assessment 3 final v2

Assessment 3

Jordan Bird - 149074887

CS1320

December 1, 2014

Assessment 3 | Jordan Bird - 149074887 Page 1 of 12

Introduction

With this paper I hope to take the problem at hand, and the two solutions given to ultimately understand the problem, evaluate the two solutions, and finally evaluate the problem solving process in comparison with other processes. In this report, I hope to fulfill the following criteria:

Show my understanding of the problem’s requirements Evaluate the solutions given and recommend one of them – showing the primary features

and benefits of the selected solution Evaluate the process of problem solving that I used in comparison to another solving

process The problem that has arisen is a real life version of a game known as ‘Sokoban’1, where the player must move boxes around a ‘level’ to certain points of the floor. The game is a very well-known puzzle, and has been used in many different contexts. Hyperspace Delivery Boy!2 Was a Pocket PC videogame title developed by the famous John Romero which used elements from Sokoban in its puzzles, mixing them with action and adventure themes to create a fully-fledged, story-driven game. The problem I am going to understand and then solve is, according to the brief, as follows, “John is the manager of a team of warehouse workers. He has observed that they

frequently run into problems when moving crates around the warehouse from their drop off points to their storage locations or from their storage points to their despatch location. It seems that John’s workers are not able to determine a suitable flow around the warehouse that would allow them to move the crates without blocking each other.”

I am also going to take a look at two proposed solutions, and evaluate them comparatively, choosing one of them as the best solution for the problem at hand. I am then finally going to evaluate my own performance throughout, keeping in mind the problem solving processes and techniques I have used in completing the various tasks.

Understanding the problem

To understand the problem at hand, I plan on making use of my own system, which is heavily inspired by my own personal opinion of effectiveness of Paul Vickers’ problem solving process’3 steps. I have previously reported the effectiveness of each of them for solving a problem, and also spoken about how steps can be merged together to become much more effective parts of the method. In light of this information, I will follow my own process which is again, heavily inspired by my opinions on Vickers’ process.

1 Hiroyuki Imabayashi. (1982). Sokoban. Available: http://www.sokoban.jp/. Last accessed 9th December 2014. 2 Monkeystone Games (2001). Hyperspace Delivery Boy!. Global release: Linux Game Publishing. 3 Paul Vickers. (2008). Chapter 2. In: How to Think Like a Programmer, Problem Solving for the Bewildered. : Cengage Learning. ISBN-10: 1408065827, ch. 2 pp. 30-37


1. Pull out the key parts To start with, I must take out the key parts of the problem in order to understand it. I am going to do this for the simple reason that seeing a simple list of the main parts of the problem will allow us to see the criteria we must achieve. The following are key features of the problem I have taken from the brief:

John is a warehouse manager There is a team of workers in the warehouse The workers transport boxes around various points in the warehouse The workers cannot figure out a good path to follow when transporting boxes John has requested a solution to the pathfinding problems occurring John has had two proposals The proposals need to be evaluated

The problem has become far more manageable with this step in mind. Looking over the main facts, it is easy to tell exactly how the situation is, without having to reread any parts of the problem. If we were to show this to another person, they would scan the points and due to their simplicity, have a good idea of the problem. After looking at the above points, we can see that the problem at hand is the process of work in the warehouse, and we must solve the issues the workers are facing. Now, with our key parts causing the problem to be far simpler, we can go on to understanding the problem further.

2. Rephrase the problem in my own words To improve my personal understanding, I feel I must read and rephrase the problem in a way that I would describe it personally.

“Warehouse manager John requests that we develop a system for his workers to use or follow, which will serve the purpose of a workflow which will not interrupt any other workers.”

As the above text shows, my personal way of writing the problem is to take the key points and arrange them into a simple explanation shows the description of the problem in the way that I currently understand it. This will serve as a base when I come to the end of my understanding process and can ultimately explain the problem with a complete understanding of it. Essentially, this could actually be the full problem, but I will not know that for sure prior to fulfilling the rest of the steps in my problem solving process.

