Quantitative Methods Assignment
Question 1
SIM Machinery is a local precision engineering manufacturer that specialised in manufacturing complex special process components for Oil & Gas and Aerospace Industries. SIM Machinery has 4 main product family: Gas Lift Valves, Dummy Valves, Orifice Valves and Safety Valve. All four products require performance test and reliability test before they can be shipped to customers.
A total of 2,880 minutes of performance test time and 1,680 minutes of reliability testing time are available next week. SIM Machinery planner has provided the possible market demand (maximum and minimum sales) for each product type. Also, total gas lift valve produced should not exceed 30% of the total production for all four product family, while total production for Dummy and Safety valve to should account for at least 25% of the total production.
Table 1: Profile of Valve Type
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|
Gas Lift Valve
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Dummy Valve
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Orifice Valve
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Safety Valve
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|
Performance Test Time (min)
|
45
|
20
|
30
|
25
|
|
Reliability Test Time (min)
|
20
|
15
|
25
|
10
|
|
Profit ($)/unit
|
$370.00
|
$175.00
|
$290.00
|
$300.00
|
|
Maximum sales
|
18
|
45
|
40
|
30
|
|
Minimum sales
|
7
|
16
|
20
|
15
|
(a) Develop a linear programming problem to determine how many pieces of each product family the company should make next week to maximize the company's profit.
(b) Use Microsoft Excel Solver to solve for the optimal solution. 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 profit of Dummy Valve increases by $10, explain if there will be any changes to the original optimal mix and total profit?
(ii) If the profits of Gas Lift Valve and Safety Valve are reduced by 30% each, explain if there will be any changes to the original optimal mix and total profit?
(iii) Due to scheduled maintenance, the reliability testing time is expected to be only 1,480 minutes. How will this affect the optimal solution?
Question 2
The Retail Sales Index (RSI) measures the short-term performance of retail industries based on the sales records of retail establishments. The RSI is presented at both current prices and constant prices. The indices at current prices measure the changes of sales values which can result from changes in both price and quantity. By removing the price effect, the indices at constant prices measure the changes in the volume of economic activity. There are several industries represented in the RSI as shown in Table 2.
Table 2: Industries in RSI
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Department Stores
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Food & Beverages
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Furniture & Household Equipment
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|
Medical Goods & Toiletries
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Mini-marts & Convenience Stores
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|
Motor Vehicles
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|
Optical Goods & Books
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|
Others
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|
Petrol Service Stations
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|
Recreational Goods
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|
Supermarkets
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|
Telecommunication Apparatus & Computers
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|
Watches & Jewellery
|
|
Wearing Apparel & Footwear
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As an analyst with a local telecommunication conglomerate, you have been tasked to provide a reliable projection for the telecommunication industry sector sales performance and growth strategy in 2017. Refer to the data file provided. The data file contains the monthly industry sector sales performance from January 2013 to June 2016. The base year is 2014 (2014 = 100).
(a) Determine and justify an appropriate forecasting model for the telecommunication apparatus and computer sector.
(b) Determine the forecast of RSI for the telecommunication apparatus and computer sector, up to June 2017.
(c) Use the forecasted values of RSI for the telecommunication apparatus and computer sector in (b), advise the company's management on projection and growth strategy for 2017.
Question 3
ABC Singapore is a leading local manufacturer of industrial fan, whose head office is based in Singapore. The fans are produced in Johor, Malaysia and then shipped to authorised distributors in Malaysia, Indonesia and Singapore. The company recently acquired another manufacturer of industrial fan that is based in Hanoi, Vietnam. Due to the tax breaks, and potential access to the Indochina market, the management is considering consolidating all its manufacturing operations in Hanoi, Vietnam.
However, by uprooting from its Malaysia plant, the company runs into the risk of losing potential clients in this region. Complicating matters is the fact that the marketing department is predicting a decline in the demand for industrial fans. The company considered four scenarios and the corresponding probabilities:
1. Demand is unchanged, with no noticeable effect on production; 10% chance.
2. Demand and production decline slightly; 15% chance.
3. Demand and production decline with moderate severity; 35% chance.
4. Demand and production decline severely; 40% chance.
The table below shows the total payoffs under each decision and scenario.
Table 3.1: Payoff (in $Millions) Table
|
Decision
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Unchanged
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Slightly
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Moderate Severity
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Severe
|
|
D1:
Operate Malaysia and Vietnam plant separately
|
$880,000
|
$830,000
|
$635,000
|
$335,000
|
|
D2:
Consolidate in Vietnam, and appoint local distributors.
|
$900,000
|
$855,000
|
$625,000
|
$315,000
|
By default, the company will appoint Vietnamese distributors to help market its product as it is cost-effective. However, the management has also considered the possibility of setting up a wholly owned or a joint venture subsidiary in Vietnam to perform the role of sole distributor (D3), if it decides to consolidate all operations to Vietnam. This arrangement could help the company to sell its product directly to customers in the Vietnam and the Indochina region, mainly, Thailand and Laos. The criteria to form a joint venture hinge on the possibility of roping a reliable local partner.
The table below shows the total payoffs under each decision and scenario for the case where the management decides to consolidate all its manufacturing operation in Vietnam and to operate either a joint venture owned sole distributor (D3a) or a wholly owned (D3b). The probability of securing a reliable local partner to form a joint venture is 30%.
Table 3.2: Payoff (in $Millions) Table For Decision to form Sole Distributorship
|
Scenario
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Unchanged
|
Slightly
|
Moderate Severity
|
Severe
|
|
D3a: Form joint venture with a local partner
|
$910,000
|
$880,000
|
$660,000
|
$310,000
|
|
D3b: Form wholly owned subsidiary
|
$915,000
|
$875,000
|
$630,000
|
$325,000
|
(a) Identify the decision to be made using the decision tree approach. Show the decision tree and compute the expected values for each node. Advise the management on the findings.
(b) Discuss and determine the expected value of perfect information. Interpret the result.