In search of optimality: A re-cast

I’ve renamed my blog to ‘in search of optimality’ from ‘in search of excellence’.

My recent reconnection with systems modelling reminded me that many, many years ago I wrote a report ‘In search of optimality: a systems technologist goes east’ (Extracts summarised in Mellalieu, 1985). The report detailed the interesting learnings I had identified based on my six months post-doctoral study tour based at Massachusetts Institute of Technology (MIT) and Lancaster University, sponsored by the New Zealand State Services Commission (NZSSC) and NZ Department opf Scientific and Industrial Research (DSIR). In both locations, I wasted hosted by the departments of operational research. My external examiner for my PhD was also from Lancaster, and I also met Peter Checkland, of soft systems fame.

The title of my report is an allusion to Peters and Waterman’s book ‘In search of excellence’. Their book had been published whilst I was in America. I read the book with great excitement,noting their examples of business excellence around me in the many places I visited.

I had  completed my PhD in which I made extensive use of applied optimisation theory. So the title of my report ‘In search of optimality’ came naturally. It now seems natural that my web-site should thus be renamed.

So what is optimality? Optimality occurs when you find the best available values of some objective function given a defined domain (Wikipedia, optimisation).I’ll explain….

During my PhD, my search was for the best way to reconfigure the domain of the New Zealand dairy industry to maximise long-term economic performance. My objective function incorporated:

• expected future values of dairy products
• factory processing costs and fixed costs
• factory process yields of products and by-products
• transport costs of milk from farm to factories, and by-products to by-product processing facilities

The problem was ‘constrained’ by factors including: factory capacities, tanker capacities, product demand, and the quantity of milk produced by farms. These factors varied on a month-by-month basis. Furthermore, there were significant seasonal and long-term variations to be considered. Mellalieu & Hall (1983)

More generally, my search engaged me in formulating the problem in mathematical terms: as a mathematical model. Once formulated as a mathematical model, mathematical algorithms can be brought to bear to find the optimal solution. In school, for example, we learn to use differential calculus to find optimal points on curved spaces. Example: A stone is thrown upwards from the surface of the moon with gravity g/6 with speed v at an angle a. What is the maximum (optimal) height that the stone reaches. What distance, d from the thrower does the stone land? Knowing that the stone travels in a parabolic curve, we can solve this problem using calculus. (For a complicated (!!!) answer to this question, see: Parabola Separation Queries and their Application to Stone Throwing, Otfried Cheong1, Hazel Everett2, Hyo-Sil Kim1 , Sylvain Lazard2, & Ren´e Schott)

More generally, there are a host of procedures that one might choose, depending on the nature of the mathematical formulation used to represent the problem under investigation. Some procedures use calculus. Others use cleverly-conceived algorithms such as Danzig’s linear programming (LP). Many procedures can be executed with pencil and paper - such as those involving the principles of calculus. However, most real-world problems require computers to manage the data sets and execute the algorithms required to identify optimality.

Part of the challenge in optimisation studies (a branch of operations research) is to identify what factors (or variables) should be incorporated into the model. How far into the future should one consider? Beyond readily-measured financial costs and market prices, how does one quantify factors such as the impact of ‘environmental footprint’? This latter problem is one of ‘multi-objective optimisation’.

Is excellence is a subset of optimality? Or are they a different names for the same concept?

If you are not searching for optimality, then what are you doing?

Postscript

A good explanation of the stone throwing problem is illustrated by the physics of the medieval/Chinese trebuchet machine. The physics, of course, is also relevant to catapaults, ballistas, guns, and rockets.

Physics of the Trebuchet. (2010, October 23). library.thinkquest.org. Retrieved October 23, 2010, from http://library.thinkquest.org/05aug/00627/phy.html

Reference

Mellalieu, P. J. (1985). Some New Directions in Systems Modeling Practice. New Jealand Journal of Technology, 1(4), 223-238.   

Mellalieu, P. J., & Hall, K. R. (1983). An Interactive Planning Model for the New Zealand Dairy Industry. Journal of the Operational Research Society, 34, 521-532. doi:10.1057/jors.1983.119 

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My first-year university experience: a white-booted techie

I arrived for my first week at university following an eight-hour car drive with several school-mates. I recall my luggage and bicycle had been dispatched from the Cambridge railway station to Palmerston North several weeks earlier.

The second day of lectures was long. The day commenced with an applied microbiology lab at 8 a.m. and a biochemistry lab that concluded at 6 p.m. An engineering laboratory concluded the week which required a further five to six hours of Saturday to write up. Fortunately, there were just a dozen of these reports to complete through the year.

