We are formulating an aggregate plan for an 8-quarter period. Our demand forecas
ID: 410617 • Letter: W
Question
We are formulating an aggregate plan for an 8-quarter period. Our demand forecast is as follows:
We will enter Quarter 1 with 0 units in inventory.
Inventory holding cost is charged as $12 per quarter per unit in average inventory. If, for example, in a given quarter Beginning Inventory was -10 units and Ending Inventory was +20 units, average inventory would be +5 units, so holding cost in that quarter would be $60.
If in a given quarter we wind up with negative Ending Inventory, we charge ourselves $60 per unit in backorder cost. This only applies to Ending Inventory.
If we used a level planning approach in this instance, what would our total (Holding + Backorder) cost be?
Quarter 1 2 3 4 5 6 7 8 Forecast 160 280 360 240 180 300 380 260Explanation / Answer
Following table presents various costs associated with following of Level strategy.
In level strategy , order quantity and hence “Quantity Received” has to be uniform.
The total value of forecasts for 8 months = 2160
Thus, quantity to be ordered each month ( i.e. Quantity Received ) = 270
Quarter
1
2
3
4
5
6
7
8
Forecast
160
280
360
240
180
300
380
260
Quantity received
270
270
270
270
270
270
270
270
Opening Inventory
0
110
100
10
40
130
100
-10
Ending Inventory
110
100
10
40
130
100
-10
0
Average inventory
55
105
55
25
85
115
45
-5
Inventory holding cost (@$12 / unit)
660
1260
660
300
1020
1380
0
Backorder cost ( @$60 per unit of ending inventory)
600
Cumulative Inventory holding cost ($) = 660 + 1260 + 660 + 300 + 1020 + 1380 = 5280
Cumulative Backorder cost = $600
Thus, total cost = Cumulative Holding cost + Cumulative Backorder cost = $5280 + $600 = $5880
TOTAL COST = $5880
Quarter
1
2
3
4
5
6
7
8
Forecast
160
280
360
240
180
300
380
260
Quantity received
270
270
270
270
270
270
270
270
Opening Inventory
0
110
100
10
40
130
100
-10
Ending Inventory
110
100
10
40
130
100
-10
0
Average inventory
55
105
55
25
85
115
45
-5
Inventory holding cost (@$12 / unit)
660
1260
660
300
1020
1380
0
Backorder cost ( @$60 per unit of ending inventory)
600
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