3. What do we know about the problem and solution? (What are the main facts?) This step is very similar to step 1. Whereas this time, I will list the key features of the solution. I will do this through diagrammatic reasoning. As I previously explained in a past paper, I make use of diagrammatic reasoning because of the following: “The practice of diagrammatic reasoning (an evolution of the simple diagram) dates back in academic just over three-hundred years ago. The work of Gottfried Leibniz (independent developer of calculus


during the time of Newton’s work4) led him to describe his philosophy with diagrams to properly show work as well as the reasoning to back up points, not to mention allow a deeper understanding of the theory5. As I wish to gain this ‘deeper understanding’ of the problem, I shall reason diagrammatically what I know the solution must do. The top of the pyramid connotates the most important features of the solution. Ie. What I must do (according to the brief). As we go down the pyramid, we see the things we should do in the solution process, arriving finally at the lowest segments and what we could do. This hierarchy can be called upon later as a checklist to how effective the solution is.

Now we have a base for our solution to be built upon. We can see things that must, should, or could be part of the ultimate solution. This further develops our understanding as it assures the solution does not

4 Smith, David Eugene (1929). A Source Book in Mathematics. New York: McGraw-Hill Book Company, inc. 5 Leibniz, G (Original Paper:1704 Open Court Book:1949). New Essays Concerning Human Understanding. LaSalle: Open Court Publishing.

Ensure safety of

the workers

Solve the issue of

path-finding

Be applied to a warehouse that

changes

Give the workers a reference of the layout of

the warehouse

References provided through materials

References provided through digital materials

Make use of John's skill in the area


miss out any of the important criteria. As well as this, the base of the pyramid shows things that would further improve our solution, and therefore this diagram will lead us to creating a far better solution in the end.

4. What is our new understanding of the problem? Conclude your findings. To conclude our understanding of the problem, my final understanding of the problem at hand and what is required of me is as follows:

“Warehouse manager John requests that we develop a system for his workers to use or follow, which will serve the purpose of a more optimized workflow, which will not interrupt any other workers. Making use of his experience in the area, providing reference to the workers, and ensuring their safety in the workplace are all concerns that must be considered.”

This deeper explanation of the solution’s requirements will aid me further in the evaluation and solving process.

5. What are the benefits of solving the problem now we understand it?

Giving a clearer understanding of the problem throughout has led me to a far more effective description and explanation of the problem. I now have a strong base for the problem solving process to be compared to, not only this, I also have a list of criteria the solution must, should, and could fill. I feel that I can now review and evaluate the two solutions in comparison to this information. Surely the more criteria they fill, the more effective a solution they provide.

6. What are the benefits of creating and implementing the solution with the key features in mind?

Obviously the main solution to optimizing a warehouse is to increase the profits of the company by decreasing unneeded expenditure and time wasting6. Not only this, if we take a look at our previous criteria that we have discovered, the benefits of solving this problem aid in keeping workers safe too, which is a very important concern. The optimization of the warehouse ensuring worker safety is a great improvement to a warehouse environment.

Solution Evaluation

Jacob’s solution

Jacob has specifically solved the problem by making use of Warehouse Manager John’s logical knowledge and experience with warehouses7. According to “Theoretical analysis on Picokosmos 17”8, the most skilled players of Sokoban rely on their heuristics – the use of experience to solve a

6 Frazelle, E (2001). World-Class Warehousing and Material Handling. : McGraw Hill Professional. 7 Aston University. (2014). CS1320 Brief. Available: https://vle.aston.ac.uk/bbcswebdav/pid-671808-dt-content-rid-2424800_1/courses/2014_CS1320/Assessments/CS1320CW03.pdf. Last accessed 9th December 2014. 8 H, David (2002). ,Theoretical analysis on Picokosmos 17. Web Publication:


problem through a ‘rule of thumb’ type way of thinking9. Jacob has noticed this and therefore wants to aid himself in solving the warehouse problem by using John’s skill. This does not necessarily produce a most optimal solution, but provides something similar nonetheless10. The problem specifically stated that the desired outcome must be achieved, not that it be the most optimized one, and therefore I feel Jacob has a very strong problem solving method in this instance. He will allow for workers to be trained through John’s experience, to have their heuristics sharpened, therefore anybody will be able to work shifts at different times and receive training to optimize the warehouse productivity over time. Jacob’s solution begins with a strong level of experience through John as a ‘guru’ type figure to manage as the workers learn. Jacob has realized that the shortest route is not necessarily the best one to use – as it may mean cutting the path of others. Because of this, he has instead opted for a traffic flow system around the warehouse to provide a much better system This is a very effective approach that we see in modern times, warehouse managers are picked for their experience in the field and have the job of using that skill to manage the warehouse11, and in this case, solve the problem. If we take a look at the ‘evaluation’ stage of George Polya’s famous problem solving strategy12 we see a list of heuristics that act as a checklist of methods that can be used by a skilled problem solver – and of course, someone who can solve the problem at hand using their own skills. The following is a list of all of these evaluation steps laid out by Polya, with the reasoning on whether Jacob has made use of them. Please note the following steps are heavily influenced by Polya’s technique, though many points have been merged or reasoned in other points.

