### Problem 1 Capacity Planning

A manager has the option of purchasing one, two, or three machines. Fixed costs and potential volumes are as follows:

Number of machines | Total Annual Fixed Costs | Corresponding Range of Output |

1 | $ 9 600 | 0 to 300 |

2 | $ 15 000 | 301 to 600 |

3 | $ 20 000 | 601 to 900 |

The variable cost if we operate only 1 machine is $10 per unit, but due to economies of scale it decreases to 9$ and 8$ if we operate together 2 and 3 machines, respectively. The price sold per item is $40.

Help the manager determine break-even point for each range. If projected annual demand is between 580 and 660 units, how many machines should the manager purchase?

### Problem 2 Forecasting

Weekly demand at ABC Corporation is as follows:

Week | Demand ($) |

1 | 98 |

2 | 112 |

3 | 100 |

4 | 101 |

5 | 115 |

6 | 105 |

7 | 99 |

8 | 102 |

9 | 112 |

10 | 102 |

11 | 108 |

12 | 96 |

Estimate demand for week 13 using a 4-week moving average as well as simple exponential smoothing with a = 0.1. Evaluate the MAD, MAPE and MSE in each case. Which of the two methods you prefer? Why?

For the exponential smoothing please use forecast 0f 104 in period 1

Week | Demand ($) | Forecast |

1 | 98 | 104 |

2 | 112 | |

3 | 100 | |

4 | 101 | |

5 | 115 | |

6 | 105 | |

7 | 99 | |

8 | 102 | |

9 | 112 | |

10 | 102 | |

11 | 108 | |

12 | 96 |

PLEASE DO NOT USE DECIMALS

### Problem 3 Forecasting

Monthly demand at A&D electronics for flat screen TVs are as follows:

Week | Demand(units) |

1 | 9,000 |

2 | 12,000 |

3 | 21,000 |

4 | 33,000 |

5 | 12,000 |

6 | 16,000 |

7 | 20,000 |

8 | 35,000 |

9 | 14,000 |

10 | 15,000 |

11 | 30,000 |

12 | 40,000 |

Estimate demand for the next two weeks (13 – what do you suggest as forecast in week 14) using simple exponential smoothing with a = 0.3 and exponential smoothing with trend adjustment (Holt’s Model) with a = 0.1 and b = 0.2.

For the simple exponential model use the level 20000. (see table below)

Week | Demand(units) | Forecast |

1 | 9,000 | 20000 |

2 | 12,000 | |

3 | 21,000 | |

4 | 33,000 | |

5 | 12,000 | |

6 | 16,000 | |

7 | 20,000 | |

8 | 35,000 | |

9 | 14,000 | |

10 | 15,000 | |

11 | 30,000 | |

12 | 40,000 |

For Holt’s model, use level at period 1 to be L= 11000 and the trend in period 1 to be T1=1400. Evaluate the MAD, MAPE and MSE in each case. Which of the two methods you prefer and why?

Week | Demand ($) | Forecast | Trend |

1 | 98 | 1100 | 1400 |

2 | 112 | ||

3 | 100 | ||

4 | 101 | ||

5 | 115 | ||

6 | 105 | ||

7 | 99 | ||

8 | 102 | ||

9 | 112 | ||

10 | 102 | ||

11 | 108 | ||

12 | 96 |

### Problem 4 Capacity and constraint management Problem

Process Flow diagram and Cycle Times for Bread Making with Two Parallel Lines

The bakery sells and produces ONLY ONE TYPE of BREAD. The bakery operates two PARALLEL baking, Lines, each equipped with a MIXER, a PROOFER and an OVEN. In addition the bakery operates a PACKAGING LINE.

Assume that the Bakery operates for 8 hours a day.

1. What is the BOTTLENECK ?

2. What is the Bottleneck Time?

3. What is the daily capacity?

4. The bakery is considering replacing some of its existing equipment with more advanced and faster equipment. The choice is between

(i) purchasing two new ovens that are each capable of baking a batch of 100 loaves in 3/4 hour, or

(ii) purchasing a new packaging line that is capable of packaging a batch of 200 loaves in 1/2 hour.

Which option would allow the greatest increase in the bakery’s overall capacity?

For (i) please answer 1,2,3,4 again

For (ii) please answer 1,2,3,4 again

### Problem 5 Decision Tree Problem

Based on the decision tree below, please indicate your decisions at points 1, 4, 5 please indicate the expected values at 2, 3, 6, 7

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