I recall having around 35 - 40 hours of contact per week: Eight courses with two hours of lectures and two or three hours of laboratories per week. Some courses, such as statistics and calculus had exercise tutorials. We technology students felt a little hard done in comparison with the arts students who had contact loads of about 20 hours per week. Their large reading and essay writing loads that meant little to us white-booted ‘techies’.

The computing course required us to submit our programmes on punch cards. Computing resources were strictly rationed with a focus on ‘getting in right first time’. There was a limit on the number of CPU seconds, line-flow, and program submissions. One campus computer. No Visual Display Unit (VDU) terminals for undergraduates. No personal computers. An electronic calculator in some laboratories. We used our engineering slide rule for conducting calculations for which we received several hours instruction. I purchased my first calculator for my fourth year of studies. By that stage, I had also been granted privileged access to a precursor to the personal computer: a Digital PDP-8 computer. “8” standing for 8 Kbyte of memory. I used this machine to assist with the calculations for my laboratories - and to program the matchstick game ‘Nim’.

The eight courses extended throughout the full year, broken into three terms. My academic mentor checked my progress towards the end of the first term. I suspect I reported I was on top of matters but felt it a bit unfair to have tests immediately after the two week study break. I now tell my own students the answer I received: that a ‘study break’ is a break FOR study.

At times the workload did seem daunting. However, I recall being reassured when I looked up at the ivy-encrusted Old Main Building in which we conducted our microbiology experiments. I thought of those students who had survived their studies, and I thought also of my inspiration, radioactivity scientist Marie Curie.

I recall some textbooks were useful in supporting our studies: chemistry, biochemistry, and statistics in particular. An added extra resource was available for statistics and calculus: the extra-mural study guides. Only in later years in my social science courses such as psychology and economics did I need to read the texts for exam purposes. For the engineering courses, all tests and exams were drawn from material presented in the course lectures. And lectures were not explicitly related to specific sections of the textbooks. Most of my texts were resold prior to the next year’s studies. I still possess my two engineering textbooks, a statistics text, and a quality  control text. I do recall finding the university libary an uninteresting source of light reading: mostly Jane Eyre genre. Not like the massive science fiction library on the shelves of Massachusetts Institute of Technology that later impressed me during my post-doc in 1983.

Was my first year a typical university first year? Like many first year students at Massey I stayed in the on-campus hostels (City Court), meeting new out-of-town students, and discovering new genre of music. I pumped out my new discoveries of Mahler and Shostakovitch symphonies on my home-made single valve 1 Watt ECL-86 amplifier. We engaged in the usual antics: re-arranging a student’s bedroom into the courtyard and inter-hostel water fights.

I had little need to visit town as the campus was self-sufficient in food and a weekly movie. Usually $10 would need to last me the last two weeks of the term.  For reference, a Chinese take-way meal was $2.00. I usually ate a huge breakfast and dinner, and scavenged leftover breakfast toast and jam for lunch. I sang in the Palmerston North Choral Society, and in a unique stage production - Te Papaoia - that recounted - apparently controversially - the history of the city and its surrounding districts. With a new-found musically-inclined friend, I joined his flat after the first term of my second year.

My first year was different in several respects from most students. Having gained a university scholarship, I requested and was granted direct entry to second year classes. Consequently, I joined classes of 20 - 50 students, rather than the larger first year classes comprising several hundred students. Most of my classmates were two or three years older than I was, but I soon became known as the swot of the class, gaining high marks especially in engineering, chemistry, computing classes.

Before I commenced my second year, I undertook a 12-week placement in a factory in Upper Hutt: Tasman Vaccine Laboratories (TVL). The plant manager loaned me the writings of management guru Peter Drucker and Douglas McGreggor. Those readings and various discussions with the senior scientist lead me to switch my major from biotechnology to industrial management.

The persistent pace and workload of my first year of tertiary study lead me to refine my already well-disciplined approach to study. I balanced time with recreational singing,  social activities and personal music listening. I maintained fitness with an exercise programme similar to 5BX and squash, but did not engage in a sports team. It would have been quite impossible to hold a part time job, but I did take employment during the ‘study breaks’ and summer break. I worked in a timber yard pulling orders one year.

See also: How can students be prepared for Practice-Based Learning? A reflection http://pogus.tumblr.com/post/989695576/pbl

Peter J Mellalieu matriculated for a Bachelor of Technology at Massey University, Palmerston North in 1973 commencing a biotechnology major. In 1976 he graduated with first class honours in industrial management and engineering.

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