QUESTION
Assignment Brief:
As an engineer, very often you have to deal with problems that involve careful consideration, analysis, optimisation, interpretation, conclusion and decision. This assignment consists of three parts (A – Decision analysis, B – Network analysis and C – Shortest path analysis). Each part comprises a case study which poses real systems challenges in terms of planning, optimization and decision making. You will need to apply appropriate methods to analyze, interpret, and provide decisions regarding the problem context and write a brief report of your recommendations (no more than 2,000 words for the whole report excluding calculations).
You will need to write a managerial report consisting of solutions on the three case study problems. Marks will be awarded based on the quality of analysis and interpretation in applying related perspectives to the case material. Your answers must be in report format, and should include
 Introduction
 calculations, results, interpretation (if needed)
 appropriate decision(s) and recommendation(s)
 critical appraisal
 conclusion
Make sure that your interpretations, discussions and conclusions are concise.
Assignment – Part A: Decision Analysis
General Electric Company is considering a £5 million research and development (R&D) project. Profit projections appear promising, but the president of General Electric Company is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the executive knows that even if the project is successful, it will require that the company build a new production facility at a cost of £20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realised. The demand of the product could be high, medium and low with corresponding revenue projection of £59 million, £45 million and £35 million, respectively. The associated probability of high demand is 0.5 and medium 0.3. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated £25 million. Under this option, the company would not build the £20 million production facility.
Managerial report:
Perform a decision analysis of the problem facing General Electric Company and prepare a report that summarises your findings, recommendations and critical appraisal. Include the following information in your report
 A decision tree that shows the logical sequence of the decision problem.
 A recommendation of a course of action to the company.
 A profit/loss table showing the possible levels of profit the company can make and the associated probabilities.
 A critical appraisal.
Assignment – Part B: Network Analysis
General Electric Company plans to modernize and expand its current Display Center Complex in Chicago, IL. The project is expected to provide room for its new businesses products. Financing has been arranged through its Finance Department. All that remains are to plan, schedule, and complete the expansion project. Information about the activities of the project is shown below.

Activity Description Immediate Predecessor Time (weeks) A B C D E F G H
I
Prepare architectural drawings Identify potential products for display Develop plan for product set up Select contractor Prepare building permits
Obtain approval for building permits Perform construction
Finalize product set up plan Setting products for display
— — A A A E
D, F
B, C
G, H
5 6
4
3
1
4
14
12
2
Managerial report:
Develop a report that presents the activity schedule and expected project completion time to modernize and expand its current Display Center Complex. In addition, take into consideration the following issues:
 Construction of the network diagram.

^{Performance of an event based analysis, i.e. obtaining earliest event times (TE) and latest event times (TL), inserting them appropriately into the diagram and, hence, obtaining the} critical path and project duration.
 Performance of an activity based analysis, i.e. obtaining total float (TF) and free float (FF), showing the values (TF and FF) in a table and, obtaining the critical path and project duration.
 A critical appraisal.
Assignment – Part C: Shortest Path Analysis
General Electric Company needs its produced items to be transported from its production house based on Oxford, England to its main warehouse in Haddington, Scotland. The network below indicates all the possible ways of shipping large boxes of items from Oxford (O) to Haddington (H) through cities indicated by the letters A, B, C, D, E, F, G. The figures alongside each stage of the journey are the costs of shipping items in boxes from starting place to the next place. The total cost of shipping items from Oxford to Haddington is the sum of the costs of the individual stages.
Managerial report:
Write a report on shortest path analysis that include the shortest route and associated cost of General Electric Company to ship items from Oxford to Haddington
ANSWER
Part A: Decision Analysis
Introduction
Decision analysis uses a set of quantitative tools to analyse different possible scenarios and assist the decision makers in any organisation to select the best sequence out of all possible ones. It creates a formal method which ensures that the decision making process is completely objective, and is not hindered by emotions. In our study, the General Electric company wants to go ahead with its R&D project, which can create a number of scenarios as depicted:
Calculation
The possible profit or loss of each of the scenario can be calculated as:
Scenario 
Profit/Loss 
Value (million £) 
Probability 
R&D Project unsuccessful 
Loss 
5 
0.5 
R&D project successful 
Profit 
At least 20 
0.5 
Now, if the project is successful, the company has an option to sell the product rights or create a production facility of its own. Selling the product rights would guarantee a 20 million £ in profit to the company. However, if the company decides to go ahead with constructing its own facility, depending on the demand of its products, three more possible scenarios are:
Scenario 
Profit/Loss 
Value (million £) 
Probability 
High demand 
Profit 
34 
0.25 
Medium demand 
Profit 
20 
0.15 
Low demand 
Profit 
10 
0.10 
Recommendation
If the company decides to go ahead with the project, the maximum loss to the company will be 5 million £ in case the R&D project is unsuccessful which has a 50% chance. However, if the project is successful, which has a 50% chance as well, there is a guaranteed profit of 20 million £, in case the company decides to just sell its products rights, without taking any further efforts on it.
