Assignment 2

Operations Management

Description Marks out of Wtg (%) Due date

Assignment 2 - Operations Management 200 20.00 12 Oct 2015

Objectives

This assignment addresses the following objectives for the course as outlined in the course specification:

• Use a variety of operational research techniques to analyse complex management problems and to synthesise and evaluate possible solutions to these problems.

• Analyse production and supply in terms of various inputs, types of costs, break even analysis, and the effect of time on the value of money.

Special Instructions

This assignment is to be electronically submitted via Study desk assignment drop-box.

Please submit as a generated PDF file or Word file. Do not submit zip files or scanned PDF files.

File name for your assignment may follow the following format:- Student surname (in capitals)_first name_ENG4004_ASS 2_S2_2015

For example JONES_Bob_ENG4004_ASS 2_S2_2015

This is not critical but helps in sorting student submissions.

QUESTION 1 (80 marks)

A gardening supply company manufactures two types of mulch bins – the Compacto and the Enviro. The production of each bin involves a certain amount of moulding, pressing and assembly as indicated below.

Department Mulch Bin

Compacto Enviro

Moulding 5 hours 6 hours

Pressing 8 hours 5 hours

Assembly 9 hours 14 hours

Next month, the company has maximum available capacities of 630 hours for assembly, 300 hours for moulding and 400 hours for pressing. The company has advance orders for 15 Compacto mulch bins and for 10 Enviro mulch bins and is committed to supplying these next month. The same profit of $6,000 is made from the sale of each mulch bin.

(i) How many Compacto and Enviro mulch bins should be manufactured next month to fulfill advance orders and maximize profits? How much profit will be made? (Assume that partially completed mulch bins can be manufactured but that only completed bins can be sold for profit. Bins on advance order have not yet been paid for.)

(50 marks)

(ii) At the optimum production mix for next month, which if any, of the three departments has any excess capacity, i.e. hours available that are not used? Indicate the amount of any excess capacity in hours.

(10 marks)

(iii) If the profit from the sale of each Enviro mulch bin increases from $6,000 to $15,000 because of its appearance on a popular TV gardening show, how would this affect the proposed production mix for the coming month?

(20 marks)

QUESTION 2 (45 marks)

A steel processing plant supplies lengths of seamless pipe for the oil industry. The pipes are produced to a specified length of 10,000±100 mm. Pipes that are outside the upper or lower tolerance value are considered to be scrap.

Samples of four (4) pipes are taken every hour to monitor the state of production. The results of sampling during the most recent 15 hour period are given in the table below.

Sample No. Sample average

mm Sample Range

mm

1

2

3

4

5 10,022

10,014

10,042

10,004

10,028 45

105

30

85

65

6

7

8

9

10 10,006

9,996

9,998

10,046

10,032 25

55

85

100

75

11

12

13

14

15 10,024

10,030

10,016

10,044

9,998 60

35

90

45

75

(i) Calculate the control limits for the range and sample average control charts and plot the control charts for the process.

(25 marks)

(ii) Determine the relative precision class and calculate modified control limits if this is warranted. Clearly indicate whether or not modified limits are needed.

(5 marks)

(iii) Comment on the state of production. In particular indicate whether or not the range and sample averages are in control, whether or not any scrap is being produced and whether or not the grand average value is appropriate.

(15 marks)

QUESTION 3 (75 marks)

The Supersports Company supplies boxed pairs of soccer boots to distribution centres in Warwick, Toowoomba and Ipswich from existing warehouses in Brisbane and Sydney. Supersports is considering locating a warehouse at the Gold Coast. Annual capacity in the warehouses is shown in the right-hand column, while annual demand is shown in the bottom row of the Table below. Transportation costs per pair of boots are shown in the small boxes. For example the cost to ship one pair of boots from Brisbane to Warwick is $2.37.

Source Destination Capacity

Warwick Toowoomba Ipswich

Brisbane $2.37

$2.25

$2.89

12,000 12,000

Sydney $2.00

$3.00

10,000 $3.27

10,000

Gold Coast $2.13

6,000 $2.50

12,000 $1.75

18,000

Demand 6,000 22,000 12,000 40,000

What is the optimum transportation plan to minimise delivery costs and what is the minimum total cost to Supersports.

Please note you must find solutions via iterations and not just putting the results from using spreadsheet or software package.

