kirsten cookies solution

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

Order Entry

Wash Bowl, Mix Ingredients Resource: Self

Capacity: 3 Cycle Time: 6 minutes

Fill Tray Resource: Roommate


Bake Resource: Oven


Start Oven Resource: Roommate, Oven

Capacity: 1 Cycle Time: 1 minute

Remove Resource: Roommate


Cool Resource: none


Pack, Collect Money Resource: Roommate


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

TimeFinish Time

Order Entry E-mail 0 minutes 00:00 00:00Wash Bowl, Mix Self 6 minutes 00:00 06:00

Fill Tray Self 2 minutes 06:00 08:00Prepare Oven Roommat

e1 minute 08:00 09:00

Bake Oven 9 minutes 09:00 18:00Remove Roommat

e0 minutes 18:00 18:00

Cool None 5 minutes 18:00 23:00Pack, Collect

MoneyRoommat

e3 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:

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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:

3. How much of your own and your roommate's valuable time will it take to fill each order?

For yourself:Activity Cycle TimeWash Bowl, Mix 6 minutesFill Tray 2 minutesTotal 8 minutes

For your roommate:Activity Cycle TimePrepare Oven 1 minuteRemove 0 minutesPack, Collect Money

3 minutes

Total 4 minutes

This is assuming all orders are for one dozen cookies.

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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 DozenActivity Resource Cycle Time Start

TimeFinish Time


Fill Tray Self 2 minutes 06:00 08:00Prepare Oven Roommat

e1 minute 08:00 09:00

Bake Oven 9 minutes 09:00 18:00Remove Roommat

e0 minutes 18:00 18:00

Cool None 5 minutes 18:00 23:00Pack, Collect

MoneyRoommat

e3 minutes 23:00 26:00

Self 8Roommate 4Total Labor Minutes

12

Two DozenActivity Resource Cycle Time Start

TimeFinish Time


Fill Tray 1 Self 2 minutes 06:00 08:00Fill 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 18:00Remove 1 Roommat

e0 minutes 18:00 18:00

Cool 1 None 5 minutes 18:00 23:00Prepare Oven 2 Roommat

e1 minute 18:00 19:00


e0 minutes 28:00 28:00

Cool 2 None 5 minutes 28:00 33:00Pack 1 Roommat

e2 minutes 23:00 25:00

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Pack 2 Roommate

2 minutes 33:00 35:00

Collect Money Roommate

1 minute 35:00 36:00


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Three DozenActivity Resource Cycle Time Start

TimeFinish Time


Fill Tray 1 Self 2 minutes 06:00 08:00Fill Tray 2 Self 2 minutes 08:00 10:00Fill Tray 3 Self 2 minutes 06:00 08:00

Prepare Oven 1 Roommate

1 minute 08:00 09:00


e0 minutes 18:00 18:00


e1 minute 18:00 19:00


e0 minutes 28:00 28:00


e1 minute 28:00 29:00


e0 minutes 38:00 38:00

Cool 3 None 5 minutes 38:00 43:00Pack 1 Roommat

e2 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


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Let's assume your time is worth $12 per hour. Your labor costs would be:# Cookies in

BatchMinutes Cost Cost per

Dozen

5

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

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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 hourPrepare Oven & Bake

(oven)30 min. per 3

dozen 6 per hour 12 per hourPrepare 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.

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Here is a Gantt chart for one two-dozen order:

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kirsten cookies solution

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