However, if the company decides to move ahead, it will need to construct its own production facility costing another 20 million £. According to the demand of the finished products, the company may generate revenues of 59, 45 and 35 million £, hence giving profits of 34, 20 and 10 million £ respectively.
Since the initial investment of 5 million £ is relatively less as compared to the possible profits, and has an even chance of 50%, it is recommended to move ahead with the first stage, i.e. the R&D project and develop its product. On its completion, the company may once again analyse whether to go ahead with constructing its facility or not, depending upon the time required for the first stage, current demand of the product, and possible changes which might have happened in this time period.
Critical Appraisal
The decision tree diagram was made according to the conditions given in the study. The recommended course of action was given according to the probabilities and possible profits and losses to the company.
Conclusion
The Decision analysis techniques gave a course of action which risks only a small amount of the company, while giving substantial profits on successful completion.
Part B: Network Analysis
Introduction
Network analysis refers to the techniques adopted to plan and manage projects in various fields. It works by dividing the projects into a number of tasks called activities, each with its own completion time, and the dependence of these activities over one another. The management of these activities is made easier through graphical representation of the plan. When a large number of activities are present, there is a need for an objective method to decide important activities, precedence of activity completion and dependence amongst themselves, since we cannot start a project from any activity. The network analysis provides explanation to all the scenarios.
In our study, the General Electric Company plans to expand its Display centre, which has been divided into nine activities. We will apply the concept of network analysis to analyse this expansion project.
Calculation
The activities constituting the project are as follows:
Activity 
Description 
Immediate Predecessor 
Time (weeks) 
A B C D E F G H I 
Prepare architectural drawings Identify potential products for display Develop plan for product set up Select contractor Prepare building permits Obtain approval for building permits Perform construction Finalize product set up plan Setting products for display 
— — A A A E D, F B, C G, H 
5 6 4 3 1 4 14 12 2 
These set of activities are arranged diagrammatically to aid in easier analysis of the situation. The network diagram for the following set of activities is as follows:
The entire project is divided into 9 activities and 10 nodes. The activities P, Q and R are dummy activities introduced to fulfil the condition that some activities cannot start until previous activities are completed as described in the table above. As depicted, they have a zero time period and only denote that the next activity can begin only once the previous activity has been completed.
We begin the Event based analysis by calculation Early start times for each node.
E1 = 0
E2 = E1+ T12 = 5
E3 = E1 + T13 = 6
E4 = E2 + T24 = 9
E5 = E2 + T25 = 8
E6 = E2 + T26 = 6
E7 = E6 + T67 = 10
E8 = max [ E7 + T78, E5 + T58] = max [24,8] = 24
E9 = max [ E4 + T49, E3 + T39] = max [21,6] = 21
E10 = E8 + T8,10 = 26
Hence the minimum overall project completion time is 26 weeks. Next we calculate the Latest start times for all nodes.
