the orange cake problem
DESCRIPTION
The Orange Cake Problem. Answer Guide. Questions. Assuming you work alone and follow the instructions above, how long will it take you to bake the cake? Is there any obvious way to shorten the preparation time? Assume that two people are available, how fast can the cake now be prepared? - PowerPoint PPT PresentationTRANSCRIPT
MGT3303 – Operations Management
The Orange Cake ProblemThe Orange Cake ProblemThe Orange Cake ProblemThe Orange Cake Problem
Answer Guide
MGT3303 – Operations Management
QuestionsQuestionsQuestionsQuestions
• Assuming you work alone and follow the instructions above, how long will it take you to bake the cake? Is there any obvious way to shorten the preparation time?
• Assume that two people are available, how fast can the cake now be prepared?
• Categorise activity as follows: process, cook, cool. How much time is spent on each category?
• What type of technology could be used to shorten the preparation time? Distinguish these improvements which do not impact quality of the cake from those that do.
• If you were commercialise this cake at a large scale, how would you design the facilities and work to achieve maximum efficiency and volume?
MGT3303 – Operations Management
Question 1Question 1Question 1Question 1
Assuming you work alone and follow the instructions above, how long will it take you to bake the cake? Is there any obvious way to
shorten the preparation time?
MGT3303 – Operations Management
Question 1Question 1Question 1Question 1
• The problem is to apply the recipe instructions on a timeline
• This does not mean adding all the elementary times!!• You have to take advantage of idle times:
–When the cake is baking, start preparing the curd–When the orange slices are being poached, start
preparing the mix
• But you have to respect sequential dependencies–You cannot pour the mix before the orange slices are
positioned…
MGT3303 – Operations Management
SolutionSolutionSolutionSolution
• You should find 153 minutes–minor variations (1 to 3
mn) are not much to worry about
–Major variations (+ 5mn) should be analysed
1 mn
SliceOranges
Mix Cook Orange Slices Leave to Cool
TinPrep.
ArrangeSlices
Strain Puree
DryMix
Whisk
Mix
MixPou
rBake Bake
45 mn
Warm UpOven
R Leave to Cool T Cut in 3 Brush Sandwich Top
Mix S
Grate
Mix P
Leave to CoolBake
30 mn19 mn
153 mn
63 mn 45 mn
MGT3303 – Operations Management
The First 63 MinutesThe First 63 MinutesThe First 63 MinutesThe First 63 Minutes
• Getting the cake ready to bake
1 mn
SliceOranges
Mix Cook Orange Slices Leave to Cool
TinPrep.
ArrangeSlices
Strain Puree
DryMix
Whisk
Mix
MixPou
r
Warm UpOven
63 mn
MGT3303 – Operations Management
The Middle 45 MinutesThe Middle 45 MinutesThe Middle 45 MinutesThe Middle 45 Minutes
• Cake is Baking• Start preparing the curd
Bake Bake
45 mn
Mix S
Grate
Mix P19 mn
MGT3303 – Operations Management
The Last 45 MinutesThe Last 45 MinutesThe Last 45 MinutesThe Last 45 Minutes
R Leave to Cool T Cut in 3 Brush Sandwich Top
Leave to CoolBake
45 mn
MGT3303 – Operations Management
Question 2Question 2Question 2Question 2
Assume that two people are available, how fast can the cake now be
prepared?
MGT3303 – Operations Management
Horizontal Division of LabourHorizontal Division of LabourHorizontal Division of LabourHorizontal Division of Labour
• By dividing “similar” tasks (whisk/strain/mix) between several persons, it is possible to compress processing times
• Overall time gets down to 147 minutes – only a 6 minutes gain in time!
SliceOranges
Mix
Cook Orange Slices Leave to Cool
TinPrep.
ArrangeSlices
Strain Puree
DryMix
Whisk
Mix
Mix Pour Bake Bake
45 mn
Warm UpOven
R Leave to Cool T Cut in 3 Brush Sandwich Top
Mix S
Grate
Mix P
Leave to CoolBake
30 mn
23 mn
147 mn
57 mn 45 mn
1 mn
MGT3303 – Operations Management
Question 3Question 3Question 3Question 3
Categorise activity as follows: process, cook, cool. How much time is spent on
each category?
MGT3303 – Operations Management
Time DistributionTime DistributionTime DistributionTime Distribution
• Why this question?–To better understand
where time is spent–To identify where time
reduction efforts should be focused
Timeline Time Masks
Process 4 3 process
24 14 process
1 1 cook
23 14 cool
Cook 20
45 10 cook
15 process
18 cool
Cool 10 2 process
20 19 cook
1 cool
147 97 244
Total
Process 86
Cook 95
Cool 63
244
MGT3303 – Operations Management
Question 4Question 4Question 4Question 4
What type of technology could be used to shorten the preparation time? Distinguish these improvements which do not impact
quality of the cake from those that do.
