MARGINAL ANALYSIS
It is difficult to develop the conditional profit table when there are a large number of scenarios and possible actions. The marginal analysis approach sidesteps an unmanageable conditional profit table. We will illustrate the procedure and its advantages through the following example.
Example
The fresh from the fields, vegetable and fruit wholesalers buys, produce and then sells to retailers. Currently, green peas are available. The wholesaler pays Rs.200 per box of peas. A box sold on the same day fetches Rs.300, otherwise it has a salvage value of Rs.50. Historical data has established the following demand for green peas.
|
Number of boxes
|
21
|
22
|
23
|
24
|
25
|
26
|
27
|
28
|
|
Probability
|
0.07
|
0.08
|
0.10
|
0.11
|
0.29
|
0.20
|
0.09
|
0.06
|
The wholesaler has decided to stock the optimal number of boxes based on the expected profit criterion.
Let us solve the problem using the conditional profit table. Note that the profit generated by the sale of one box is Rs.100 and the loss incurred on an unsold box is Rs.150.00.
Conditional Profit Table
|
Stocking level
|
Daily Demand
|
Expected profit
|
|
21
(0.07)
|
22
(0.08)
|
23
(0.10)
|
24
(0.11)
|
25
(0.29)
|
26
(0.20)
|
27
(0.09)
|
28
(0.06)
|
|
21
22
23
24
25
26
27
28
|
2100
1950
1800
1650
1500
1350
1200
1050
|
2100
2200
2050
1900
1750
1600
1450
1300
|
2100
2200
2300
2150
2000
1850
1700
1550
|
2100
2200
2300
2400
2250
2100
1950
1800
|
2100
2200
2300
2400
2500
2350
2200
2050
|
2100
2200
2300
2400
2500
2600
2450
2300
|
2100
2200
2300
2400
2500
2600
2700
2550
|
2100
2200
2300
2400
2500
2600
2700
2800
|
2100.00
2182.50
2245.00
2282.50
2292.50
2230.00
2117.50
1982.50
|
From the table, we see that the optimal stocking level is 25 (which generates the maximum expected profit of Rs.2,292.50).
As it can be seen, this approach is tedious and the conditional profit table is bound to become unmanageable.