Reference no: EM132189721

ASSIGNMENT - ANALYTICAL TECHNIQUES FOR SUPPLY CHAIN MANAGEMENT

Introduction

Case 1: Linear Programming Model Building and Computer Solution

Q1.1 Cranfield Grill

Cranfield Grill is an upscale restaurant located in Cranfield Village, Bedford. To help plan an advertising campaign for the coming Christmas season, the restaurant's management team hired a team of master's students studying at Cranfield University MSc Logistics, Procurement, and Supply Chain Management programmes (referred to as Team Cranfield from here onwards).

The restaurant's management team asked Team Cranfield to help them distribute an advertising budget of £279,000 across TV, radio, and online advertising media. Team Cranfield consulted with other students in MSc Strategic Marketing and came up with a table on the exposure effectiveness of each advertising medium and corresponding new customers expected per ad. They have also done desk research to identify the cost per ad for each advertising medium. The information they synthesised is given in Sheet Q1.1 in 'ATS Assignment Data.xlsx'.

Exposure rating is a measure of the value of the ad to both existing customers and potential new customers. It is a function of the image, message recall, and visual and audio appeal. As expected, more expensive television ad has higher exposure rating with the greatest potential to reach new customers.

Team Cranfield, combining their learnings and discussions with their friends in the MSc Strategic Marketing Programme, suggested that exposure and reach were only applicable to the first few ads in each medium. For TV, the exposure rating of 90 and the number of new customers reached per ad of 4000 were reliable only for the first 10 TV ads.

After 10 ads, the benefits were expected to decline. For planning purposes, Team Cranfield suggested to reduce the exposure rating to 55 and the estimate of new customers reached per ad to 1500 for any TV ad beyond 10.

For radio ads, Team Cranfield predicted the proposed exposure of 25 and new customers reached per ad of2000 to be reliable for 15 ads, but then reducing the exposure to 20 and the number of new customers reached per ad to 1200. Similarly, for online ads, the exposure of 10 and the new customers reached per ad of 1000 were reliable for 20 ads. The exposure declined to 5 and the new customers reached per ad declined to 800 beyond 20 online ads.

Cranfield Grill agreed to maximise the total exposure rating across all media as the objective of their Christmas advertising campaign. Since Cranfield Grill wants to attract new customers, they wish to reach at least 100,000 new customers. To balance the advertising campaign and make use of all advertising media, Cranfield Grill adopted the following guidelines:

1. They would like to use at least twice as many radio ads as TV ads.

2. They would like to use at most 20 TV ads.

3. They would like to spend at least £140,000 on TV ads.

4. They would like to spend at most £99,000 on radio ads.

5. They would like to spend at least £30,000 on online ads.

Team Cranfield set on to meet Cranfield Grill's expectations. As a member of Team Cranfield, please build and solve Cranfield Grill's advertising campaign problem. The distribution of marks are as follows:

a. Identify the decision variables.

b. Build the objective function and the constraints.

c. Transfer your model to Excel and solve. Please write in your report the total exposure and the total number of potential new customers reached for each ad medium.

d. How would the total exposure change if Cranfield Grill had an addition £10,000?

e. Please discuss how sensitive Cranfield Grill's solution is to exposure ratings.

f. How would the solution change if Cranfield Grill's objective was to maximise the total number of new customers reached?

g. Which objective function (max exposure versus max new customers reached) makes more sense? Why?

Q1.2 Cranfield Materials

Cranfield Materials manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centres. One of their products, the Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Cranfield Materials has a production schedule to produce 5000 Liftmasters to be made next month.

Cranfield Materials purchases the motors from a supplier in Northampton, but they have an option to either manufacture the frames, supports, and straps themselves or purchase them from a supplier. Manufacturing and purchasing costs per unit are given in Sheet Q1.2 of 'ATS Assignment Data.xlsx'.

