LGT5171: Assignment Essay

LGT5171: Assignment

Guidelines:

• An electronic version of solutions should be uploaded to Learn@PolyU.

• You should type your answers in a pdf/word file.

• The file name should start with your name, e.g., “Leung Wing Yi.pdf” or “Leung Wing

Yi-Assignment.pdf”.

• Due time: 23:59, 31 Mar (Thurs)

• You can use calculators, but you must show your calculations.

• The values of “X” in Question 2 and “Y” in Question 5 are shown in the table below.

Different students may have different values of “X” and “Y”. You should use the values

that are in the same row as your Student ID in the table.

Student No. “X” in Q2 “Y” in Q5

21061559G 180 1500

21064101G 190 1600

21006161G 180 1800

21105833G 190 1500

21063889G 180 1500

21066829G 190 1600

21108771G 180 1800

21106229G 190 1500

21058465G 180 1600

21105978G 190 1800

21050996G 180 1500

21066477G 180 1600

21001296G 180 1800

21068464G 190 1500

21036312G 180 1600

21069737G 180 1500

21064246G 190 1600

21053646G 180 1800

21060454G 180 1500

21109273G 190 1600

21060385G 180 1800

21052373G 180 1500

21057415G 190 1600

21026748G 190 1800

21063219G 190 1500

21053492G 180 1600

21026702G 180 1800

21060461G 190 1500

21052023G 190 1600

21026587G 180 1800

21055748G 190 1500

21068487G 190 1600

21045091G 180 1800

Question 1 (3 points)

The following table shows the times required to complete each of seven jobs in a two-machine flow. Each job must follow the same sequence, beginning with machine A and moving to

machine B.

Job Machine A time Machine B time

a 8 4

b 5 11

c 9 14

d 16 6

e 10 7

f 2 10

g 18 10

Q1.1 Determine a sequence that will minimize makespan time. (1 point)

Q1.2 For the sequence determined in Q1.1, what is the idle time for machine B? (1 point)

Q1.3 For the sequence determined in Q1.1, how much would machine B’s idle time be reduced

by splitting the last two jobs in the sequence in half (“splitting a job (e.g., job a) in half” means

splitting job a into two jobs a1 and a2 with the same processing time 4 on machine A and 2 on

machine B)? (1 point)

Question 2 (4 points)

(Replace “X” in the question with its value in the table in the guideline.) A supermarket sells

two types of toy cars (type I and type II). The unit price for type I toy car is $250 and for type

II toy car is $280. The unit costs for type I and type II toy cars are $180 and $200, respectively,

and the salvage values are $120 and $130, respectively. The monthly demands of the two types

of toy cars are independent, and the relative frequencies of monthly demand are listed in the

following table. There is a rack used to display the toy cars with the capacity of 6 toy cars.

Suppose that only the toy cars displayed on the rack can be purchased by customers.

Table 2.1: Monthly demand of two types of toy cars

Type I toy car Type II toy car Demand Relative frequency Demand Relative frequency

2 0.1 0 0.05

3 0.15 1 0.05

4 0.25 2 0.15

5 0.25 3 0.35

6 0.2 4 0.3

7 0.05 5 0.1

Q2.1 How many type I toy cars and how many type II toy cars should be displayed on the rack to maximize the expected total profit of the two types of toy cars? (2 points)

Q2.2 The supermarket will sell a new type of toy cars (type III) with the unit price of $300, the

unit cost of $210, and the salvage value of $150. The monthly demand distribution of type III

toy cars is as follows (the monthly demand distribution for type I and type II toy cars will not

change).

Table 2.2: Monthly demand of type III toy cars

Type III toy car Demand Relative frequency

1 0.1

2 0.2

3 0.35

4 0.2

5 0.15

A new display rack will be rented (both the old display rack and the new display rack will be

used). The capacity and the rent for a new display rack is shown in Table 2.3.

Table 2.3: Capacity and rent of a new display rack

Display rack Capacity (toy car) Rent per month ($)

R1 3 140

R2 4 X

R3 5 230

Which display rack should be rented? How many type I, type II and type III toy cars should be

displayed on the two racks (the old one owned by the supermarket and the new one rented)? (2

points)

Question 3 (4 points)

Consider a project with 12 activities A1, A2, …, A12. A1 is the first activity starting from day

0 and A12 is the last activity. Consider the dependency relations and the activity durations

provided below.