L10 = 26
L8= L10 – T10,8 = 24
L9 = L8 – T89 = 24
L7 = L8 – T78 = 10
L6 = L7 – T67 = 6
L5 = L8 – T58 = 24
L4 = L9 – T49 = 12
L3 = L9 – T39 = 24
L2 = min [ L5 – T25 , L4 – T24 , L6 – T46 ] = min [21,5,8] = 5
L1 = L2 – T12 = 0
Float is a term used to denote the amount of Free time available to a particular activity or a route, by which that activity may be delayed if necessary, without slowing down the progress of the project. This is possible because certain activities are more critical for the project, on which future activities depend, while others are not much important and can be completed slowly. For calculating float values, we use the following equation: Fij = Lj – Ei – Tij
Activity 
i 
j 
Lj 
Ei 
Tij 
Fij 
A 
1 
2 
5 
0 
5 
0 
B 
1 
3 
24 
0 
6 
18 
C 
2 
4 
12 
5 
4 
3 
D 
2 
5 
24 
5 
3 
16 
E 
2 
6 
6 
5 
1 
0 
F 
6 
7 
10 
6 
4 
0 
G 
7 
8 
24 
10 
14 
0 
H 
4 
9 
24 
9 
12 
3 
I 
8 
10 
26 
24 
2 
0 
P 
5 
8 
24 
8 
0 
16 
Q 
3 
9 
24 
6 
0 
18 
R 
9 
10 
26 
21 
0 
5 
Hence the critical activities with float as zero are A, E, F, G, I which forms the critical path for the project.
The diagram using the Activity based analysis is as follows:
The boxes represent activities and the four numbers depict Early start time, Early finish time, Latest finish time and Latest start time, in clockwise order, starting from the top left corner. Activities P, Q, R are dummy activities. Since the Activities A, E, F, G, I form the critical path, their float values will be zero.
The Total float value = Latest finish time (of activity) – Early finish time (of activity)
TF(B) = 24 – 6 = 18
TF(C) = 12 – 9 = 3
TF(D) = 24 – 8 = 16
TF(H) = 24 – 21 = 3
Free float value = Early start time (of next activity) – Early finish time (of activity) – 1
FF(B) = 25 – 6 – 1 = 18
FF(C) = 10 – 9 – 1 = 0
FF(D) = 25 – 8 – 1 = 16
FF(H) = 25 – 21 – 1 = 3
Recommendation
Since the path AEFGI is the critical path, it is advised that no hindrance is present in these activities as delaying them will result in the extension of project time, while all other activities might already be finished, leading to wastage of manpower as well as increasing machine lending and operation costs.
Critical Appraisal
 Critical path
 Free float and total float zero meaning
The critical path is found as that set of activities which have zero free float, meaning that the overall time completion depends largely on these set of activities. Total float calculated depicts the free time or slack available for that particular activity route, by which even if the activities are delayed, the project will still be finished on time. In our study ACHRI path has a free float of 3 which means delaying this activity route by three weeks won’t affect the project. However, free float depicts free time available to particular activities. As can be clearly seen for route ACHRI, activity C has a free float of 0 while H has 3 weeks, which means C has to be completed to ensure next activity may be started and project completes on time.
Conclusion
The Network analysis provides the critical path for the project and hence gives us the targets to be essentially achieved so that the project is completed as desired.
Part C: Shortest path Analysis
Introduction
Shortest path analysis is used to find the shortest route between two nodes through various routes, in order to maximise the efficiency of the works involved. In our study, the General Electric Company needs to finished items to be transported from Oxford, England to Haddington, Scotland. However, there are many possible routes, going through eight cities, each involving different costs. Finding the shortest possible route between Oxford and Haddington will reduce the associated costs of transportation for the company.
Calculation
The diagram for our study is as follows:
The values on the arrows represent the cost incurred by the company during transportation. For each node, the total cost required to reach there is calculated by taking the minimum value of all possible paths.
On doing this step, we get the following diagram:
Next, we begin connecting the paths backwards which led us to the value at the final node and we get our shortest path:
Hence, the shortest path comes out to be OBEH with the total cost to the company being 8 + 5 + 10 = 23 units.
Recommendation
The company is recommended to follow OBEH path for the transportation of its items. Also, path OBFH comes out to be the second most effective, costing 24 units and hence, can be used for transportation if required.
Critical Appraisal
The analysis makes use of shortest path algorithm. The proposed path costs 23 units to the company.
References
 Network analysis example [Online]. Available at : http://people.brunel.ac.uk/~mastjjb/jeb/or/netmore.html
 Decision analysis material [Online]. Available at: https://home.ubalt.edu/ntsbarsh/opre640a/PartIX.htm
 Network analysis [Online]. Available at: http://people.brunel.ac.uk/~mastjjb/jeb/or/netanal.html
 Shortest path analysis and algorithm [Online]. Available at: https://en.wikipedia.org/wiki/Shortest_path_problem
 Decision Analysis [Online]. Available at: https://en.wikipedia.org/wiki/Decision_analysis
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