BA 5001 FINAL COURSEWORK

• Final coursework: Lamberts Heating •  • Submission date: Friday 24th May 2013•  • This coursework is worth 40% of your final mark for this module.

• Part A: 50 marks• Part B: 20 marks• Part C: 30 marks

PART B : INSTALLING THE NEW MACHINERY

Activity

  Normal Duration in weeks

Preceding activity

Minimum Duration[Each day saved cost

£200]

A: Order new machinery 2 None 2B: Plan new physical layout of

factory3 None 3

C: Determine changes needed in existing machinery

3 None 3

D Receive new equipment 10 A 8E Hire new employee to

supervise the operation of the new machinery

7 A 6

F Make changes needed to accommodate new machinery

15 B 13

G: Make changes needed in existing machinery

9 C 7

H: Train existing employees to use new machinery

7 D,E 6

I: Install new machinery 4 F 3J: Disassemble old machinery 5 G 4K: Conduct employee safety

training on new installation2 H,I 2

PART B : INSTRUCTIONS

• You may complete this task manually or by using MS project.

• Assuming that the project starts on Monday 3rd June 2013, determine the shortest duration for the entire project, using the normal duration times. Specify the date at which the project can finish and the number of weeks required.

• Produce a Gantt chart showing the starting and finishing times of each activity

• Identify which activities form the critical path(s) of the project.

PART B : EXAMPLE FROM BOOKLET

• Estate Agency : pages 113 to 115 for manual example

• Estate Agency: pages 124 to 127 for MS Project

ESTATE AGENTS: NETWORK DIAGRAM

A 0 9   C 9 14                

9 0 9 5 10 15              

                             

                             

        D 9 12   E 12 15 G 15 16

        3 9 12   3 12 15   1 15 16

                           

B 0 7 F 7 11                

7  4  11   4 11 15                                             

The critical path is ADEG. The shortest finishing time for the project is 16 weeks.

ESTATE AGENTS: FLOATS

• Float = Latest finish time (LFT) – Earliest finish time (EFT)

Activity

EFT LFT float Critical

A 9 9 0 yes

B 7 11 4  

C 14 15 1  

D 12 12 0 yes

E 15 15 0 yes

F 11 15 4  

G 16 16 0 yes

ESTATE AGENTS : GANTT CHART

A

B

C

D

E

F

G

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Estate Agents

no activity duration float

days

USING MS PROJECT: NETWORK DIAGRAM

USING MS PROJECT: GANTT CHART

PART B : CONTINUED

• If the project could be speeded up by a maximum of 3 weeks at a cost of £200 a day, where should this money be spent? Produce a new network diagram to show the new critical path(s) and total duration.

• example of crashing on pages 117 to 120 (coursework is easier than this )

• make sure you take note of the minimum durations

• calculate the extra cost of speeding up the project

PART B : REPORT (ABOUT 500 WORDS)

Give details of the proposed calendar of works, making it clear which activities are critical and which activities have some slack. This section should be written so that the management can understand the advice being given without reference to the work in the appendix. Give details of the starting date, the finishing date and the duration of the project.Explain how, by spending more money, the project duration can be shortened. Explain which activities have been shortened and which activities are now critical. Give details of the starting date, the finishing date and the duration of the project. Give details of the extra cost involved in shortening the project.•  

FINAL COURSEWORK : PART C

• Cost of procuring boilersThis part of the coursework requires you to use linear programming techniques to determine the best way to minimise the cost of supplying boilers to Lamberts Heating As well as manufacturing radiators (as mentioned in Part A), Lamberts Heating is also reviewing the way it procures boilers to enable the installation of domestic heating systems.

PART C : IDENTIFY THE DECISION VARIABLES

The purchasing department has identified three possible suppliers of boilers; Apex, Brunswich and Centrale. It has also identified five kinds of domestic boiler that it wants to purchase so it can supply and fit these boilers to a variety of sizes of homes.The five boilers are known and coded by Italian numbers as most are manufactured in Italy ; Uno (1), Duo (2), Tre (3), Quattro (4) and Cinque (5).

