of different varieties during the planning horizon are as follows:
month expected availability (in 1000s of boxes)
Hamlin Pera Valencia
1 300 250 0
2 350 350 50
3 100 500 100
for each variety 3.5 3.7 3.4
2There are limits on the percentage of juice of each variety allowed in each product.
These are as follows.
• Standard can have at most 30% Hamlin juice, must have at least 60% Pera juice,
and at most 40% Valencia juice.
• Dairy can have at most 35% Hamlin juice, must have at least 50% Pera juice, and
between 15% and 50% Valencia juice.
Juice made in a month can be sold in that month itself, or later. Unsold juices may
be stored in refrigerated tanks at a cost of £10/tonne/month for all varieties.
The cost of purchasing, picking, and transporting the fruit to the juice plant is
estimated to be £1/box for each variety. The cost of running the juice plant is a fixed
amount of £0.5 million/month, and the plant has adequate capacity and workforce to
handle all the fruit expected to be available in each month of the planning horizon.
Your tasks are as follows:
1. Juice inventories are negligible at the beginning of the planning horizon. The
company would like to have no juice inventories at the end of the planning horizon.
It is required to determine a production plan that maximises the company’s
net profit during the planning horizon. Formulate a corresponding mathematical
model and solve it using XPRESS-IVE.
2. In part 1, possible capacity limitations to the juice plant have been ignored. The
equipment at the plant can process 0.4 million boxes of Pera oranges per month
if this is the only variety processed. Hamlin oranges use 10% more capacity, and
Valencia oranges 10% less capacity. The effective plant capacity will therefore
depend on the proportion of the different varieties processed. Revise your model
from part 1 to take into account these processing capacity constraints and solve
the resulting model using XPRESS-IVE.
3. Orange growers in northern Brazil produce a lot of Valencia oranges. A truckload
of Valencia oranges consists of 1000 boxes. Let λ denote the cost for purchasing and
transporting a truckload of oranges from the north to the juice plant. Evaluate the
effect of increasing the availability of Valencia oranges on the optimal production
plan, treating λ as an optimal parameter.
4. Reconsider part (1) with the planning horizon being 12 months with the demands
and the expected availabilities in the first three months are still unchanged.
However, for months 4-12, the demands and the expected availabilities are the
same with those in month 3. Please compare the answers among three cases: (a)
The factory must be opened every month, (b) There is option to open/close the
factory in each month and c) The factory must be opened for at least 10 months
throughout the year.