1. Analogy – Jacob has noticed that the obstacles are providing a problem within the

flow of the warehouse. Making use of the floor plan he has proposed, he can redesign the warehouse by moving objects. The ‘analogous’ problem will be solved and therefore Jacob has followed the Analogy heuristic.

2. Generalization – The problem solved by Jacob is very generalized. I have noticed that the solution he has proposed would work with any indoor environment where workers must move about. For example, the provision of a floor plan, route, and routes of other workers could be provided to a large store during the Christmas Shopping Rush and also solve that problem too. For this reason, I feel that Jacob has followed this second heuristic.

3. Induction and Variation of the problem - Jacob has rearranged the problem and in the process realized that the workers are not the problem, it is the fault of no definite routes and obstacles that the warehouse is not optimized. He follows this heuristic by challenging those problems instead of the preliminary one.

4. Auxiliary problem – in addition to the previous point, solving the problem of obstacles and a definite route around the warehouse would push Jacob in the direction of a solution and therefore the auxiliary problem solving that he has done will help him.

9 Pearl, J (1983). Heuristics: Intelligent Search Strategies for Computer Problem Solving. New York: Addison-Wesley 10 Epstein, S. Pacini, R. Denes-Raj, V. Heier, H (1996). Journal of Personality and Social Psychology. "Individual differences in intuitive-experiential and analytical-rational thinking styles" 11 Richards, G (2011). Warehouse Management: A Complete Guide to Improving Efficiency and Minimizing Costs in the Modern Warehouse. ISBN-10: 0749460741: Kogan Page. 12 Polya, G (2002). How To Solve It. Princeton University: Princeton University Press; Princeton Science Li edition (April 25, 2004). p.36.


5. Relation to other past problems – Jacob unfortunately falls at this step as he has not backed up his reasoning by mentioning how a solution like his has helped in the past. After doing some research, I have seen that there is much in the way of route planning in the warehouse13. This means Jacob may have simply forgotten to mention this in his solution, but we must assume not as to be sure. Therefore Jacob’s solution does not fulfil this point.

6. Specialization –Jacob has failed again in researching other problems, as he has not provided us with another more specialized problem similar to the one we are faced with. Jacob has not backed up his points with referenced secondary research and therefore we assume that none has been done – as it would have been provided in the solution to aid in consideration.

7. Draw a figure - I feel that due to the fact Jacob has come up with a routing situation, he must have either come up with an algorithm or visual diagram to show it. This therefore I feel that Jacob will have solved this stage though not provided and therefore loosely.

To conclude Jacob’s method of making use of John’s experience, although the problem solving method isn’t perfect – it is realistic. This is the most important point of the process, it may not lead to a winning move in the game Sokoban as it may produce a longer solution than needed, but I feel that it is a great solution for the problem at hand because in a realistic world, the warehouse cannot be at 100% optimization at all time. I feel that Jacob takes into account the realistic expectations of the warehouse, and therefore his solution is a very strong one. Compared with my understanding of the problem:

Ensure the safety of the workers – Yes - Jacob’s flow system will ensure workers will not bump into each other causing damage and harm

Solve the issue of path finding – Yes – a directional flow will solve the problems in pathfinding around the warehouse

Be applied to a warehouse that changes – Maybe – if the solution were to be implemented every day, the references would be that of the current layout of the warehouse.

Give workers reference to the layout – Yes – the reference material planned will show the workers the physical layout of the warehouse

References provided through materials – Yes – Jacob plans on providing reference material to the workers

References provided through digital materials - No Make use of John’s skill and knowledge – Yes – Jacob has realized John has experience in

the field, and uses him as a leadership figure to run the flow system in the warehouse. Improvements with evaluation in mind: I believe that for Jacob to strengthen his solution (though it is already a very potent idea), he must provide secondary research and diagrammatic figures to back up his solution. This would make it much more accessible to a warehouse manager, as many parts of it would already be proven. Jacob could also possibly implement a digital system into the solution too, to fill one more of the ‘could’ criteria set out. Primary features and benefits:

13 Proteus Software Ltd.. (2014). Logistics Supply Chain - Route Planning & Scheduling. Available: http://www.proteussoftware.com/logistics-supply-chain-route-planning-scheduling. Last accessed 9th December 2014.