Three departments involved in the production of the components are cutting, milling, and shaping. The time in minutes required per unit to process each component in each department, along with the available capacity of the departments are given again in Sheet Q1.2 of 'ATS Assignment Data.xlsx'.

a. Formulate and solve a linear programming model for this make-or-buy decision problem. How many of each component should be manufactured and how many should be purchased?

b. What is the total cost of manufacturing and purchasing plan?

c. For which departments should Cranfield Materials seek additional processing time? What would be the effect of one additional hour on the total cost?

d. Cranfield Materials identified another supplier for frames with a cost of £45 / frame. Should they pursue this opportunity? Why or why not?

e. What are some of the limitations of this approach?

Case 2: Decision Models

Q2.1 Decision Trees

The government is attempting to determine whether the containers carrying food arriving to the UK should be tested for food fraud. Food fraud commonly encompasses a wide range of deliberate fraudulent acts.

The focus of the government however, is on one type of food fraud: the intentional and economically-motivated adulteration of foods. This is the fraudulent addition of non- authentic substances, or the removal or replacement of authentic substances without the purchaser's knowledge, for economic gain of the seller. The two main types of economically-motivated adulteration are:

1. Sale of food which is unfit and potentially harmful, such as: recycling of animal by-products back into the food chain; packing and selling of meat with unknown origin; knowingly selling goods past their 'use by' date.

2. Deliberate mislabelling of food, such as: products substituted with a cheaper alternative, e. g. farmed salmon sold as wild, or Basmati rice adulterated with cheaper varieties; false statements about the source of ingredients, i.e. their geographic, plant, or animal origin.

For the purposes of this decision exercise, the government focuses on type 2 of the intentional and economically-motivated food fraud: deliberate mislabelling. The decision will be made based on a financial basis.

Assume each container accepted to enter the country and brings fraudulent food products costs the government £200,000 and each container that enters the country and does not have any fraudulent food products contributes £25,000 to the national economy. Assume that 10% of all potential containers to enter the country have fraudulent food products. The government may admit all containers, no containers, or test containers for fraudulent food products before determining whether they should be admitted.

It costs £10000 to test a container for fraudulent food products; and the test result is either positive or negative. When the test result is positive, then the container has fraudulent food products 95% of the time. However, 15% of all containers that have fraudulent food products test negative.

A container that does not have any fraudulent food products tests negative99.5% of the time. The government's goal is to maximise per potential container the expected benefits minus the expected costs.

a. Use a decision tree analysis to aid in this undertaking. Hint: Expecting a sequential decision analysis with probabilities estimated using the Bayes' Rule.

b. Calculate the Expected Value of Perfect Information

c. Calculate the Expected Value of Sample Information

d. Under what circumstances would this approach be preferable?

Q2.2 Analytical Hierarchy Process

Supplier selection is a major strategic decision that affects supply chain management. Although there are instances of supplier selection solely based on costs; most businesses now recognise the problem is not that simple and consider criteria other than cost; specifically, environmental and social criteria as well, to reflect the three pillars of sustainability.

After a state-of-the-art literature review, the main criteria and sub-criteria for selecting suppliers are identified and then their importance for supplier selection is rated by a group of 12 experts on a scale of 1-10 where 10 meant high importance and 1 meant low importance. The average importance ratings of each sub-criteria under Economic, Environmental, and Social Criteria are given below.

Criteria	Sub-Criteria	Importance
C1 Economic	C11: Cost	6.7
	C12: Quality	9
	C13: Lead Time	9.1
	C14: Energy Efficiency	7.2
C2: Environmental	C21: CO2 emissions	8
	C22: Water consumption	7.5
	C23: Resource consumption	7.2
C3: Social	C31: Employee satisfaction	8.3
	C32: Support of Professional Development	7.8
	C33: Work-Life Balance	6.9
	C34: Ethical Labour Practices	8.4

The company has also rated the main criteria using the Pairwise Comparison Rating Scale:

1. Equally preferred

2. Equally to moderately preferred

3. Moderately preferred

4. Moderately to strongly preferred

5. Strongly preferred

6. Strongly to very strongly preferred

7. Very strongly preferred

8. Very strongly to extremely preferred

9. Extremely preferred

Their pairwise comparisons of Economic, Environmental, and Social criteria are as follows:

Economic	9	8	7	6	5	4	3	2	1	2	3	4	5	6	7	8	9	Environmental
Economic	9	8	7	6	5	4	3	2	1	2	3	4	5	6	7	8	9	Social
Environmental	9	8	7	6	5	4	3	2	1	2	3	4	5	6	7	8	9	Social

The company has8 suppliers to choose from. After a thorough investigation of the suppliers, they have produced a rating of each supplier under each sub-criteria they have identified. These ratings are given in Sheet Q2.2 of 'ATS Assignment Data.xlsx'.

a. Identify the weights of the main criteria.

b. Check the consistency of the decision maker in their assessment of the main criteria.

c. Complete the AHP analysis and produce a rank order of the eight suppliers.

d. What other criteria do you think they should have considered?

This question is loosely based on Azimifard, A., Moosavirad, S. H., & Ariafar, S. (2018). Selecting sustainable supplier countries for Iran's steel industry at three levels by using AHP and TOPSIS methods. Resources Policy, 57, 30-44.

Case 3: Probability Distributions and Sampling

Q3.1Probability Distributions in Logistics and Supply Chain Management

Choose three examples of the application of probability theory in either logistics or supply chain management. How might knowledge of probability in each of the examples aid the management of the system?

Q3.2Grocery Retailer's Delivery Problem

A grocery retailer is fulfilling online grocery orders from its stores. The distance from one if its retail stores to the customers' addresses is measured for 100 grocery deliveries in the past week. The data are given in Sheet Q3.2 of 'ATS Assignment Data.xlsx'. The retailer would like to invest in autonomous robots for delivering orders to reduce the negative impact on the environment from emissions. These robots are large enough to fit one order per delivery. Assuming the data provided for home deliveries made in the past follows a normal distribution,

a. Plot the histogram of distance from store per order

b. State the mean and the standard deviation of the sample along with five number summary

c. What should be the range of the autonomous robot, if the retailer plans for it to deliver 4 orders without having to recharge 99% of the time?

Case 4: Hypothesis Testing and Regression

Q4.1 A Logistics Company's Fleet

A logistics company operating in Europe has a fleet of 1,000 articulated vehicles. Owing to increased fuel prices, they are considering to deploy a training on energy-efficient driving across their drivers so that they can maximise the miles travelled per gallon of fuel. Before investing in this training widely; they wanted to run a pilot. They asked for volunteers among their drivers and they had 77 drivers willing to sit in the training.

They had recorded average miles per gallon for each driver who participated in the training. From the rest of the drivers who had not taken the training yet, they randomly selected 83 drivers and recorded their average miles per gallon. These data can be found on Sheet Q4.1 of 'ATS Assignment Data.xlsx'. The logistics company would like to know if the training helped their drivers before deciding to deploy it across all their drivers.

a. State the null and the alternative hypotheses.

b. Conduct the appropriate test at alpha = 0.05 significance level to establish whether the training worked.

c. Would an extremely risk averse organisation/manager make the same decision?

d. Discuss the caveats in this approach.

Q4.2 A Fashion Retailer's Sales Forecast

A fashion retailer has 567 stores across the country. Some of these stores are on high streets and some are located inside shopping malls.

The fashion retailer collected sales data on a Fridaylast month for each store they had. They suspect that thedaily sales can be explained by the number of customers arriving at the store per day, the store area in square meters, store type, and the number of sales staff in the store helping customers to find what they are looking for.

Luckily, they have a system to record the number of customers arriving at the store and they can pull the sales data from the ERP system. Human Resources Department provided the number of sales staff on the floor for that Friday and the Accounting Department sent the store area data. See the Sheet Q4.2 of 'ATS Assignment Data.xlsx' for these data.

a. Develop a multiple regression model to explain the variability in net sales. Interpret the regression results.

b. The company is expecting to open a new, 200 square-meters store in a shopping mall to be staffed with 6 sales people. Assuming they will expect500 customers to visit the store per day, what net sales can they expect?

c. Check whether the assumptions of multiple linear regression are met.

d. Is multiple regression an appropriate approach to address the fashion retailer's problem? Explain why or why not?