[BUS229] Quantitative Research Methods and Data Analytics Dm
Individual Report
In this report, you are required to answer ALL FIVE QUESTIONS. Your answers are to be presented in a single report format, and in answering these questions, please
• State and explain all assumptions, on which your answers are based; • support any answers with the appropriate calculations to arrive at the answer.
While each individual answer might have a different word count from the others, the overall word count should not exceed 2,500 (+ or – 10%) words. Late submissions will be penalised according to School regulations.
In case during the term a student is affected by EXTENUATING CIRCUMSTANCES that might prevent her/him from submitting the work on time, the student should contact the module organis) as soon as possible when the problem occurs and no later than the submission deadline . Extenuating circumstances will be evaluated in accordance with College regulations . Under no circumstances can submissions via email be accepted. Under no circumstances should students attempt to hand in their work directly to the lecturer or to the class teacher.
Q1. Explain the four assumptions of Linear Programming, i.e., Certainty, Divisibility, Proportionality and Additivity, and discuss their impacts on applications of Linear Programming. (20 Marks)
Q2. The SOUTHERN CONFEDERATION OF KIBBUTZIM is a group of three kibbutzim (communal farming communities) in Israel. Overall planning for this group is done in its Coordinating Technical Office. This office currently is planning agricultural production for coming year.
The agricultural output of each kibbutz is limited by both the amount of available irrigable land and the quantity of water allocated for irrigation by the Water Commissioner (a national government official). These data are following:
Kibbutz Usable Land (Acres) Water Allocation (Acres Feet) 1 400 600 2 600 800 3 300 375
[BUS229] Quantitative Research Methods and Data Analytics Dr Eun-Seok Kim
The crops suited for this region include sugar beets, cotton, and sorghum, and these are the three being considered for the upcoming season. These crops differ primarily in their expected net return per acre and their consumption of water. In addition, the Ministry of Agriculture has set a maximum quota for the total acreage that can be devoted to each of these crops by the Southern Confederation of Kibbutzim, as shown in a table below.
Crop Maximum Quota (Acres)
Water Consumption (Acre Feet/Acre)
Net Return ($/Acre)
Sugar beets 600 3 1,000 Cotton 500 2 750 Sorghum 325 1 250
Because of the limited water available for irrigation, the Southern Confederation of Kibbutzim will not be able to use all its irrigable land for planting crops in the upcoming season. To ensure equity between the three kibbutzim, it has been agreed that every kibbutz will plant same proportion of its available irrigable land. For example, if kibbutz 1 plants 200 of its available 400 acres, then kibbutz 2 must plant 300 of its 600 acres, while kibbutz 3 plant 150 acres of its 300 acres. However, any combination of the crops may be grown at any of the kibbutzim. The job facing the Coordination Technical Office is to plan how many acres to devote to each crop at the respective kibbutzim while satisfying the given restrictions. The objective is to maximize the total net return to the Southern Confederation of Kibbutzim as a whole.
a) Formulate the decision problem as a LP and solve it using Excel Solver. (10 marks)
b) Discuss on the obtained results and make suggestions. For example, how sensitive is the optimal solution? (10 marks)
Q3. The Rogers Construction Company is trying to decide whether to make a bid on a project against 4 competitors. The lowest bid will win the contract and be paid the amount they bid. It believes it will cost the company £10,000 to complete the project (if it wins the contract) and £350 to prepare the bid. Based on historical data, Rogers believes each competitor’s bid has a normal distribution with mean £15,000 and standard deviation £1,500.
a) Set up a simulation model to help the company make the decision of how much to bid. (10 marks) b) Discuss on the obtained results and make suggestions. For example, what if the competitor’s bid has different distributions? (10 marks)
[BUS229] Quantitative Research Methods and Data Analytics Dr Eun-Seok Kim
Q4. A large multinational oil company is considering its strategy in the North See. The UK government has announced that a new drilling site in the North Sea will be offered for sale on a competitive tender basis, the site going to the company making the highest bid. Provisional exploration of the site indicates that, over its life, it can be expected to generate revenue of around £1,500 million if the oil reserves turn out to be high, but only £500 million if they turn out to be low. Seismic tests have indicated that the probability of high reserves is 0.60.
If the company is successful in its bid, it will also have to decide whether to construct a new oil rig for the site or to move an existing oil rig which is currently operating at an uneconomic site. The costs of the new rig are around £250 million and for moving the existing rig around £100 million. A new rig would be able to boost production by £150 million if reserve levels turned out to be high. The company has decided that if it is to bid for the site, the maximum bid it can afford at present, because of its cash flow situation, is £750 million. In the past, 70 percent of the company’s bids for such sites have been successful.
However, the company is also under pressure to refurbish some of its existing rigs for both efficiency and safety reasons. The £750 million could be used for this purpose instead. If the money is used for refurbishment, there is a 50 percent chance of increasing efficiency to generate a return on the £750 million of 5 percent, and a 50 percent chance of generating a return of 10 percent. If the decision to refurbish takes place after the bid has been made and failed, another £500 million will be required for refurbishment.
a) Construct a decision tree for this problem. (10 marks)
b) Using the decision tree, suggest a suitable decision for management. For example, what is the maximum bid the company would consider? What is the value of perfect information about the size of the reserves on the new site? (10 marks)
Q5. The file ‘House Sales.xlsx’ contains monthly data on the number of new one-family houses sold in the United States (in thousands) from January 1991 through December 2014.
a) Discuss whether a simple exponential smoothing work with this data set or not. (10 marks)
b) Forecast number of new one-family houses sold in each month from January 2015 to June 2015 using an appropriate forecasting technique. (10 marks)
