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Semester I Examinations 20 10 / 2011
Exam Code(s) 1EM1,^ 3BC1, 4BC2, 4BC5, 4BF1, 1APE1, 1OA1, 3BCM
Exam(s) B.Commerce B.Sc. BIS Project and Construction Management M.Appl.Sc Erasmus & Visiting
Module Code(s) IE309, IE Module(s) Operations Research Operations Research I Paper No. 1 Repeat Paper External Examiner(s) Prof. Jiju Antony Internal Examiner(s) *Ms. M. Dempsey Professor Peter McHugh
Instructions: Answer any 3 questions.
Show all your work clearly and explain your work. All questions will be marked equally. Marks are allocated to explanations, method and solutions. Where you may think that additional information is needed, please clearly state so and make appropriate assumptions and/or use reasonable estimates that will enable you to proceed.
Duration (^) 2 Hours
No. of Pages Cover + 6 pages College/Discipline Engineering and Informatics/Mechanical and Biomedical Engineering Course Co-ordinator(s) Ms Mary Dempsey
Requirements : MCQ Handout Statistical Tables Graph Paper Normal Log Graph Paper Other Material
Q
Shock Electronics Company produces two products, the P-Pod, a portable music player, and the RedBerry, an internet enabled red telephone. The production process for each process is similar. Both require a certain number of hours of electronic work and a certain number of labour hours in the assembly area. Each P-Pod takes 4 hours of electronic work and 2 hours in the assembly work. Each RedBerry takes 3 hours of electronic work and 1 hour in the assembly work. During the current production period, 240 hours of electronic time are available and 100 hours of assembly time are available. Each P-Pod sold yields a profit of €7 and each RedBerry produced may be sold for a €5 profit.
The formulation of this problem should satisfy four requirements for standard LP
There are limited resources and there is an explicit objective function
The equations are linear The resources are homogenous (everything is in one unit of measure)
The decision variables are divisible and nonnegative (we can make a fractional part of a P-Pod and a RedBerry
i) Illustrate this scenario ii) Formulate the problem in Mathematical Terms as a Linear Programming Problem iii) Graph this problem using X 1 and X 2 co-ordinate planes iv) Find the optimal mix of P-Pods and RedBerrys to be produced using the simplex method v) If it were deemed undesirable to make a fractional part of a P-Pod or RedBerry what technique would you use? vi) What resource or product issues face the Shock Electronic Company vii) Give three application areas where LP is commonly used.
Q3 BioFlex operates three processing factories, Galway 1, Galway 2 and Galway
- These factories focus on processing raw material namely willow, for use as a Bio fuel. The processed willow is shipped to three distribution centres in Europe labelled, DC1, DC 2 and DC 3. The containers of willow are then broken into orders and then shipped to three warehouses W1, W2, W3 in response to replenishment orders at supplier sites throughout Europe. Each of the factories has a known monthly production capacity, and the warehouses have placed their demands for next month. The following tables summarise the data that have been collected for this planning problem. Knowing the costs (in Euro) of transporting goods from factories to distribution centres and from distribution centres to warehouses. BioFlex is interested in scheduling its material flow of willow at the minimum possible cost.
Distribution Centre Factory
DC 1 DC 2 DC 3 Capacity (tons) Galway 1 10 13 12 60 Galway 2 12 11 10 60 Galway 3 14 10 8 80
i) Translate this transhipment problem into a transportation problem. ii) Formulate the transhipment problem as a linear programming problem. iii) Explain how one can restrict a route in this transhipment model.
To From
Warehouse 1
Warehouse 2 Warehouse 3
DC 1 12 16 20 DC 2 14 22 22 DC 3 8 10 24 Demand (tons)
Source Transhipment Sink 1
Q4 a) Conor Brady Corporation, headquartered in Athlone, wants to assign three recently hired, operations research specialist graduates, Lisa Braehmer, Thomas Burke and Liam Bushell, to regional offices. However, the firm also has an opening in Dublin and would send one of the three there if it were more economical than a move to Cork, Belfast or Galway. It will cost €1000 to relocate Braehmer to Dublin, €800 to relocate Burke there, and €1500 to move Bushell. What is the optimal assignment of personnel to offices? (Hint: Use a Dummy Row.)
Office
Hiree
Cork Galway Belfast
Braehmer 800 1100 1200 Burke 500 1600 1300 Bushell 500 1000 2300
i) Using the Hungarian Solution method, evaluate an optimal solution for this assignment problem ii) Is this the only optimal solution?
Q4 b) Sam Shipping transports willow for BioFlex by six trucks from Galway to mainland Europe. The different routes between Galway and the six cities in Europe and the length of time, in hours, required by a truck to travel each route are shown below Eoghan Duffy, the shipping manager, wants to determine the best routes (in terms of minimum travel time) for the trucks to take to reach their destinations. Solve using the shortest distance solution technique.
Determine the shortest route from the origin (node 1) to the six destinations (nodes 2 through 7)
Activity Description Immediate Predecessors
Time (weeks)
A Build internal components
B Modify roof and floor
C Construct collection stack
A 2
D Pour concrete and install frame
AB 4
E Build high temperature burner
C 4
F Install pollution control system
C 3
G Install air pollution device
D,E 5
H Inspect and test F,G 2
Given the information above
i) Draw the project network ii) Calculate the Early and Late times for start and finish of each activity iii) Identify the critical path iv) Identify the activities with slack