Realism – The solution is realistic and therefore can be applied to the real world. A solution for the game could provide a starting point, but limitations of the world would have to be dealt with for it to be used in a warehouse. Jacob’s solution is not affected by limitations of the world, and in fact embraces them by making use of John’s experience.

Readily usable – Only requiring human planning and paper resources, the solution is easily usable straight away.

Cheap – This solution makes use of John’s experience, and printouts of routes and floor plans. It would be a very cheap system to implement.

Reusable – As explained in Polya’s Generalization step, Jacob’s solution is very general and therefore would be effective in not only other warehouses, but also completely other situations. John may want to apply the solution to the warehouse vehicles coming to and from the warehouse, or maybe even in the offices. These examples show the solution to be a very reusable system that can be applied elsewhere if need be.

Alison’s solution

Alison begins with stating that she is to solve the problem via providing a solution to the much similar Sokoban game and then applying her findings to the warehouse. She begins by telling us that the boxes can be pushed and pulled as well, which gives us a very weak first impression as this is actually different game with different rules known as ‘Pukoban’14 that allows for boxes to be pushed and pulled. With this in mind, Alison goes on to say that her solution for the game is to create a computer generated model of the warehouse floor plan, where the player(s) will move workers around to solve the problem, and the players will in effect learn to move around the warehouse in a more proper manor, effectively learning from experience. I feel to properly compare and select a solution, I must use the same evaluation method as used in the first solution, Polya’s steps of evaluating a process with my own personal ideology behind the points and merging some/changing some.

1. Analogy – Alison speaks of the floor plan of the warehouse changing between each area, and therefore goes on to say that she would create a 3d rendition of the warehouse for the workers to use as a reference. This is an analogous problem that has been solved with the addition of a worker’s reference, and therefore she has completed this heuristic,

2. Generalization – The nature of the problem, as was with Jacob’s solution too, allows for the problem to be used in different circumstances. Alison’s solution solely requires a floor plan to be generated, and therefore the solution can be applied to almost any environment of work.

3. Induction and Variation of the problem – Alison has realized that the workers will learn skills on their own through experience, and has given them a little guidance via the 3d floor plan.

4. Auxillary problem – Beyond providing a floor plan, no auxiliary problems have been solved, and therefore this heuristic has not been dealt with.

5. Relation to other past problems and Specialisation – No evidence of past instances where the problem has been solved in this way has been provided.

14 Zubaran, T. Ritt, M.. (Date of publication unknown). Agent motion planning with pull and push moves. Available: http://www.lbd.dcc.ufmg.br/colecoes/enia/2011/0011.pdf. Last accessed 9th December 2014.


6. done – as it would have been provided in the solution to aid in consideration. 7. Draw a figure – Figuratively, the 3d model represents the problem in a visual

manner. Compared with my understanding of the problem:

Ensure the safety of the workers –No – The ‘learn from mistakes’ approach that Alison has taken may result in dangerous situations earlier on, this is not acceptable.

Solve the issue of path finding – Yes – The workers will ultimately figure out a path from experience.

Be applied to a warehouse that changes – Yes – the application of skill after it has been learned will allow for other layouts of warehouse.

Give workers reference to the layout – Yes – The 3d representation will provide reference to the workers

References provided through materials – Yes – as above References provided through digital materials – Yes – as above Make use of John’s skill and knowledge – No – The workers are left to develop their skills

independently

Improvements with the evaluation in mind: Alison’s solution requires a lot of work before it becomes a viable solution. To do this, I would advise her to complete the following criteria as to therefore fulfil Polya’s expectations in an evaluation of a good solution,

As was with the previous problem, no research has been given to strengthen the solutions in mind. If I were John, choosing a solution, I would rather see instances where the solution or a solution that is very similar, has been used elsewhere. We do have the one point that the solving of the puzzle game will be applied to the warehouse, but beyond this assumption, no evidence is given. No auxiliary problems have been solved, which is very important in this instance. Jacob has accounted for realistic situations such as safety concern and differing of storage areas etc, whereas Alison has left the workers to learn and work on their own with no real guidance other than their own skill. John’s experience is very useful, and Alison has not made use of it. Alison must ensure the safety, and therefore the ‘learn from mistakes’ approach is not acceptable whatsoever. To overcome this she needs to develop a set system for everyone that doesn’t interchange between individuals. Alison could make use of John’s skill, as he is the warehouse manager and could provide a strong leadership figure to the workers.

