Question

Asked Oct 16, 2019

Consider the case of Conrad's Cookie Company, where he and two of his friends (Jared and Jack) are working to make and sell cookies. They have just one oven and can bake up to two dozen cookies at a time. The oven can bake two dozen cookies simultaneously (of similar or different ingredients) or one dozen only. If one dozen is baking in the oven, baking time will not be any different from baking two dozen simultaneously. The sequence of baking steps and respective durations are below.

Mixing and Spooning (together) |
3 minutes of labor time per dozen |

Loading |
1 minutes per dozen. |

Baking |
8 minutes of baking time for one or two. |

Cooling |
6 minutes; |

Packing |
5 minutes of labor time per dozen cookies |

Payment (to be done after packing only) |
1 minutes of labor time per order |

If all orders are 4 dozen cookies,

a) What is the best way to assign Conrad and his friends to jobs in order to maximize capacity? Find highest theoretical capacity and bottleneck of the process.

b) Draw a Gantt Chart in Excel for the process of part (a). Once system warms up, is the capacity the same as what you found in part (a)? Find throughput time of orders. Throughput time is from order placement until payment processing completion.

Step 1

Given all orders of size 4 dozen cookies and since the last step (payment) is done for the entire order we ignore the duration of payment for determining the optimal duration. Since the oven can deliver 2 dozen at the same time as for 1 dozen we compare the timings differences when we work the pipeline as 1 versus 2 dozen cookies.

1 dozen cookie case:

Total time = 3 + 1 + 8 + 6 + 5 = 23 min per dozen i.e. 92 min per 4 dozen (one order size) excluding the payment time.

2 dozen cookie case:

Total time = 3 x 2 + 1 x 2 + 8 + 6 + 5 x 2 = 32 min per 2 dozen, i.e. 64 min per 4 dozen (one order size) excluding the payment time.

Hence it is best to process 2 dozen cookies together at each stage. In the second case the maximum duration is taken in the packing stage which takes 5 x 2 = 10 min per 2 dozen cookies. This is the bottleneck in the entire process.

Step 2

After the initial warm up the system enters a steady state and assuming we have a pipeline size of 2 dozen cookies and given the fact that in this case the bottleneck is the packing stage taking 10 min, hence 2 dozen cookies come out every 10 min.

Step 3

The throughput time is the time of the entire process using the 2 dozen pipeline case plus the paymen...

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