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Lecture

MSCI432 Lecture Notes - Shortage, Carrying Cost


Department
Management Sciences
Course Code
MSCI432
Professor
Binyamin Mantin

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Nahmias Chapter#3
ANS. a) Smoothing costs are those that result from making changes from one planning period
to the next. In aggregate planning, the most disruptive change usually is changing the
work force level. Even with fixed work force sizes, however, changes in production
levels can also be disruptive.
b) A bottleneck occurs when the capacity of the productive system is insufficient to
meet a sudden surge in the demand. Bottlenecks can also occur in a particular part of
the productive system due to the breakdown of a key piece of equipment or the
shortage of a critical resource.
c) System capacity is related to the idea of bottlenecks. Capacity is exceeded when
unanticipated surges in the demand occur, scarce resources are unavailable, or there is
a drop in the labour pool due to strikes or a change in worker demographics.
d) The planning horizon is the number of periods of demand forecast used to generate
the aggregate plan. If the horizon is too short, there may be insufficient time to build
inventories to meet future demand surges and if it is too long the reliability of the
demand forecasts is likely to be low.
ANS The primary difficulty would be to properly define an aggregate unit of production.
Since the workers have a variety of different skills and the jobs accepted by the shop are
very different, it is unlikely that aggregate planning would be very useful for this type of
operation.

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ANS a) Cum
Cum Net Net
#Units/ #Units Demand Demand
Worker /Worker Forecast Forecast Min #
Year (in 1000) (in 1000) (in 1000) (in 1000) Workers
1 30 30 280 280 10
2 30 60 120 400 7
3 30 90 200 600 7
4 30 120 110 710 6
5 30 150 135 845 6
Minimum constant work force = 10 workers

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b) Cum Cum
#Units/ Yearly Yearly Net Ending
Year Worker Production Production Demand Inventory
1 30 300 300 280 20
2 30 300 600 400 200
3 30 300 900 600 300
4 30 300 1200 710 490
5 30 300 1500 845 655
1665
CH = 500, CF = 1,000, CI = .04 per package and payroll costs are $25,000 per year per
worker. There are exactly 10 - 3 = 7 workers hired in year 1. Hence the total cost of the
constant work force plan is (500)(7) + (.04)(1665000) + (10)(25,000)(5) = $1,320,100.
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