May 4, 2010

Kristens Cookies Company

Solution to Kristen's Cookie Company (A)
Before answering specific questions, it is useful to make a diagram of the overall process:



Note that in this diagram, activities are arranged in columns to indicate which resources are being used. Inside each activity symbol are written the capacity (in dozens of cookies) and the cycle time (in minutes).


1. How long will it take for you to fill a rush order?
Assuming this order is for one dozen cookies, we will need to do the following:
Activity
Resource
Cycle Time
Start Time
Finish Time
Order Entry
E-mail
0 minutes
00:00
00:00
Wash Bowl, Mix
Self
6 minutes
00:00
06:00
Fill Tray
Self
2 minutes
06:00
08:00
Prepare Oven
Roommate
1 minute
08:00
09:00
Bake
Oven
9 minutes
09:00
18:00
Remove
Roommate
0 minutes
18:00
18:00
Cool
None
5 minutes
18:00
23:00
Pack, Collect Money
Roommate
3 minutes
23:00
26:00
Therefore, the minimum time to fill an order is 26 minutes. We can illustrate the sequence of events with a Gantt chart:




2. How many orders can you fill in a night, assuming you are open four hours each night?
Here is a Gantt chart for two batches of one dozen cookies each. It doesn't take twice as long to produce two batches as it does to produce one batch, because you can start mixing the second batch without having to wait for the whole first-batch process to be completed (you can start washing out the bowl as soon as you finish filling the tray). It is possible to produce two batches in 36 minutes.

In general, a formula for the number of minutes to produce n one-dozen batches is given by this expression:
16+10n

3. How much of your own and your roommate's valuable time will it take to fill each order?
For yourself:
Activity
Cycle Time
Wash Bowl, Mix
6 minutes
Fill Tray
2 minutes
Total
8 minutes
For your roommate:
Activity
Cycle Time
Prepare Oven
1 minute
Remove
0 minutes
Pack, Collect Money
3 minutes
Total
4 minutes
This is assuming all orders are for one dozen cookies.
4. Because your baking trays can hold exactly one dozen cookies, you will produce and sell cookies by the dozen. Should you give any discount for people who order two dozen cookies, three dozen cookies, or more? If so, how much? Will it take any longer to fill a two-dozen cookie order than a one-dozen cookie order?
First, let's consider costs. The cost of ingredients and the box are the same, no matter how many dozen you bake. So the only resource that might differ with the size of the batch is labor.
One Dozen
Activity
Resource
Cycle Time
Start Time
Finish Time
Order Entry
E-mail
0 minutes
00:00
00:00
Wash Bowl, Mix
Self
6 minutes
00:00
06:00
Fill Tray
Self
2 minutes
06:00
08:00
Prepare Oven
Roommate
1 minute
08:00
09:00
Bake
Oven
9 minutes
09:00
18:00
Remove
Roommate
0 minutes
18:00
18:00
Cool
None
5 minutes
18:00
23:00
Pack, Collect Money
Roommate
3 minutes
23:00
26:00

Self
8
Roommate
4
Total Labor Minutes
12

Two Dozen
Activity
Resource
Cycle Time
Start Time
Finish Time
Order Entry
E-mail
0 minutes
00:00
00:00
Wash Bowl, Mix
Self
6 minutes
00:00
06:00
Fill Tray 1
Self
2 minutes
06:00
08:00
Fill Tray 2
Self
2 minutes
08:00
10:00
Prepare Oven 1
Roommate
1 minute
08:00
09:00
Bake 1
Oven
9 minutes
09:00
18:00
Remove 1
Roommate
0 minutes
18:00
18:00
Cool 1
None
5 minutes
18:00
23:00
Prepare Oven 2
Roommate
1 minute
18:00
19:00
Bake 2
Oven
9 minutes
19:00
28:00
Remove 2
Roommate
0 minutes
28:00
28:00
Cool 2
None
5 minutes
28:00
33:00
Pack 1
Roommate
2 minutes
23:00
25:00
Pack 2
Roommate
2 minutes
33:00
35:00
Collect Money
Roommate
1 minute
35:00
36:00