PART C : IDENTIFY THE CONSTRAINTS

The table below gives the cost of each boiler (in £s) from each supplier. The final row of the table specifies the minimum requirement of each type of boiler per year. Please note that not all boilers are available from each supplier.•    Uno Duo Tre Quattro Cinque

Apex 500 750 300 --- 450

Brunswich --- 725 320 875 420

Centrale 480 775 310 900 ---

Requirement

(number of boilers)

 

2000

 

1500

 

3000

 

2500

 

2200

PART C : IDENTIFY THE CONSTRAINTS

There are certain limitations that have to be taken into account; • Apex can supply no more than 1,000 of the Tre

boiler each year.• Brunswich can supply no more than 800 of the

Duo boiler each year.• Centrale can supply no more than 1,800 Uno

boilers each year.• Lamberts Heating wants to meet its requirement

for the number of boilers needed each year at the minimum cost.

EXAMPLE FROM MODULE BOOKLET PAGE 105

 HomeFarm

 yield per acre

 cost per acre

  

 Meadow Farm

 yield per acre

 cost per acre

 corn

 400 barrels

 £100

  

 corn

 650 barrels

 £120

 wheat

 300 barrels

 £90

  

 wheat

 350 barrels

 £80

Farm ProductionA farmer has two farms, Home Farm and Meadow Farm, in which he grows corn and wheat.Both farms are 40 acres in size.To satisfy a contract with a local mill, the farmer must produce 7,000 barrels of corn and 11,000 barrels of wheat each year. The farmer wishes to minimise the cost of meeting the contract.The data for each farm is given below:

DEFINITION OF DECISION VARIABLES

Variables: We need to distinguish between production at Home and Meadow Farm.

Let CH be the number of acres of corn planted at Home FarmLet CM be the number of acres of corn planted at Meadow FarmLet WH be the number of acres of wheat planted at Home FarmLet WM be the number of acres of wheat planted at Meadow Farm

FORMULATION OF PROBLEM

Minimise Cost:Minimise 100CH + 90WH + 120CM + 80WM

subject to:yield corn(1) 400CH + 650CM ≥ 7,000 wheat(2) 300WH + 350WM ≥11,000area Home Farm (3) CH + WH ≤ 40 Meadow Farm (4) CM + WM ≤ 40• CH ≥ 0, CM ≥ 0, WH ≥ 0 WM≥ 0

FARM PRODUCTION : INPUT

farms

corn home corn meadow wheat home wheat meadow0 0 0 0

minimise 100 120 90 80 0corn 400 650 0 >= 7000

wheat 300 350 0 >= 11000home farm 1 1 0 <= 40

meadow farm 1 1 0 <= 40

FARM’S ANSWER REPORT

Objective Cell (Min)Cell Name Original Value Final Value

$F$5 minimise 0 3861.538462

Variable CellsCell Name Original Value Final Value Integer

$B$4 corn home 0 0 Contin$C$4 corn meadow 0 10.76923077 Contin$D$4 wheat home 0 2.564102564 Contin$E$4 wheat meadow 0 29.23076923 Contin

ConstraintsCell Name Cell Value Formula Status Slack

$F$6 corn 7000 $F$6>=$H$6 Binding 0$F$7 wheat 11000 $F$7>=$H$7 Binding 0$F$8 home farm 2.564102564 $F$8<=$H$8 Not Binding 37.43589744$F$9 meadow farm 40 $F$9<=$H$9 Binding 0

FARM’S SENSITIVITY REPORT

Variable CellsFinal Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$4 corn home 0 10.76923077 100 1E+30 10.76923077$C$4 corn meadow 10.76923077 0 120 17.5 145$D$4 wheat home 2.564102564 0 90 15 21.42857143$E$4 wheat meadow 29.23076923 0 80 25 17.5

ConstraintsFinal Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$F$6 corn 7000 0.223076923 7000 19000 1428.571429$F$7 wheat 11000 0.3 11000 11230.76923 769.2307692$F$8 home farm 2.564102564 0 40 1E+30 37.43589744$F$9 meadow farm 40 -25 40 2.197802198 29.23076923

COURSEWORK REQUIREMENTS: APPENDIX

• Define the meaning of any decision variables you are using.

• Formulate the situation as a linear programming problem.

• Include your computer input of the problem (and show any formulae used)

• Include the “Answer Report” and “Sensitivity Report” printouts

COURSEWORK REQUIREMENTS: REPORT [ABOUT 500 WORDS]

Write a brief report to the management of Lambert Heating detailing the cheapest way of meeting their need for boilers.This report, written in a formal style of English, should include:The nature of the problem being solvedThe suggested purchasing plan The cost of the suggested purchasing plan.The robustness of the plan. Provide details of the ranges of costs of boilers from each suggested supplier for which your suggested plan remains optimal, and advise the company when they will have to generate a new plan

COURSEWORK REQUIREMENTS

Do not just provide lists but consider your answers in the context of the question.

