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Semester I Examinations 2011 / 2012
Exam Code(s) 1EM1, 3BC1, 4BC2, 4BC5, 4BF1, 1APE1, 1APE2, 2APE1, 2APE2, 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) Dr. Ralph Riedel Internal Examiner(s) *Ms. M. Dempsey Professor Sean Leen
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 + 5 pages College/Discipline Engineering and Informatics/Mechanical and Biomedical Engineering Course Co-ordinator(s) Mary Dempsey
Requirements : MCQ Handout Statistical Tables Graph Paper Normal Log Graph Paper Other Material
Q
Sheen Glass Company produces bottles for the wine industry and distributes these directly to vineyards. The two products are a 1 litre clear glass bottles, and 1 litre red bottles. The production process for each bottle is similar. Both require a certain number of hours of glass production work and a certain number of machine moulding labour hours. Each clear glass bottle requires 8 hours of glass production work and 4 hours of machine work. Each red bottle takes 6 hours of glass production work and 2 hour of machine work. During the current production period, 2400 hours of glass production time are available and 1000 hours of machine time are available. Each clear bottle sold yields a profit of €3 and each red bottle a profit of €
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 clear bottle and a red bottle
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 clear bottles and red bottles to be produced using the simplex method v) If it were deemed undesirable to make a fractional part of a clear bottle or a red bottle what technique would you use? vi) What resource or product issues face the Sheen Glass Company vii) Give three application areas where LP is commonly used.
Q3 a) Sheen Glass Company produces glass bottles. The fixed monthly cost of production is €800.00 and the variable cost per bottle is €0.65. The bottles sell for €1.
For a monthly volume of 30,000 bottles, determine the
i) Total cost, ii) Total revenue iii) Profit. iv) Monthly break-even volume (to the nearest decimal point) for the Sheen Glass Company.
Q3 b) Sheen Glass Company operates three processing factories, Ireland 1, Ireland 2 and Ireland 3. These factories focus on processing bottles for use in the wine producing French market. The processed bottles are shipped to two distribution centres in France labelled, France 1 and France 2. The containers of bottles are then broken into orders and then shipped to three warehouses in response to replenishment orders at supplier sites throughout the rest of France. 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/bottles/month) of transporting goods from factories to distribution centres and from distribution centres to warehouses. Sheen Glass is interested in scheduling its material flow of bottles at the minimum possible cost.
Distribution Centre Factory
France 1
France 2
Capacity (bottles/month)
Ireland 1 12 15 600 Ireland 2 14 13 1200 Ireland 3 16 12 800
i) Draw the graphical network of routes representing the information above. ii) Translate this transhipment problem into a transportation problem. iii) Formulate the transhipment problem as a linear programming problem. iv) How would you restrict a route in the example
v) What does it imply when a solution is degenerate?
To From
Warehouse 1 Warehouse 2 Warehouse 3
France 1 14 18 22 France 2 16 24 24 Demand (bottles/mont h)
Q4 a) Francis Carr the operations director of Sheen Glass Co ., headquartered in Dublin, is expanding the business into the Asian market. He has recruited four excellent NUI Galway operations research specialists to head up the Asian offices in Beijing, China, Bangkok, Thailand, Kuala Lumpur, Malaysia and Jakarta, Indonesia. He wants to assign Christina Callanan, Margaret Grimes, Gary McAndrew and Patrick Murphy to each of the Asian offices. The associated cost of transferring resources is summarised below.
Office
Hiree
China Thailand Malaysia Indonesia
Callanan 210k 90k 180k 160k Grimes 100k 70k 130k 200k McAndrew 175k 105k 140k 170k Murphy 80k 65k 105k 120k
i) Using the Hungarian Solution method, evaluate an optimal solution for this assignment problem ii) Is this the only optimal solution? iii) You have just found out that Patrick Murphy speaks Cantonese (widely spoken in China). How will you reflect this additional information in your decision making process?
Q4 b) Margaret Grimes has been relocated by Sheen Glass Co to Malaysia. Margaret arrived in Malaysia and spent her first 3 weeks in a 5* resort hotel. While she was staying in the resort she noticed that management was in the process of installing a new broadband system, which would be connected to all the villas in the resort. To minimise disruption the resort team would like to use the conduits (telephone and electricity) already in place and minimise the amount of cable used. After getting to know the managers over her stay at the resort Margaret offers to use her knowledge in Operations Research techniques to solve the issue. The network below represents the 6 villas to be connected in the resort. Connect all the sites using the least amount of cable. Assume the role of Margaret and solve this problem using the greedy algorithm solution technique.