Self
10
Roommate
7
Total Labor Minutes
17
Three Dozen
Activity
Resource
Cycle Time
Start Time
Finish Time
Order Entry
E-mail
0 minutes
00:00
00:00
Wash Bowl, Mix
Self
6 minutes
00:00
06:00
Fill Tray 1
Self
2 minutes
06:00
08:00
Fill Tray 2
Self
2 minutes
08:00
10:00
Fill Tray 3
Self
2 minutes
06:00
08:00
Prepare Oven 1
Roommate
1 minute
08:00
09:00
Bake 1
Oven
9 minutes
09:00
18:00
Remove 1
Roommate
0 minutes
18:00
18:00
Cool 1
None
5 minutes
18:00
23:00
Prepare Oven 2
Roommate
1 minute
18:00
19:00
Bake 2
Oven
9 minutes
19:00
28:00
Remove 2
Roommate
0 minutes
28:00
28:00
Cool 2
None
5 minutes
28:00
33:00
Prepare Oven 3
Roommate
1 minute
28:00
29:00
Bake 3
Oven
9 minutes
29:00
38:00
Remove 3
Roommate
0 minutes
38:00
38:00
Cool 3
None
5 minutes
38:00
43:00
Pack 1
Roommate
2 minutes
23:00
25:00
Pack 2
Roommate
2 minutes
33:00
35:00
Pack 3
Roommate
2 minutes
43:00
45:00
Collect Money
Roommate
1 minute
45:00
46:00

Self
12
Roommate
10
Total Labor Minutes
22
Let's assume your time is worth $12 per hour. Your labor costs would be:
# Cookies in Batch
Minutes
Cost
Cost per Dozen
1 dozen
12
$2.40
$2.40
2 dozen
17
$3.40
$1.70
3 dozen
22
$4.40
$1.47
It looks like you could afford to give a discount for two- and three-dozen orders. A two-dozen order doesn't cost twice as much as a one-dozen order.

5. How many food processors and baking trays will you need?
The number of baking trays ought to equal the maximum number of trays you will be using at any one time. The highest volume production imaginable would be if we produced three-dozen orders continuously, a scenario depicted in this Gantt chart:


It's hard to read the activities along the left axis because they are jammed together, but the food processor is only used in the mixing stage, and we ought to be able to see that the processor is idle for long periods of time, and that the real bottleneck is the oven. Buying another food processor won't improve the productivity of the system at all.
There are only three kinds of activities that require a tray: filling the tray, baking (including preparing the oven), and cooling. The Gantt chart shows that we are using at most three trays in the filling activity at any given time (and in fact this is only because this particular plan calls for filling three trays in rapid succession, after which two of them sit waiting for an opportunity to get into the oven). There is never more than one tray in the oven at any given time, nor is there ever any more than one tray cooling. So we could certainly get by with five trays, and maybe four or even three if we adjust the mixing and filling part of the operation.
On the other hand, trays are cheap, and it would be a shame if we ever had to keep the oven (the bottleneck) waiting for lack of a tray. It is reasonable to have "plenty" of trays on hand, whether that means five, or ten, or whatever.

6. Are there any changes you can make in your production plans that will allow you to make better cookies or more cookies in less time or at lower cost? For example, is there a bottleneck operation in your production process that you can expand cheaply? What is the effect of adding another oven? How much would you be willing to pay for an additional oven?
The bottleneck is the oven, which means there is no point in looking at expanding the capacity of any other resource unless the operation's baking capacity is expanded first.
If we had two ovens, we could make cookies faster. But how much faster?
This gets complicated, but we can think about it by looking at the capacities of the various stages in our process:
Stage
Time
Dozens per Hour
(1 Oven)
Dozens per Hour
(2 Oven)
Wash Bowl, Mix, Fill Tray
(yourself)
12 min. for 3 dozen
15 per hour
15 per hour
Prepare Oven & Bake
(oven)
30 min. per 3 dozen
6 per hour
12 per hour
Prepare Oven, Pack, Collect Money
(roommate)
10 min. per 3 dozen*
18 per hour
18 per hour
* all in one order
Even with the second oven, the oven stage will still be the bottleneck. To decide how much we would be willing to pay for another oven, we would have to do some more complicated analysis (including finding out what the distribution of orders would look like — how many for one dozen, how many for two dozen, etc.). Then we could project the increase in revenue and perform some present value analysis on the incremental improvement in our revenue.
Here is a Gantt chart for one two-dozen order:


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Kristens Cookies Resume
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3 comments:

  1. The final Gantt chart seems to be wrong, if you decide to use 2 ovens why would you wait for the first oven to be done cooking before you start the second oven? If you were to be efficient you would be running both ovens almost simultaneously, should take 27 minutes to finish 2 dozens with 2 ovens.

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