Quantitative Methods Assignment -
Question 1 -
Cha Cha Pte Ltd is a home-grown company that supplies pre-mixed tea leaves to the regional hotels and restaurants. Their two best seller tea leaf blends are Fragrance026 and Scent012. Due to the upcoming festive season, there is a consolidated order commitment for at least 150 kg of Fragrance026, and 200 kg of Scent012. To produce 1 kg of Fragrance026, it should contain at most 55 percent dried figs while each kg of Scent012 should contain at least 65 percent of orange peel. The source for orange peel comes from two mixtures; mixture Alpha and mixture Beta. Mixture Alpha contains 70 percent orange peel and 20 percent dried figs, while mixture Beta contains 25 percent orange peel and 60 percent dried figs. Mixture Alpha costs 85 cents per kg and mixture Beta costs 40 cents per kg. The company CEO would like to know the cost-effective way of mixing Alpha and Beta.
(a) Develop the portfolio selection case as a linear programming problem. Please explain clearly how you choose the decision variables, formulate the objective function and constraints.
(b) Solve for the optimal solution using Microsoft Excel Solver. Show the relevant solution output and sensitivity output.
(c) Interpret the reports and discuss the following scenarios (without re-solving it using Microsoft Excel Solver):
(i) If the cost of Mixture Alpha is 50 cents, explain if there will be any changes to the original optimal mix?
(ii) If the order for Fragrance026 is actually 50kg instead of 150kg, what would be the implications on the total cost on acquiring mixture Alpha and Beta?
Question 2 - Singapore's Tourist Arrival
A bridge between the East and the West for centuries, Singapore embraces tradition and modernity. Colourful ethnic precincts amongst efficient business centres, and serene gardens set against sleek skyscrapers, Singapore is a fascinating destination for leisure and business travellers (MTI, 2015).
Over the years, there has been remarkable transformation in Singapore's tourism landscape and there are various reported record growth in both tourism receipts and visitor arrivals. Since 2004, Singapore has grown her tourism receipts by almost 2.5 times while visitor arrivals also almost doubled (MTI, 2015).
A common key performance indicator is the International Visitor Arrivals which refer to travellers taking a trip to Singapore whose length of stay is less than a year. This excludes:
- All Malaysian citizens arriving by land;
- Returning Singapore citizens, permanent residents and pass holders
- Non-resident air and sea crew (except for sea crew flying in to join a ship); and
- Air transit and transfer passengers.
Arrival statistics are reported by country of residence based on information from Disembarkation/Embarkation (D/E) Cards by the Immigration and Checkpoints Authority of Singapore (STB, 2015).
Using the data in Tables 2.1, 2.2 and 2.3 below, produce forecasts of the Visitor Arrivals in Singapore (Total, ASEAN and China) and prepare a report according to the requirements listed.
Table 2.1: Total Visitor Arrivals in Singapore TOTAL VISITOR ARRIVALS (in Thousands)
|
Year
|
Quarter
|
|
1
|
2
|
3
|
4
|
|
2011
|
3118
|
3237
|
3486
|
3329
|
|
2012
|
3576
|
3506
|
3648
|
3765
|
|
2013
|
3882
|
3851
|
4079
|
3755
|
|
2014
|
3881
|
3635
|
3870
|
3708
|
|
2015
|
3643
|
|
|
|
Table 2.2: Visitor Arrivals in Singapore Originating from ASEAN VISITOR ARRIVALS - From ASEAN (in Thousands)
|
Year
|
Quarter
|
|
1
|
2
|
3
|
4
|
|
2011
|
1209
|
1394
|
1397
|
1412
|
|
2012
|
1341
|
1487
|
1406
|
1544
|
|
2013
|
1389
|
1589
|
1543
|
1644
|
|
2014
|
1446
|
1614
|
1484
|
1567
|
|
2015
|
1290
|
|
|
|
Table 2.3: Visitor Arrivals in Singapore Originating from China VISITOR ARRIVALS - From CHINA (in Thousands)
|
Year
|
Quarter
|
|
1
|
2
|
3
|
4
|
|
2011
|
411
|
346
|
472
|
347
|
|
2012
|
542
|
436
|
537
|
518
|
|
2013
|
647
|
593
|
670
|
358
|
|
2014
|
557
|
314
|
460
|
390
|
|
2015
|
509
|
|
|
|
Source: partially extracted from Department of Statistics (2015) Statistical Tables from Economic Survey of Singapore
https://www.singstat.gov.sg/docs/default-source/default-document- library/statistics/browse_by_theme/economy/statistical_tables/essa111.xlsx (Accessed 8th July 2015)
(a) Provide an understanding and background discussion on the methodology of forecasting.
(b) Determine the seasonality of the data by conducting an in-depth seasonality analysis for Table 1, 2 and 3. For each quarter, indicate the seasonal indexes, the deseasonalised time series and the trend line that will fit the deseasonalised time series. Adjust the seasonal indexes, if necessary. Provide justification on the appropriateness of seasonality analysis.
(c) Understand and comment on possible forecast errors and the cause of these errors.
(d) Develop an overall conclusion of your forecasting findings, policy observations and recommendations.
Question 3 -
SIMSIM Pte Ltd is a boutique fund manager and venture capitalist. It has recently took part in a Series B round of financing exercise and has been presented with four potential proposal (P1, P2, P3 and P4). The analyst has been tasked to provide some insights in decisions to be made.
Table 3.1: Payoff (in $Millions) Table
|
|
ECONOMIC CONDITION
|
|
Poor
|
Average
|
Good
|
Excellent
|
|
PROPOSAL
|
(S1)
|
(S2)
|
(S3)
|
(S4)
|
|
P1
|
50
|
75
|
20
|
30
|
|
P2
|
80
|
15
|
40
|
50
|
|
P3
|
-100
|
300
|
-50
|
10
|
|
P4
|
25
|
25
|
25
|
25
|
|
Probabilities
|
0.4
|
0.2
|
0.25
|
0.15
|
(a) Identify the decisions to be made if the corporate strategy is to undertake an optimistic stand or a conservative stand. Show your workings.
(b) Determine the decision to be made using the decision tree approach. Show the decision tree and compute the expected values for each node as well as determine the expected value of perfect information. Interpret the results.
References:
Ministry of Trade and Industry Singapore - Insights: Tourism 2015 goals. Website:
https://www.mti.gov.sg/MTIInsights/Pages/Investments.aspx (Accessed 8th July 2015)
Singapore Tourism Board - Statistics and Market Insights. Website:
https://www.stb.gov.sg/statistics-and-market-insights/pages/statistics-Visitor-Arrivals.aspx (Accessed 8th July 2015)
Statistical Tables from Economic Survey of Singapore, Department of Statistics. Website:
https://www.singstat.gov.sg/docs/default-source/default-document- library/statistics/browse_by_theme/economy/statistical_tables/essa111.xlsx (Accessed 8th July 2015).