Operations Management

Description Marks out of Wtg (%) Due date

Assignment 2 - Operations Management 200 20.00 12 Oct 2015

Objectives

This assignment addresses the following objectives for the course as outlined in the course specification:

• Use a variety of operational research techniques to analyse complex management problems and to synthesise and evaluate possible solutions to these problems.

• Analyse production and supply in terms of various inputs, types of costs, break even analysis, and the effect of time on the value of money.

Special Instructions

This assignment is to be electronically submitted via Study desk assignment drop-box.

Please submit as a generated PDF file or Word file. Do not submit zip files or scanned PDF files.

File name for your assignment may follow the following format:- Student surname (in capitals)_first name_ENG4004_ASS 2_S2_2015

For example JONES_Bob_ENG4004_ASS 2_S2_2015

This is not critical but helps in sorting student submissions.

QUESTION 1 (80 marks)

A gardening supply company manufactures two types of mulch bins – the Compacto and the Enviro. The production of each bin involves a certain amount of moulding, pressing and assembly as indicated below.

Department Mulch Bin

Compacto Enviro

Moulding 5 hours 6 hours

Pressing 8 hours 5 hours

Assembly 9 hours 14 hours

Next month, the company has maximum available capacities of 630 hours for assembly, 300 hours for moulding and 400 hours for pressing. The company has advance orders for 15 Compacto mulch bins and for 10 Enviro mulch bins and is committed to supplying these next month. The same profit of $6,000 is made from the sale of each mulch bin.

(i) How many Compacto and Enviro mulch bins should be manufactured next month to fulfill advance orders and maximize profits? How much profit will be made? (Assume that partially completed mulch bins can be manufactured but that only completed bins can be sold for profit. Bins on advance order have not yet been paid for.)

(50 marks)

(ii) At the optimum production mix for next month, which if any, of the three departments has any excess capacity, i.e. hours available that are not used? Indicate the amount of any excess capacity in hours.

(10 marks)

(iii) If the profit from the sale of each Enviro mulch bin increases from $6,000 to $15,000 because of its appearance on a popular TV gardening show, how would this affect the proposed production mix for the coming month?

(20 marks)

QUESTION 2 (45 marks)

A steel processing plant supplies lengths of seamless pipe for the oil industry. The pipes are produced to a specified length of 10,000±100 mm. Pipes that are outside the upper or lower tolerance value are considered to be scrap.

Samples of four (4) pipes are taken every hour to monitor the state of production. The results of sampling during the most recent 15 hour period are given in the table below.

Sample No. Sample average

mm Sample Range

mm

1

2

3

4

5 10,022

10,014

10,042

10,004

10,028 45

105

30

85

65

6

7

8

9

10 10,006

9,996

9,998

10,046

10,032 25

55

85

100

75

11

12

13

14

15 10,024

10,030

10,016

10,044

9,998 60

35

90

45

75

(i) Calculate the control limits for the range and sample average control charts and plot the control charts for the process.

(25 marks)

(ii) Determine the relative precision class and calculate modified control limits if this is warranted. Clearly indicate whether or not modified limits are needed.

(5 marks)

(iii) Comment on the state of production. In particular indicate whether or not the range and sample averages are in control, whether or not any scrap is being produced and whether or not the grand average value is appropriate.

(15 marks)

QUESTION 3 (75 marks)

The Supersports Company supplies boxed pairs of soccer boots to distribution centres in Warwick, Toowoomba and Ipswich from existing warehouses in Brisbane and Sydney. Supersports is considering locating a warehouse at the Gold Coast. Annual capacity in the warehouses is shown in the right-hand column, while annual demand is shown in the bottom row of the Table below. Transportation costs per pair of boots are shown in the small boxes. For example the cost to ship one pair of boots from Brisbane to Warwick is $2.37.

Source Destination Capacity

Warwick Toowoomba Ipswich

Brisbane $2.37

$2.25

$2.89

12,000 12,000

Sydney $2.00

$3.00

10,000 $3.27

10,000

Gold Coast $2.13

6,000 $2.50

12,000 $1.75

18,000

Demand 6,000 22,000 12,000 40,000

What is the optimum transportation plan to minimise delivery costs and what is the minimum total cost to Supersports.

Please note you must find solutions via iterations and not just putting the results from using spreadsheet or software package.

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