Alison’s solution is very weak, as it is purely providing a 3d model of the area for workers to reference from. Beyond this, she has left them to learn on their own through trial and error. This could result in a dangerous situation in the place of work and therefore would not be a viable way of thinking.


Primary features and benefits: Strong representation – visualizing the warehouse is extremely easy when provided with

a 3D representation of the room. Trains workers – workers will gain skill when learning, following this solution

Comparison

Alison wants the warehouse workers to train their heuristics independently. The development of Heuristics is a hard-coded evolutionary trait15 and therefore would have happened whether this or any solution was applied or not. Therefore, other than the use of a 3d generated model of the warehouse, Alison hasn’t actually come up with a proper solution. She has provided a starting point for a solution to be implemented, by converting it with reality, as Jacob has already done. Whereas, on the other hand, Jacob has made use of the warehouse manager’s experience and will provide resources to create a solution that is much more applicable to the real world. Therefore with this in mind, I feel Jacob’s solution is far superior to the other provided. Alison’s solution is a great way to solve the Sokoban, or rather the Pukoban game, but the problem at hand is a real world representation that contains factors that she simply hasn’t accounted for. Whereas Jacob’s solution could viably be applied to the warehouse environment. If this were a report on a problem solving strategy for the game, then I would have chosen Alison as she has seemingly followed the ideas from Sokoban’s review in Computer Gaming World16 which describes the method of learning the level completion skill that she speaks of quite directly. Alison’s ‘learning from mistakes’ may endanger the workers, and therefore this completely negates Alison’s solution, as it would be a crime to implement.

15 Gigerenzer, Gerd (1991). How to Make Cognitive Illusions Disappear: Beyond "Heuristics and Biases". European Review of Social Psychology: University of Salzburg, Austria. 16 Wagner, R (1988). Computer Gaming World: Puzzling Encounters. : Golden Empire Publications. p42-43.


Problem Solving Process

What did I do to solve this problem?

To solve the problem, I first started with steps heavily inspired by Paul Vickers’ HTTLAP problem solving process, changing some of the points to fit the problem better, not to mention also taking out some points that I did not feel were applicable to the situation. I did this as it contains a very effective method for understanding a problem. Due to past experience with this process, I found it comfortable to go through the steps that I found most effective in previous experiences. I feel that making use of this process to understand the problem at hand was very useful as it provided a set of criteria that the solution must meet, which I could then use to evaluate each of the two solutions, ultimately leading to the solution that I chose to be the strongest, and most useful. Secondly, when evaluating the solutions, I used two problem solving methods. I did this as it would negate any forgotten points (if there were any). First of all, I used the method I developed which was very heavily inspired by the well-known HTTLAP process to develop the set of criteria that a solution must, should, and could meet. I applied these points to the solutions and developed half of my evaluation through it. Secondly, I took George Polya’s ‘How to Solve it’ method, as it has a very detailed list of heuristics which allow for a deeper look into the problem. I applied the checklist of heuristics, renaming and changing them to fit the problem, as well as taking away those completely non-applicable to the situation. This was very useful as it showed me the heuristic skills that the two had used. I believe due to using two processes together, the solution I chose, and the action of choosing it, were backed up strongly. I compiled the findings from both of these processes to compare the two solutions, showing which one had fulfilled more than the other. Improvements To evaluate my own performance, I believe that there is always room for improvement. I feel that the use of the two processes in the evaluating solutions part of my essay was most definitely the strongest part. In light of this fact, I feel that my understanding of the problem would be far deeper if I had used multiple methods in the planning stage, as oppose to only Paul Vickers’ method. Also, I believe that drawing more research from the processes in the warehouse would provide more understanding of the problem, and therefore a better evaluation as the two are very closely coupled. I believe that if I were to repeat this exercise in the future, I would extend it. What I mean by this is, I would extend the first section to encapsulate myself actually solving the problem itself. This would provide me with, a list of criteria, a basis for the evaluation, and an effective solution itself. I would then take these pieces of information, and when cross-referenced with the solutions given, I would in turn then be able to evaluate the solution much more effectively. This would strengthen my own thought process due to realizing my own mistakes, but also strengthen my evaluation as it would show their mistakes too.


Final Conclusion

To provide a final conclusion, I will lay out an extended version of my starting criteria and reason with myself on how I have done that in this project. Once I feel the criteria are all filled, then I will be confident that my report is complete.