MGT3303 – Operations Management
Time ImprovementsTime ImprovementsTime ImprovementsTime Improvements
• Three categories:–Technology input
• Use tools and devices which increase output
–Cooling Time• Question whether or not they are necessary?
–Human Specialisation• When you prepare the cake several times, tasks
which are originally difficult (e.g. slicing the cake in 3) become easy
• Concept of a learning curve
MGT3303 – Operations Management
Technology InputTechnology InputTechnology InputTechnology Input
• Oven–A fan oven cooks slower but more evenly–With a conventional oven, cooking time could be
brought down to 35 mn–This may have a negative impact on quality?
• Puree Preparation–The hand mortar process is tedious–A hand blender does the job better and quicker (
1 mn instead of 10)
MGT3303 – Operations Management
Cooling TimesCooling TimesCooling TimesCooling Times
• Poached Orange Slices–It is difficult to manipulate the slices when they
are hot–But it is feasible with a skilled used of a spatula!–The puree can be blended hot–So, cooling time can be brought down to 2 mn
MGT3303 – Operations Management
Cooling TimesCooling TimesCooling TimesCooling Times
• Cake–It is difficult to cut the cake when it is straight
hot out of the oven–Again, experiencing with knifes and how to hold
the cake means it is possible to slice the cake when it is still warm.
–Reduce the cooling time from 20 mn to 10 mn
MGT3303 – Operations Management
Cooling TimesCooling TimesCooling TimesCooling Times
• Curd–A bit too “runny” when hot, and tends to spread
out too fast at the sandwiching time–Cooling time can be reduced to 10 mn, but not
much more!
MGT3303 – Operations Management
Learning CurvesLearning CurvesLearning CurvesLearning Curves
• Once the operator is skilled, elementary times are reduced–Note: this works well only when tasks are repeated a large
number of time (division)• Slicing the oranges: 2mn• Mix for poaching: 1 mn• Whisk eggs+sugar: 3 mn• Mix dry mix + puree: 2 mn• Grate: 3 mn• Straining poached oranges: skipped altogether as by
selecting the right slices and letting the drip a bit save adding liquid later on
• Cut the cake in 3: 2 mn• Brush: 3 mn• Sandwich: 3 mn• Top: 1 mn
MGT3303 – Operations Management
New Process TimesNew Process TimesNew Process TimesNew Process Times
• The cake can now be prepared in 86 mn
• Better use of parallel processing!
S.O
M
Cook Orange Slices C
TinPrep.
ArrangeSlices
P
DryMix
WhiskMix
Mix Pour Bake
35 mn
Warm UpOven
R Leave to Cool TCutin 3
BrushSandwich
T
Mix SGrate Mix P Leave to CoolBake
86 mn
1 mn
MGT3303 – Operations Management
Question 5Question 5Question 5Question 5
If you were commercialise this cake at a large scale, how would you design
the facilities and work to achieve maximum efficiency and volume?
MGT3303 – Operations Management
Suggested LayoutSuggested LayoutSuggested LayoutSuggested Layout
Cook
Slicingand
Mixing
3.1
6m
4.30m
Poached Orange Station
TinPrep
3.3
0m
11.80m
Mix Preparation(Dry+Puree+Pour)
Ove
n C
onve
yor
Bel
t
3.3
0m
3.96m
FinishingStation
Coo
ling
Con
veyo
r B
elt
Cutting& Sandwiching
CookPrep.
3.1
6m
4.30m
Curd Preparation Station
Cool
ToPackaging
MGT3303 – Operations Management
Why this layout?Why this layout?Why this layout?Why this layout?
• Use existing “process centres” between cooking and cooling operations
• Note that each of these process centres demand about 10 minutes of work–The curd preparation station takes 10 minutes
with 1 worker (per cake)–The finishing station also demands 10 mn / cake–The mix preparation demands 11 mn at two
people – shift the tin preparation, layout slices to the poached orange station• Make sense: do not carry the slices
–The poached orange station is under-loaded
MGT3303 – Operations Management
Output?Output?Output?Output?
• With this staffing level:–Output is one cake every 10 minutes, or 6 cakes per hour,
or 48 cakes a day for an 8 hour working day–For a belt speed of 1 m/mn for the oven conveyor:
• Cooking time is 35 mn – so length is 3.5 m• A cake is loaded/emptied every 10 mn • Plenty of space! (only 3.5 cakes in the oven)
• 48 cakes per day is not much!–We are a very, very long way from mass production–How could you improve this output?
MGT3303 – Operations Management
Increasing OutputIncreasing OutputIncreasing OutputIncreasing Output
• By applying further the principle of horizontal division of labour:–More operators for more elementary tasks
• See assembly line design
• Automation
–More technology inputs• Special tools, cooking and cooling technology