At present, Apex can supply no more than 1,000 of the Tre boiler each year. If this limit was changed so that Apex could now supply 1,100 Tre boilers, explain what effect this would have on the total minimum cost?

FARM PRODUCTION : NOTES FOR A REPORT

This is taken from page 106 of the module booklet1. Planting Plan• In order to minimise the planting costs, the following

should be implemented:• Plant Home Farm with 2.56 acres of wheat • Plant Meadow Farm with 10.77 acres of corn and

29.23 acres of wheat.• This will incur costs of £3,861.54, the minimum that

can be achieved.

FARM PRODUCTION : NOTES

• 2. Implications of Suggested Planting Programme

• The planting plan given above will result in exactly 7,000 barrels of corn and exactly 11,000 barrels of wheat being produced.

• [S1 = 0, S2 = 0]• 37.44 acres of Home Farm will not be planted,

whilst all 40 acres of Meadow Farm will be used.

FARM PRODUCTION : NOTES

• 3. Scope of the recommendations• 3.1 Change in Costs• The planting plan given above will result in a

minimum cost whilst the following conditions hold:• * The cost of planting corn at Home Farm stays above

£89.23 per acre.• * The cost of planting corn at Meadow Farm stays

below £137.50 per acre.• * The cost of planting wheat at Home Farm stays in

the range £68.57 to £105 per acres.• * The cost of planting wheat at Meadow Farm stays in

the range £62.50 to £105 per acre.

FARM PRODUCTION : NOTES

• If any one of the conditions above fails to hold then a new planting plan will be required. Furthermore, if two or more of the present costs change, a new plan will be required.

• As these ranges are relatively large, the proposed plan should hold good for some time

FARM PRODUCTION : NOTES• 3.2 Change in Contract• The proposed plan exactly meets the contracts for

7,000 barrels of corn and 11,000 barrels of wheat.• If the requirement for corn was to increase by one

barrel, the extra costs incurred in meeting this target would be 22.3 pence. This marginal cost of 22.3 pence per barrel applies for levels of production between 5,571.43 and 26,000 barrels.

• If the minimum amount of wheat required was increased, the extra cost would be 30 pence per barrel. This extra cost per barrel will apply whilst the contract for wheat lies in the range 10,230.8 to 22,230.8 barrels.

• If the minimum requirement for corn or wheat fell outside these ranges, a new planting plan would be required.

FARM PRODUCTION : NOTES

3.3 Changes in Farm Size• In total only 2.56 acres of Home Farm are being

used. Clearly it would not make sense to consider increasing the size of Home Farm.All 40 acres of Meadow Farm are being used. If the size of Meadow Farm could be increased by 1 acre the minimum cost could be reduced by £25. This marginal reduction in cost applies when the size of Meadow Farm lies in the range 10.77 acres to 42.2 acres.

• Similarly, if the size of Meadow Farm is reduced by 1 acre, the minimum cost will rise by £25.

FARM PRODUCTION : NOTES

If we could increase the size of Meadow Farm by 1 acre, we could produce an extra 350 barrels at Meadow Farm at a cost of £80.• At the same time we would reduce the yield from

Home Farm by 350 barrels • i.e. 350/300 = 1.16666 acres. This reduction

would save 1.16666*90 =105.• Thus the net reduction would be 105 - 80 =

£25 ]

MARKING SCHEME: PART B

• 40

Input data for original problem shown 2

Correct Network diagram produced 4

Reduced time input data 2

Reduced time correct network diagram 2

total 10Mention start data and finish date . Mention duration = 24 weeks (2) 4

Mention critical activities, giving full description of each activity for full marks (3) making it clear what critical means (2). List activities that have some slack (3) make it clear what slack means (2)

12

Advice client as to how reduce time 2

Mention new start data and new finish date , duration and cost 4

Mention the new critical activities giving full description of each activity for full marks (2) making it clear what critical means (2)

8

total 30

40

MARKING SCHEME: PART C

appendix Defining variables 6 Stating objective function 2 Stating constraints 9 Showing correct excel input data 2 Showing all of the output data 4 total 23report Explaining the problem . 5 Explaining the suggest purchasing plan . 8

Stating the minimum cost 3 Robustness: This plan remains optimal whilst the costs of

Uno from Apex are ???, Due from Apex are ??? etc17

If the Apex could supply 100 more Tre boilers year, how would the minimum cost change

4

total 37 total 60