# IB9BS0 Supply Chain Analytics exam

University of Warwick

April 2021

IB9BS0 Supply Chain Analytics

Instructions

This is an open book (UNRESTRICTED) examination.

Time allowed: 2 hours

This exam consists of 7 questions on 7 pages. All questions should be answered.

The marks are stated against each question. The total number of marks is 100.

# [Question 1] (20% of total marks)

Shoe Zone is a footwear retailer, and they are now preparing for the next year winter catalogue. They do sell different brands of shoes online. The management team needs to decide how many pairs of women’s boots to order in advance from Clarks Ltd. From the past experience, they have observed that demand for their boots varies between 900 and 1700 pairs with different probabilities as presented in the following table.

 Demand 900 1100 1410 1700 1200 1606 Probability 0.08 0.05 0.28 0.24 0.15 0.2

Each pair will cost £90 to make. In addition, there is a transportation cost from the supplier as £2 per pair of boots. They plan to sell each pair at a price of £114. The remaining boots at the end of winter season will be sold at half-price. They would like to maximise expected profit.

1. Calculate the average demand. Briefly explain whether an ordering strategy as being the average

demand is profitable or not. Find the expected number of sold and unsold pairs of boots. Compute

the expected profit.                                                                                                                                                                       [8 marks]

1. Find the optimal order quantity and calculate the expected profit using the newsvendor model.

[12 marks]

(Continued…/)

# 2] (6% of total marks)

Consider the following three supply chain structures:

1. Product is stored at retailer and can be picked up directly by customer
2. Product is stored at the distributor and shipped from the distributor to the customer
3. Product is stored at the manufacturer, and shipped directly from manufacturer to customer

Rank the supply chain structures for suitability (1 = most suitable, 3 = least suitable) depending on the following product characteristics. Briefly explain your answer.

1. i) Slow-moving (very low demand) ii) Many product sources (e.g., customers order different products together)  iii)       High product variety

# [Question 3] (24% of total marks)

World Beer Supply (WBS) is a speciality beer supplier delivering 96 different brands of beer to 50,000 customers all over the UK, grouped into 29 regions. They have three central warehouses, and four regional distribution centres. Customers are either served from a regional distribution centre, or directly from the central warehouse. The regional distribution centres have their inventory replenished from the central warehouse once a week. Due to increased demand, WBS plans to build a fifth regional distribution centre. Five different possible locations have been identified.

You may assume that you have access to all the necessary data, including

• The expected demand in each region di
• The transportation cost per unit of demand from each warehouse/distribution centre to each region tij
• The capacity of each warehouse/distribution centre Kj
• The fixed operating cost for each warehouse/distribution centre O

1. You want to identify the location for the sixth regional distribution centre that results in the lowest overall cost (fixed operating cost plus transportation cost). Write down a mixed integer linear programme to determine the optimal location for the new regional distribution centre. Clearly describe the decision variables, the objective function, and the

constraints.                                                                                                                                                        [21 marks]

1. List three simplifying assumptions you made in the model.                                       [3 marks]

(Continued…/)

# [Question 4] (15% of total marks)

Tesco has recently opened a new depot located in Birmingham. They are currently planning a transportation network that aims to deliver goods from the depot to seven other Tesco Superstores and Tesco Extra shops (labelled as 1, 2, 3, 4, 5 6, and 7) in West Midlands. The monthly average amount of goods to be delivered from the depot to each shop is estimated as 6, 6, 3, 8, 7, 5, and 4 tonnes, respectively. The distance between shops and depot (labelled as D) is presented in terms of miles in the following table.

 D 1 2 3 4 5 6 7 D — 4 4 2 4 5 2 4 1 4 — 5 6 8 8 4 3 2 4 5 — 2 5 8 6 7 3 2 6 2 — 2 5 4 7 4 4 8 5 2 — 3 4 7 5 5 8 8 5 3 — 4 7 6 2 4 6 4 4 4 — 3 7 4 3 7 7 7 7 3 —

The management team would like to operate with the minimum number of trucks in their fleet and to specify the routes of trucks to deliver goods from the depot to each store. They assume that each truck has a capacity of 15 tonnes of goods to carry.

Apply the savings algorithm to determine the minimum number of trucks and their routes.

[15 marks]

(Continued…/)

# 5] (16% of total marks)

Rabbit Ltd. is a manufacturer of computer components in Taiwan. Its largest customers are various famous brands including Acer, Apple, Dell, and HP.

Rabbit adopts a continuous review policy to manage the inventory at its Distribution Centre (DC) and wants to maintain a cycle service level of 95 percent. The lead time from manufacturing to DC is currently 9 weeks. The previous month had been challenging: Apple asked for 5,000 more units than were available at the DC, whereas Acer and Dell ordered 3,500 units and 4,000 units fewer, respectively. Although there was sufficient inventory available at the DC in the form of basic product, Rabbit was not able to meet Apple’s demand because the excess inventory available was labeled and packaged for Acer and Dell. To allow more flexibility for Rabbit to accept such additional orders from customers by simply switching the inventory, the senior logistics supply chain manager proposes to postpone the labeling and packaging work to the DC, where the lead time of manufacturing and transportation remains unchanged. However, the management at the DC is worried about the additional labeling and packaging work which would cost \$0.5 more per unit. Weekly demand is shown in the table below. In each case, the mean denotes the average demand per week, and SD denotes the standard deviation of the demand per week. Furthermore, all demands follow the normal distribution. The value of a graphics card is \$200. As per the rule of thumb of the industry, Rabbit used a holding cost of 25 percent when making all inventory decisions.

 Customer Mean demand SD of demand Acer 1,000 7,000 Apple 700 600 Dell 900 600 HP 500 400

1. What is the annual inventory cost before postponement (please specify units)? [4 marks]
2. How would the inventory cost change if postponement would be implemented (please

specify units)? Would you recommend it?                                                                                                                                                                                                                                                [10 marks]

1. Assume other measures would lead to a reduction in lead time. Would this make

postponement (please explain briefly)      [2 marks] a. Less attractive

1. More attractive
2. Equally (un-)attractive

(Continued…/)

# [Question 6] (4% of total marks)

Consider the following QSUM table, based on mean =8, standard deviation =1, smallest deviation to detect =0.5. What are the values of A and B in the table?

# Sample                  x_i                                                     Ci+                      Ci-

• 88 0             0
• 19 0.94       0
• 11 1.8         0 4         7.47     A             B
• 02 0             1.01
• 42 1.17       0
• 57 1.49       0
• 08 1.32       0
• 24 3.31       0
• 07 4.13       0

(Continued…/)

# 7] (15% of total marks)

Consider four jobs (labelled as 1, 2, 3, and 4) in the table below. Jobs need to be processed on three machines (labelled as M1, M2 and M3) with operations exactly in the sequence as listed for each job. Due date of each job is also provided in the following table.

 Jobs Operations (machine, processing time) Due Date 1 (M2, 2); (M3, 2); (M1, 1); (M2, 2); (M1, 2) 8 2 (M1, 4); (M2, 1); (M3,1); (M2, 3) 16 3 (M2, 3); (M3, 2); (M1, 2); (M2, 1); (M1, 2) 10 4 (M1, 1); (M2, 3); (M3, 3) 12

Schedule them using the Shortest Processing Time dispatching rule and draw a GANTT chart of the final schedule. You may use the grid given below.

Find the completion time for each job and calculate the total tardiness.                                                                                                                                                                     [15 Marks]

 Machine\Time 1 2 3 4 5 6 7 8 9 10 11 12 … M1 M2 M3