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Network
Flow Programming Models |
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Aggregate Production Scheduling with Overtime |
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A company is planning its aggregate production schedule for the
next three months. Units may be produced on regular time or overtime.
The relevant costs and capacities are shown in the table below.
The demands for each month, that must be met, are also shown.
Units produced in a particular month may be sold in that month
or kept in inventory until sale in a later month. There is a $1
cost per unit for each month an item is kept in inventory. Initially
there are 15 items in inventory. Sales may be backordered at a
cost of $2 per unit per month
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Capacity
(Units)
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Production Cost
($ per Unit)
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Period
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Reg. Time
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Overtime
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Reg. Time
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Overtime
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Demand
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1
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100
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20
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14
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18
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60
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2
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100
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10
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17
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22
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80
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3
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60
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20
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17
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22
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140
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a. Construct and solve the model to find the optimum production
plan .
b. Construct the model when the inventory cost depends on
the total time an item is stored. The cost is: $1 per unit for
items kept in inventory for 1 month, $3 for items kept for 2
months, and $5 for items kept for 3 months. The initial inventory
has been in storage for 1 month. Solve the model with this change.
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