the orange cake problem

MGT3303 – Operations Management

The Orange Cake ProblemThe Orange Cake ProblemThe Orange Cake ProblemThe Orange Cake Problem

Answer Guide


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?


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?



• 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…


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


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


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


The Last 45 MinutesThe Last 45 MinutesThe Last 45 MinutesThe Last 45 Minutes


Leave to CoolBake

45 mn



Assume that two people are available, how fast can the cake now be

prepared?


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


Mix S

Grate

Mix P

Leave to CoolBake

30 mn

23 mn

147 mn

57 mn 45 mn

1 mn



Categorise activity as follows: process, cook, cool. How much time is spent on

each category?


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



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.


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


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)


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



• 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



• 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!


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


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



If you were commercialise this cake at a large scale, how would you design

the facilities and work to achieve maximum efficiency and volume?


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


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


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?


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

the orange cake problem

Documents

preparation time

time distributionwhy

cake ready

time reduction efforts

processing timesoverall

type of technology

obvious way

elementary times