Assessment 3: Case 1
Recycling is an important and complex activity in Country A. To enable timely operations, the country
is divided into 10 sectors and recycling operations are commenced simultaneously in each sector. The
recyclable garbage is collected from public bins, loaded into trucks, and transported to recycling sites.
Each site can accommodate different amounts of recyclable garbage because of its available land size
at the facility. The annual capacities for five recycling sites are given in the table below (in
1 2 3 4 5
Capacity 20 20 30 15 15
Each recycling site is installed with facilities that have different recycling efficiencies which are
summarised in the table below (in percentages):
1 2 3 4 5
Efficiency 35% 40% 20% 60% 55%
The cost of collecting and transporting recyclable garbage primarily depends on the distance between
the sectors and the recycling sites. The following table summarises the distances between each sector
and each recycling site (in kilometres):
Sector 1 2 3 4 5
1 13.6 5.6 19.6 29.6 37.2
2 9.6 8.4 33.2 36.4 35.2
Page 2 of 3
3 5.6 11.6 14.8 37.6 34.4
4 10.4 14.4 18.0 32.8 35.6
5 6.0 12.4 8.4 31.6 35.2
6 16.8 19.6 26.0 30.8 24.4
7 19.2 24.8 39.6 24.8 22.8
8 21.6 24.0 20.8 30.4 19.6
9 12.4 16.4 26.4 30.0 28.8
10 12.8 26.0 28.4 24.0 33.2
Using historical data, the country estimates the annual volume of the recyclable garbage for each
sector in the coming year shown in the table below (in megatonnes):
Estimated Recyclable Garbage
1 2 3 4 5 6 7 8 9 10
10 8 4 7 5 6 10 8 5 6
It will cost approximately $113,918 to move one megatonne of recycling garbage for one kilometre.
The management would like to maximise the amount of recycled garbage and minimise the
a. Formulate a multiple-objective linear programming (MOLP) model for this problem in a Word
file with a brief description of an equation, and implement it in an Excel spreadsheet.
b. Determine the optimal value for each objective in the problem.
c. Suppose the management considers maximising the amount of recycled garbage to be two
times as important as minimising the transportation cost. Formulate a GP model to optimise
both objectives simultaneously with a brief description of an equation in a Word file, and
implement the MOLP model in an Excel spreadsheet. What do the results suggest?
Page 3 of 3
Guidelines: 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); do
this only for an optimisation problem.
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
a. Do not forget to submit the Excel spreadsheet together with the Word report
a. Briefly state what answer that you obtain
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
c. Cross-referencing and citations are correct, if any
d. All headings and sections are in place
e. Images or figures are clear
f. The writing is readable. You may use Flesch–Kincaid readability tests to evaluate your report.