Activity Duration Immediate predecessor

A1 6 None

A2 3 A1

A3 4 A1

A4 8 A1

A5 10 A2

A6 9 A3

A7 16 A3

A8 13 A4

A9 8 A5

A10 10 A6

A11 6 A7, A9, A10

A12 3 A8, A11

Q3.1 For each activity, compute the late start, the late completion, and the slack time. (1 point)

Q3.2 Twelve persons P1, P2, …, P12 are assigned to activities A1, A2, … A12, respectively. If

P5 asks for leave for 5 days (from day 12 to day 16), can the leave application be approved

without affecting the completion of the project? If A5 can also be completed by P6, P7 or P8,

which person can be assigned to A5 without affecting the completion of the project (The person

assigned to A5 also needs to complete his/her own activity)? (2 points)

Q3.3 Which activity whose duration reduces by 3 will lead to the decrease of the duration of

the whole project by 2? (Please show all the possible activities.) (1 point)

Question 4 (4 points)

Given the following information, develop a material requirement plan that will lead to 1000

units and 600 units of product A being available at the beginning of week 6 and week 8,

respectively. (L4L means lot-for-lot.)

Note: The figure means one A consists of one B and two Cs, one B consists of three Ds and

one E, and one C consists of one D and two Fs.

Master schedule:

Period 1 2 3 4 5 6 7 8

Quantity of A 1000 600

A, Lead time (LT)=1, L4L 1 2 3 4 5 6 7 8

Gross requirements Scheduled receipts Projected on hand 150 Net requirements Planned order receipts Planned order releases

B, LT=2, Fixed Q=70 1 2 3 4 5 6 7 8

Gross requirements Scheduled receipts Projected on hand 200 Net requirements Planned order receipts Planned order releases

C, LT=1, L4L 1 2 3 4 5 6 7 8

Gross requirements Scheduled receipts Projected on hand 0 Net requirements Planned order receipts Planned order releases

D, LT=1, Fixed Q=200 1 2 3 4 5 6 7 8

Gross requirements Scheduled receipts 200 Projected on hand 180 Net requirements Planned order receipts Planned order releases

E, LT=2, L4L 1 2 3 4 5 6 7 8

Gross requirements Scheduled receipts Projected on hand 260 Net requirements Planned order receipts Planned order releases

F, LT=1, L4L 1 2 3 4 5 6 7 8

Gross requirements Scheduled receipts 150 Projected on hand 0 Net requirements Planned order receipts Planned order releases

Question 5 (2 points)

An inventory ordering system for a new production item P1 is to be set up. Every three weeks

(21 days) inventory is counted and a new order is placed. The daily usage rate for P1 is normally

distributed. The manager has gathered the following information about the item:

Item P1

Average daily demand 150 units

Standard deviation 10 units per day

Unit cost $20

Annual holding cost 20% of unit cost

Ordering cost per order $100

Lead time 1 week

Acceptable stockout risk 2%

Q5.1 Compute the order quantity for P1 if 1000 units are on hand at the time the order is placed.

(1 point)

Q5.2 What is the order quantity for P1 if Y units are on hand at the time the order is placed?

(Replace “Y” in the question with its value in the table in the guideline.) (1 point)

Question 6 (3 Points)

Component “XG-2021” has an average daily independent demand as spare parts of 80 units, a

ordering cost of $1000 per order, a holding cost of $0.01 per unit per day. The lead time for this

product is nine days, and the standard deviation of demand is two units per day. The firm wants

to have a 99% service level for this spare part.

Q6.1 Please use the EOQ formula to compute the optimal order quantity 𝑄0. (1 point)

Q6.2 Please compute reorder point. (1 point)

Q6.3 How often should orders be placed for this product if they are placed at regular intervals

using a periodic review system (i.e., calculate the length of an order cycle when the optimal

order quantity is used and the actual daily demand is a constant that is equal to the average daily

demand)? (1 point)