My First-Ever £150 Optimization Problem
Last Tuesday officially marked the end of my MSc study (Operational Research with Data Science) at the University of Edinburgh (UoE). It was indeed a special year — imagine spending the entire year learning online in a tiny studio with minimal social gatherings. Heck, the pandemic made my eyesight worse. This is also another reason I would prefer printed copies of notes and books over their digital counterparts (and yes, recycle some of them later).
A £150 Problem… for Starters.
So something bugged me when I was leisurely spending my final week in the beautiful city of Edinburgh. Look, I have approximately £150 for printing from the university’s School of Math (I am grateful for their generosity). That’s a considerable amount of funds for a student!
Should I print my course materials with the fund and send them back to my home (Malaysia)? Is it worth it?
In case you are wondering why I did not print all of my notes earlier, it was because I have tried adapting myself to the “new norm” of e-learning and am now left with strained eyes.
And I thought this could be my first ever optimization problem in real life. So, immediately after my thesis submission on 27/8/2021, I only had exactly 7 days to solve and to apply the solutions (if any) to my problem before my flight back to Malaysia (Apa khabar?). Tick tock.
How Many Pages per PDF?
My initial plan was to spend my 14-day quarantine period in Malaysia to slowly download and organize all materials from the university’s virtual learning platform, Learn. Change of plan. Now, I need to gather simple details such as number of pages per document to make this work. Sounds hectic right? I am glad that I did not sacrifice any travel plan for this problem.
As you can tell, it can get quite painful to retrieve these information one by one whilst organizing my downloaded contents on my external hard disk. It took me two nights to grind through the process, but at least I am now free to do something else during the quarantine period. Yay!
A total of 1787 pages are available for printing (grayscale, double-sided)! The goal is to print out the contents for as many courses as possible (I would like to further break down the categories into content types, such as lectures, tutorials, problem sheets, etc., for printing selection, but that means adding to inconvenience when organizing the hardcopies later).
I will walk you through my thought process in the remaining sections of this article and show you my full optimization model in the end. Read on and cheers!
Cost to ‘Whirrrrr’ This?
Now that I have gathered all materials for printing, I need to know the printing cost to define the budget constraint properly. It’s time to look at the university page for the print and copy costs:
A quick calculation reveals that the budget would suffice for the printing of all materials. But, in the interest of practicalities, we would need to introduce more constraints to the optimization problem. For instance, I will need to justify that printing documents in UoE and send them back to Malaysia is a cheaper option.
Below is the typical printing cost in Malaysia. Of course, these days, shops offer a discount on bulk printing (e.g., RM0.05 unit price above 1000 pcs), but not all information can be shared publicly due to copyright reasons. Do note that the discount also varies across shops. Hence, I will use the typical unit cost for the cost comparison constraint.
Sending Parcel Back Home!
Cool, I got all the information I need for printing; what about the logistics then? Thankfully, my ‘castle gang’ buddies told me that I could use the economical sea freight service by Demaga Logistics. I took a screenshot of the quotation on Whatsapp:
As I am only sending documents, I do not require that much space compared to other items, so I have decided to go with the medium-sized box. Instead of paying £15 to receive an empty box, I had to spend the same amount to source a size-equivalent box from Argos in-store due to time concerns.
Understanding the box dimensions and weight limitations helps define the height and weight constraints. Inside the James Clerk Maxwell Building (JCMB) printing room, we use the 80gsm uncoated white A4 paper. They each weigh 5g and has 100 microns in thickness.
Ta-da! My Full Optimization Model.
If you have made it this far, kudos! Because I am about to show you my full binary linear programming problems (BIPs) below:
As you can observe, not only that I have to satisfy the budget constraint, I must ensure that printing in UoE is cheaper, at the same time providing enough box space & weight capacity for the documents. From lines 2, 4, and 5, I have also included tolerances for printing errors, defects (box & paper dimensions), and additional box contents (paper covers, binders, box magazine file holders, etc.).
Let’s take a look at the optimization outcomes:
Hooray — If I can apply this solution, I’d save £12.545 (adding another £5 would mean I can get a nice lamb shank from the Makars Gourmet Mash Bar)! Even better, there will be plenty of space left in the box for me to include other items in the parcel (let’s add souvenirs). Wonderful.
The Final Step: Turning it Real.
I was extremely excited to turn the optimization outcomes into reality as soon as I could solve them on Wednesday (1/9/2021). Over the next 3 days, I spent 2 hours at the JCMB building to print and organize the hardcopy materials before continuing with my daily travel plan. Trust me, this is just another excuse to connect a little bit deeper with the university before heading back home. Blame the pandemic, ops.
Great news — everything went well according to the plan. I had more balance than expected due to a smaller printing error (I spent the remaining budget to print my travel documents).
The final weight of my printed materials is slightly heavier (by ~600g) due to the addition of thick paper covers, binding materials, and some box racks. Note that this has already been discussed in the previous section.
Finally, I have also filled my parcel with joys, apart from the printed materials! I can’t wait to send them back to Malaysia.
Wrapping Up & Final Thoughts
I am thrilled to be able to apply a small part of my MSc knowledge in solving this printing problem (jumped like a little kid when I was done packing my parcel). Although this problem is simple compared to so many Operational Research applications (OR) today, I see this as a beginning of OR implementation in my daily life. Needless to say, I already have fun plans for my upcoming mini-projects. Hopefully, I can manage it well when I enter work-life in October!
At the time of writing, I am serving the 14-day quarantine order at Impiana KLCC, Malaysia — chilling and thinking about life.
Problem Value: £150.
Time Spent on Problem: 14 hours, across 7 days.
