GMDS 5113 Quantitative Techniques and Decision Making

Question 1 Quantitative Analysis, Data and Measurement

A retail company is experiencing inconsistent performance across its branches. Management plans to use quantitative analysis to understand the differences and improve its decision-making. Data collected include monthly sales, customer satisfaction, employee experience, branch location, number of customers, customer complaints, energy consumption and waste generated by each branch.

Management is also concerned that decisions based purely on financial performance may overlook employee well-being, customer interests and the environmental impact of branch operations.

a) Explain how the quantitative analysis approach can be applied to help management evaluate branch performance and support managerial decision-making.

b) Discuss how computers and quantitative tools can assist management in analysing large amounts of business data and evaluating alternative courses of action.

c) Classify the following variables according to their appropriate measurement scales and explain your classification:

i. Branch location

ii. Customer satisfaction level

iii. Number of customers iv. Monthly sales revenue

d) Explain why managers should consider ethical and responsible use of data when using quantitative information to evaluate employees, customers and branch performance.

Question 2 Describing and Interpreting Data

A logistics company is evaluating the performance of two delivery teams. Management has obtained the following information:

The company wants to improve delivery performance while also reducing unnecessary fuel consumption as part of its sustainability initiatives.

a) Explain what the mean, median and standard deviation indicate about the performance of the two teams.

b) Compare the consistency of the delivery performance of Team A and Team B. Support your answer using the information provided.

c) Explain why management should consider both measures of central location and dispersion rather than relying only on average performance.

d) Based on the information provided, discuss how quantitative data can support management in making decisions that balance operational performance and environmental sustainability.

Question 3 Probability Concepts And Applications

An e-commerce company faces uncertainty relating to customer demand, delivery delays and product returns. Historical records indicate that approximately 20% of deliveries are delayed, while 10% of products are returned by customers.

Frequent delivery delays may increase transportation costs, additional delivery trips, fuel consumption and customer dissatisfaction. Management therefore wants to use probability information to improve planning and reduce operational inefficiencies.

a) Explain the concept of probability and how probability information can assist managers in making decisions involving uncertainty.

b) Interpret what a 20% probability of delivery delay means and explain how management could use this information when planning its delivery operations.

c) Distinguish between discrete and continuous probability distributions. Provide ONE (1) relevant business example for each type.

e) Evaluate how probability information could help the company reduce operational risks while supporting responsible and sustainable business practices.

Question 4 Decision Analysis, Ethical Leadership And Responsible Decisionmaking

A manufacturing company plans to expand its production capacity. Management is considering three alternatives:

Alternative A: Build a large conventional facility

Alternative B: Build a smaller energy-efficient facility

Alternative C: Postpone the expansion

The large facility may generate higher financial returns when market demand is strong but will require greater energy and resource consumption. The smaller facility provides lower potential financial returns but incorporates energy-efficient technologies and produces less waste.

Management must therefore consider financial performance together with environmental impact, employee welfare and its responsibility to stakeholders.

a) Explain the differences between decision making under certainty, uncertainty and risk. Relate your explanation to the company’s expansion decision.

b) Assuming that management does not know the probabilities of future market conditions, explain how the following approaches could influence its decision:

i. Maximax
ii. Maximin
iii. Minimax Regret

c) Evaluate how sustainability considerations should be incorporated alongside quantitative and financial information when evaluating the three alternatives.

d) As a manager, discuss how ethical leadership and responsible decision-making should guide the final decision when financial objectives may conflict with environmental and stakeholder interests.

Experts Answer on Above Questions on Business Statistics

Analysis, data and Measurement

Quantitative analysis
It is possible for the management to analyse branches by utilising measurable indicators like monthly sales, customer numbers, satisfaction, complaints, energy use and waste. With the help of statistical analysis, it can be possible to identify high and low performing branches, and also the relationship between variables and areas that need corrective actions.

Computers and quantitative tools

With the help of computers, it can be possible to process large datasets quickly by utilising statistical software. The data can be utilised to calculate different indicators including averages, trends and correlations, and identify unusual performance across any of the branches, and take appropriate decisions before implementing them.

Measurement scales

Branch location can be measured using nominal scale, as locations are categories that have no ranking. Customer satisfaction level uses ordinal scale because satisfaction categories have an order and the differences between the levels are not necessarily equal. The number of customers needs to be measured using ratio scale, as it has a meaningful zero and ratios are meaningful. The monthly sales revenue should also be measured using ratio scale.

Ethical and responsible data use

The ethical use of data is important and managers should make sure that they do not discriminate against employees or branches. The information about the customer and the employee needs to be protected, analyse accurately and should be utilised for genuine purposes. Employees should also not be judged by managers using one metric because it might produce unfair conclusions.

Describing and interpreting data

Mean, median and standard deviation – the mean value indicates that both teams have an average of 35 minutes per delivery and the median value implies that the delivery time of Team A is 34 minutes and Team B is 31 minutes. The standard deviation shows that Team A has 3 minutes and Team B has 9 minutes. This implies that Team B requires a higher delivery time and varies significantly around its average. In terms of usage of fuel, Team A uses 2.8 litres and Team B uses 3.6 litres per delivery.
Consistency – In terms of consistency, Team A is more consistent and its delivery time is 3 minutes as compared to 9 minutes for Team B.
Central location and dispersion – the mean value indicates that the team appears identical at 35 minutes. But there is a significant difference noted from the median and standard deviation, as Team B has lower median but greater variation whereas Team A has more stable delivery time. Managers can therefore make informed decisions by utilising typical performance and variability together.

Operational and environmental decisions

The lower fuel consumption by Team A and lower delivery time variation implies that there is an opportunity to reduce the usage of fuel and maintain consistent service. It is also possible for the management to investigate the reason behind Team B using 3.6 litres and has a 9 minute standard deviation. This will help in introducing route optimisation, driver training and vehicle efficiency measures.

Probability concepts and application

Probability – managers can make use of probability to estimate uncertain events and plan their resources accordingly such as delivery capacity, inventory and contingency measures.
20% probability of delivery delay – A 20% probability implies that 20 out of every 100 deliveries are delayed. Managers can make use of this information to schedule contingency delivery capacity, allow additional deliberate time, plan for alternative routes and prepare customers for potential delays.
Discrete versus continuous distribution – discrete involves countable outcomes and continuous can take any value within a range.
Risk reduction and sustainability – with the help of probability data, it can be possible for the company to anticipate delays and return and allocate resources before the problem takes place.

Decision analysis, ethical leadership and responsible decision making

Certainty, uncertainty and risk – Certainty implies awareness about the outcome of each alternative, and allows managers to predict the result of different alternatives with confidence. Risk indicates the possibility of several outcomes and their probabilities can be estimated. Uncertainty indicates the possibility of several outcomes and their probabilities are unknown.

Design approaches – the design approaches are maximum which implies the selection of alternative with highest possible payoff, and maximin is the selection of alternative with best worst case payoff. The minimax regret is the selection of alternatives that produces the smallest maximum opportunity loss compared to the best decision.

Sustainability considerations – it is important for the management to consider sustainability aspects like energy consumption, waste generation, operating cost, emission, resource use and effect on different stakeholders. The energy efficient technology and lower waste of alternative B should be evident in the decision analysis of management.

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