Principles of Teamwork Learning how to function as a team member, and make your team succeed is one of the key objectives of this course. You can not get a good grade without it. Team work requires work. Not a free lunch. Pays off though.

The indisputable laws of teamwork The Law of Significance. People try to achieve great things by themselves mainly because of the size of their ego, their level of insecurity, or simple naiveté and temperament. The Law of the Big Picture. The goal is more important than the role. Members must be willing to subordinate their roles and personal agendas to support the team vision. The Law of the Niche. All players have a place where they add the most value. Essentially, when the right team member is in the right place, everyone benefits. The Law of The Bad Apple. Rotten attitudes ruin a team. The first place to start is with yourself. Are you at our best? The Law of Countability. Teammates must be able to count on each other when it counts. Are you dedicated to the team’s success? Can people depend on you? The Law of Communication. Interaction fuels action. Effective teams have teammates who are constantly talking, and listening to each other. The Law of Dividends. Investing in the team compounds over time. Make the decision to build a team

Principles of Teamwork An important heuristic: Set up regular meeting times, rather than planning ad-hoc meetings. At least once a week + a back-up time. Tie to HW deadlines. You can not skip a meeting, unless the whole team decides it is not needed.

Break out in group will earn activity points for the in-class work. Now, a real life problem inspired by a real problem shared with me by a North Carolina software company. Break out in group will earn activity points for the in-class work. SET-UP: A sports equipment company manufactures 3 types of balls: golf, ping-pong, and tennis. The sizes (radii) of the balls are 2, 3, and 5 cm respectively, the balls are featherweight. The company ships each ball type separately, but uses only one size of container for all its shipping needs. The container is a perfect cube made out of padded, thermally insulating novel material (nano-carbon + trace amounts of gold) manufactured by just one company in the World. The boxes are loaded on the trucks by a single worker, using only her sheer muscle power. A lion’s share of the shipping cost is in the cost of getting the truck from A to B, so sending trucks partially filled with the merchandize is guaranteed to be non-optimal. PROBLEM: What is the optimal box size that will minimize the shipping costs? How many balls of each type will fit into such box (to within 10 % relative error)? ----- Meeting Notes (3/21/13 13:25) ----- Assume that once they have figured out exactly which box size is best, they can special order big trucks to fit the boxes precisely. In other words, truck dimensions can be tweaked a bit. Trucks are large.

The shipping problem cont’d Initial brainstorming: Boxes are expensive. Cost = (cost per box) x( number of boxes per truck). Each truck must be filled with boxes, so we really need to minimize cost per truck.

The shipping problem cont’d So it looks like we need to minimize the amount of expensive carton used per box, while preserving the total volume of all the boxes that fill up the truck. Is this it? (don’t focus on the “distilled” problem yet!) Strategy for complex problems: Is this it? Is this “distilled” problem the only one we need to solve? Have we left anything out?

The shipping problem cont’d Remember, we need to maximize the amount of merchandize (balls) per truck. Are we going to have more of them in larger boxes or smaller boxes? Second problem: packing of hard spheres. What is the best packing?

The shipping problem cont’d Remember, we need to maximize the amount of merchandize (balls) per truck. Are we going to have more of them in larger boxes or smaller boxes? Second problem: packing of hard spheres. What is the best packing (that is the one that minimizes empty space)? Is the best packing achieved in larger or smaller boxes?

The shipping problem cont’d Heuristic: divide and conquer. Complex problem divided into simpler parts. The problem-solving group may break down into two parts now.

The shipping problem cont’d Problem I: Do we need large boxes or small boxes? Box sides that touch each other are “wasted”, so need fewest touching sides, that is largest boxes within the other given constraints.

The shipping problem cont’d Problem II: Spheres packed inside the box. What box size will optimize the packing, that is minimize the “wasted” empty space? Heuristic: simplify.

The shipping problem cont’d Problem II: Spheres packed inside the box. What box size will optimize the packing, that is minimize the “wasted” empty space? Heuristic: simplify. 3D -> 2D (circles in a square) Get a feel for it. One circle.

The shipping problem cont’d Problem II: Spheres packed inside the box. Heuristic: circles in a sphere. Maximize packing density = (volume of spheres)/(volume of box) http://www.stetson.edu/~efriedma/packing.html

Next step Heuristic: get your feet wet. Roll up your sleeves. Try a few examples to see the trend.

The shipping problem cont’d What have we learned from the 2D case? Optimal packing occurs for the number of packed balls = k^2: 1, 4, 9, 16… The dependence of the packing ratio on the box size is not monotonic, but appears to reach an asymptotic value of ~ 0.78 for large size box. The undulations subside for large box size (many spheres) So, if we want true optimal packing, the box size should be such that that integer # balls of 2,3,5 (diameters 4,6,10) fit. Least Common Denominator = 60. a=60*m, where m is an integer. We want the largest box the loader can handle. The largest box that works for us, m=2, a=120.

The shipping problem cont’d What have we learned from the 2D case? However, in real life, it will be difficult to arrange the balls in a precise manner that gives this optima packing, for a large box and lots of small balls. For this large k, suboptimal packing (k^2 not close to optimal) does not matter all that much. For large box size a >> ball we can achieve a close to optimal packing even without being perfect. So, no reason to have the exact box dimensions to pack K^2 balls Just fill the box and shake it well…

The shipping problem cont’d Now back to the spheres: http://en.wikipedia.org/wiki/Sphere_packing More complex, but essentially the same thing conceptually. We don’t have exact solutions like in 3D, but we know that when box size >> ball size, any “good” packing is close to optimal. So, all we need is just a large box! Just shake the box well, let the balls settle, and you are likely to get close to optimal. Exact result: most optimal packing of identical spheres fills ~ 3/4 of the total volume. When the dimensions of the volume >> ball size, the shape of the box does not matter (the relative number of balls touching the walls is small, compared to the total number of balls filling the volume) Given the size of the box of ~1x1x1 m, its volume is 1m^3. The balls will take up 3/4 of it, from which we can compute the number of balls of each type.

The shipping problem cont’d Our tactical steps (heurtsics ) from the beginning: Brainstorm Divide and Conquer Simplify Get hands dirty. Explore trends.

For the curious: What is the packing ratio for biomolecules? Biomolecules are tightly packed collections of hard spheres (atoms).