Understanding the problem (Describe the problem) Describe the problem – In the first section, I made use of a method similar to Paul Vickers’

method to understand the problem. It ultimately resulted in a deeply detailed description of the problem itself.

Show key features – the diagrammatic reasoning section of the Understanding the Problem part showed the main key features of the solution at the top of the pyramid and other features lower down. Key features of the actual problem were listed in bullet form under pull out the key parts.

Show the proposed benefit – The benefits of the solution were listed under the benefits of the creating and implementing the solution.

Show the relationship of the two previous points – In the same benefits section as mentioned, we talk about the top key points in conjuction with the benefit of them actually being solved and implemented into the solution. Solution evaluation

Show how each addresses the key issues of the problem – I listed the key points that I had previously laid out in the first section, and then compared whether the two solutions had met them.

Identify the best solution – With the result of the above point in mind, as well as of course Polya’s list of heuristics, the best solution was plainly obvious and therefore became extremely easy to pick out due to it fitting these criteria almost perfectly (in comparison with the other solution.) it also showed that Alison’s solution was unfit for the workplace, which was not obvious at first. Problem solving process

Describe and evaluate the process in comparison with HTTLAP and/or another process – I compared my problem solving process with Vickers’ and Polya’s teachings as it was very heavily inspired by their teachings. I evaluated the positive points in my essay, as well as those that could be done better – and how I would do them better too.

Use outside resources in aiding a deeper understanding of the process – after researching warehouse management for some sections (as referenced) I also looked into the teachings of Vickers and Polya for problem solving processes to be inspired by. I also looked into journals of personality and psychology as we were dealing with human beings who must be treated as such (which was another reason Alison’s solution was irresponsible). Not only this though, I also read up on the Sokoban game, actually noticing that the game Alison had solved was not infact Sokoban. Many other readings can be seen via the reasoned references throughout.


References

Aston University. (2014). CS1320 Brief. Available: https://vle.aston.ac.uk/bbcswebdav/pid-671808-dt-content-rid-2424800_1/courses/2014_CS1320/Assessments/CS1320CW03.pdf. Last accessed 9th December 2014. Epstein, S. Pacini, R. Denes-Raj, V. Heier, H (1996). Journal of Personality and Social Psychology. "Individual differences in intuitive-experiential and analytical-rational thinking styles" Frazelle, E (2001). World-Class Warehousing and Material Handling. : McGraw Hill Professional. Gigerenzer, Gerd (1991). How to Make Cognitive Illusions Disappear: Beyond "Heuristics and Biases". European Review of Social Psychology: University of Salzburg, Austria. H, David (2002). ,Theoretical analysis on Picokosmos 17. Web Publication: Hiroyuki Imabayashi. (1982). Sokoban. Available: http://www.sokoban.jp/. Last accessed 9th December 2014. Leibniz, G (Original Paper:1704 Open Court Book:1949). New Essays Concerning Human Understanding. LaSalle: Open Court Publishing. Monkeystone Games (2001). Hyperspace Delivery Boy!. Global release: Linux Game Publishing. Paul Vickers. (2008). Chapter 2. In: How to Think Like a Programmer, Problem Solving for the Bewildered. : Cengage Learning. ISBN-10: 1408065827, ch. 2 pp. 30-37 Pearl, J (1983). Heuristics: Intelligent Search Strategies for Computer Problem Solving. New York: Addison-Wesley Polya, G (2002). How To Solve It. Princeton University: Princeton University Press; Princeton Science Li edition (April 25, 2004). p.36. Proteus Software Ltd.. (2014). Logistics Supply Chain - Route Planning & Scheduling. Available: http://www.proteussoftware.com/logistics-supply-chain-route-planning-scheduling. Last accessed 9th December 2014. Richards, G (2011). Warehouse Management: A Complete Guide to Improving Efficiency and Minimizing Costs in the Modern Warehouse. ISBN-10: 0749460741: Kogan Page. Smith, David Eugene (1929). A Source Book in Mathematics. New York: McGraw-Hill Book Company, inc Wagner, R (1988). Computer Gaming World: Puzzling Encounters. : Golden Empire Publications. p42-43. Zubaran, T. Ritt, M.. (Date of publication unknown). Agent motion planning with pull and push moves. Available: http://www.lbd.dcc.ufmg.br/colecoes/enia/2011/0011.pdf. Last accessed 9th December 2014.

assessment 3 final v2

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