SYST 4050 Supply Chain Management



OPIM 4050 Supply Chain Management – Homework 3 Solutions

1. Answer Exercise 2 from Chapter 6 about Unipart, a manufacturer of auto parts.

“so Year 1’s costs are incurred now and Year 2 costs are incurred in a year” means

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Step 1. Draw the decision tree:

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Step 2. Calculate the NPV (there are multiple ways to do this, one method is shown below)

For Parts4U

|Scenario |C0 + C1/(1+k) = NPV |Prob |NPV*Prob |

|150, 150 |150*0.05 + (150*0.05)/1.2 = 13.75 |0.375 |5.15 |

|150, 135 |150*0.05 + (135*0.05)/1.2 = 13.125 |0.375 |4.92 |

|135, 135 |135*0.05 + (135*0.05)/1.2 = 12.375 |0.125 |1.55 |

|135, 121.5 |135*0.05 + (121.5*0.05)/1.2 = 11.8125 |0.125 |1.48 |

|NPV for Parts4U |13.10 million |

For AllMRO

|Scenario |C0 + C1/(1+k) = NPV |Prob |NPV*Prob |

|150, 150 |10 + 150*0.01 + (150*0.01)/1.2 = 12.75 |0.375 |4.78 |

|150, 135 |10 + 150*0.01 + (135*0.01)/1.2 = 12.625 |0.375 |4.73 |

|135, 135 |10 + 135*0.01 + (135*0.01)/1.2 = 12.475 |0.125 |1.56 |

|135, 121.5 |10 + 135*0.01 + (121.5*0.01)/1.2 = 12.3625 |0.125 |1.55 |

|NPV for AllMRO |12.62 million |

The NPV of the commission is lower for AllMRO. Hence, choose AllMRO.

2. Use the following demand data for parts (a) and (b)

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a) What is the demand forecast for periods 7 and 8 when using the 3-period moving average forecasting method?

The forecast for period 7 depends on the level for period 6

F7 = L6

The level for period 6 is the average demand of periods 6, 5, and 4

L6 = (D6 + D5 + D4) / 3 = (987 + 1128 + 911) / 3 = 1008.67

Hence, F7 = 1008.67

The forecast for period 8 depends on the level for period 7 (we cannot calculate the level for period 7, so we can use the level for period 6)

F8 = L6

Hence, F8 = 1008.67

b) What is the demand forecast for periods 1 and 2 when using the simple exponential smoothing forecasting method with smoothing parameter ( = 0.2?

The forecast for period 1 depends on the level for period 0

F1 = L0

The level for period 0 is the average demand over all periods

L0 = (D6 + D5 + D4 + D3 + D2 + D1) / 6 = (987 + 1128 + 911 + 897 + 979 + 1019) / 6 = 986.83

Hence, F1 = 986.83

The forecast for period 2 depends on the level for period 1

F2 = L1

The level for period 1 can be calculated as follows

L1 = (D1 + (1 – ()L0 = 0.2*1019 + 0.8*986.83 = 993.26

Hence, F2 = 993.26

Use the following demand, level, and trend data for parts (c)

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c) What is the demand forecast for periods 1 and 2 when using Holt’s method with smoothing parameters ( = 0.1 and ( = 0.1?

The forecast for period 1 depends on the level and trend for period 0

F1 = L0 + T0

The level and trend for period 0 are given

L0 + T0 = 105 + 11 = 116

Hence, F1 = 116

The forecast for period 2 depends on the level and trend for period 1

F2 = L1 + T1

The level for period 1 can be calculated as follows

L1 = (D1 + (1 – ()(L0 + T0) = 0.1*123 + 0.9*(105 + 11) = 116.7

The trend for period 1 can be calculated as follows

T1 = ((L1 – L0) + (1 – ()T0 = 0.1*(116.7 – 105) + 0.9*11 = 11.07

Thus the sum of level and trend for period 1 is

L1 + T1 = 116.7 + 11.07 = 127.77

Hence, F2 = 127.77

Use the following demand and forecast data for parts (d) and (e)

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d) For periods 1, 2, and 3, calculate the:

• Forecast Errors (Et)

• Absolute Deviation (At)

• Mean Absolute Percentage Error (MAPEt)

• Mean Squared Error (MSEt)

E1 = F1 – D1 = 203 – 213 = –10

E2 = F2 – D2 = 254 – 246 = 8

E3 = F3 – D3 = 290 – 276 = 14

A1 = |E1| = 10

A2 = |E2| = 8

A3 = |E3| = 14

Let us first calculate the Absolute Percentage Error (APE) before calculating the Mean Absolute Percentage Error (basically, the average of Absolute Percentage Error)

APE1 = (A1/D1)*100 = (10/213)*100 = 4.69

APE2 = (A2/D2)*100 = (8/246)*100 = 3.25

APE3 = (A3/D3)*100 = (14/276)*100 = 5.07

MAPE1 = (APE1) / 1 = (4.69) / 1 = 4.69

MAPE2 = (APE1 + APE2) / 2 = (4.69 + 3.25) / 2 = 3.97

MAPE3 = (APE1 + APE2 + APE3) / 3 = (4.69 + 3.25 + 5.07) / 3 = 4.34

MSE1 = (E12) / 1 = (100) / 1 = 100

MSE2 = (E12 + E22) / 1 = (100 + 64) / 2 = 82

MSE3 = (E12 + E22 + E32) / 1 = (100 + 64 + 196) / 3 = 120

e) For period 3, calculate the mean absolute deviation (MADt) and provide an estimate for the standard deviation of the forecast error for period 3.

MAD3 = (A1 + A2 + A3) / 3 = (10 + 8 + 14) / 3 = 10.67

To estimate the standard deviation of the forecast error for period 3 we take 1.25*MAD3

Hence, STDEV(Forecast Error) =1.25*10.67 = 13.34

3. Use the data in Exercise 1 from Chapter 7 about ABC Corporation (see also online template).

a) Use the static forecasting method to forecast monthly demand for ABC Corporation for year 6.

See online Excel sheet

b) Evaluate the Forecast Errors (Et), Absolute Deviation (At), Bias (biast), Mean Absolute Deviation (MADt), Tracking Signal (TSt), Mean Absolute Percentage Error (MAPEt), and the Mean Squared Error (MSEt).

See online Excel sheet

c) Looking at the tracking signal only (see TrackingSignal tab), is the forecast considered to be good or bad?

The forecast is mostly good, but it could be better as there are three tracking signal points that fall below -6.

-----------------------

t = 1

t = 0

No

Cashflow

150

135

135

121.5

150

135

No

Cashflow

t = 0

t = 1

0.75

0.25

0.5

0.5

0.5

0.5

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