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Autumn Examinations 2007 / 2008
Exam Code(s) 4CS, 3BI1,3BC1, 4BC2, 4BC3, 4BF1, 1EM1, 1OA Exam(s) B.Comm Degree B.Sc. Degree BIS Degree Industrial Engineering Erasmus & Visiting
Module Code(s) IE309, IE Module(s) Operations Research Operations Research I
Paper No. I
External Examiner(s) Prof. Jiju Anthony Internal Examiner(s) *Ms. M. Dempsey Dr. D. O’Sullivan
Instructions: Answer any 3 questions. Show all your work clearly and explain your work. All questions will be marked equally. Duration 2 hrs No. of Pages Cover + 4 Department(s) Industrial Engineering
Course Co-ordinator(s) Mary Dempsey
Requirements : Graph Paper Normal
Q1 Cell phone manufacturers UFone make 3 mobile phone models: 5501 , 5502 and
- UFone are limited to producing 1000 of the 5501 phones, 1000 of the 5502 phones and 600 of the 5503 phones each month.
UFone also has a limited supply of batteries for the month for the 5501 and the 5502 models. UFone has 450 Batteries for the 5501 and 1200 Batteries for the 5502 model. The 5501 requires 3 hours of assembly time the 5502 requires 4 hours of assembly time and the 5503 requires 2.5 hours of assembly time.
Ufone has 290 hours of assembly time available for the coming month. UFone estimates it makes €90 profit on each 5501 model, €125 profit on each 5502 model and €80 profit on each 5503 model.
i) Formulate the problem in Mathematical Terms as a Linear Programming Problem ii) Find the optimum point using the simplex method iii) Identify the binding constraints for this problem
Q2 M Tech ships Cell Phones from their plants to warehouses for later distribution to retail shops. The phones are designed and manufactured at plants A, B, and C. The Distribution Centres are located in D, E, F, and G.
Plant Supply A 300, B 500, C 450, Distribution Centre Demand D 350, E 400, F 300, G 200,
Shipping Cost Table in Euro From To
A B C
E 2.0 1.8 1.
D 2.7 3.1 1.
F 3.5 2.3 1.
G 1.5 1.9 2.
i) Draw the graphical network of routes representing the information above ii) Formulate the transportation tableau iii) Develop an initial solution using Northwest Corner Rule iv) Develop an initial solution using Least Cost Method v) Compare the answers from part iii) and part iv) and comment on your findings vi) Test the preferred initial solution for optimality and generate the optimal solution.
Q4 PM Ltd. acquired contracts for five new projects that now require Project Managers. There are currently six possible managers available for assignment to these projects. Time required for project completion is a factor in profit, and completion time is, in turn, a function of the experience and leadership style of the project manager. The table below shows the managers who are available and their expected time of completion (in months) for each project.
Expected completion time (months)
Manager Project 1 Project 2 Project 3 Project 4 Project 5
Aoibhin 3.8 4.0 3.0 4.1 3. Eoghan 2.0 1.5 2.5 1.75 2. Matthew 2.7 3.6 1.6 2.9 3. Dan 4.3 4.6 7.1 4.4 2. Alex 3.7 3.2 2.1 4.3 1. Ciara 1.8 2.2 2.8 1.2 5.
i) Using the Hungarian Solution method, evaluate an optimal solution for this assignment problem. What assignments should be made so that the total time of completion is minimised
ii) Who will not be assigned at this time?
iii) Is this the only optimal solution?
Q4 b) Given the following network, with distances shown in kilometres, find the shortest route from node 1 to each of the other nodes.
Q5 a) M Tech electronics is considering expanding its facilities. Three options are being examined; a major expansion, a minor expansion and no expansion. Depending upon the state of the economy various outcomes may occur. After considerable discussion, everyone has agreed that the following payoff table is appropriate (the numbers represent additional yearly profits or losses).
Decision Alternative
Good Economic Conditions
Fair Economic Conditions
Poor Economic Conditions
Major Expansion 180,000 30,000 -60, Minor Expansion 80,000 40,000 -15, No Expansion 0 0 0
Determine the best decision by using the following decision criteria:
i) Maximax ii) Maximin iii) Minimax regret iv) Hurticz with α = 0.
Q5 b) A state of the art University Campus accessible only through a security check point is in the process of installing a new security system, including television monitoring which will be connected to all research, teaching and administrative areas of the University. To minimise disruption management would like to use conduits (for telephone and electricity) that are already in place. It is even more important to reduce installation cost by minimising the total length of cable used. The network below represents this problem. Each node is a site to be connected and the arcs show the conduits already in place. The objective is to connect all these sites using the least amount of cable. Use the greedy algorithm to solve this problem
